2013

Speaker: Takahiko Yoshida (Meiji University)

Title: Theory of local index and its applications

Date & Time: Friday, June 12nd, 16:30-

Place: Room 8-618

Abstract: We report some recent progress on joint work with H. Fujita
and M. Furuta on an index theory for Dirac-type operators on possibly
non-compact Riemannian manifolds. In our work, we make use of a
torus fibration structure on the boundary, and perturb a Dirac-type
operator in terms of first-order differential operators along fibers
on the boundary which satisfy a certain acyclic condition. The
perturbation has an interpretation of being an adiabatic limit, or an
infinite-dimensional analogue, of the Witten deformation. We also
explain applications to the geometric quantization of Lagrangian
fibrations, the quantization conjecture by Guillemin-Sternberg that
implies that quantization commutes with the reduction, and the Danilov
formula for the equivariant Riemann-Roch indices of toric varieties.

Speaker: Shintaro Kuroki (University of Tokyo)

Title：On a classification of low dimensional torus manifolds

Date & Time: Friday, May 22nd, 16:30-

Place: Room 8-618

Speaker: Asuka Takatsu (Tokyo Metropolitan University)

Title: Wasserstein/Information geometry and its applications

Date & Time: Friday, May 15th, 16:30-

Place: Room 8-618

Speaker: Shinji Ohno (Tokyo Metropolitan University)

Title: Weakly reflective submanifolds in compact symmetric spaces

Date & Time: Friday, May 1st, 16:30-

Place: Room 8-618

Speaker: Yong Seung Cho (Ewha Womans University)

Title: Gromov-Witten type invariant on almost contact metric manifolds

Date: Time: Friday, April 24th, 15:00-

Place: Room 8-618

Speaker: Simon Blatt (Karlsruher Institut fur Technologie)

Title: The gradient flow of the Mobius energy

Date & Time: Wednesday, February 11th, 15:00--16:00

Place: Room 8-610

Speaker: Hojoo Lee (KIAS)

Title: Poincare's lemma and generalizations of Calabi's correspondence

Date & Time: Tuesday, September 16th, 16:30--17:30

Place: Room 8-618

Abstract: We present generalizations of Calabi's duality between minimal surface equation in Euclidean space and maximal surface equation in Lorentz-Minkowski space-time.

RIMS Workshop

Development of group actions and submanifold theory

http://tmugs.math.se.tmu.ac.jp/rims2014/index-en.html

Speaker: Yuta Wakasugi (Osaka University)

Title: Movement of time-delayed hot spots in Euclidean space

Date & Time: Friday, June 13th, 17:00--18:00

Place: Room 8-610

Abstract: In this talk, we consider the behaviour of maxima of solutions to initial value problems of dissipative wave equations. It is well-known that solutions to dissipative wave equations asymptotically approach
(in time) solutions of the heat equation, so from this, it is expected that similar results hold with regard to the behaviour of maxima. We shall introduce our results which correspond to work by Chavel-Karp
(1990) and Jimbo-Sakaguchi (1994). Our proof uses a result by Nishihara (2003), on a generalization to arbitrary dimension of the decomposition of fundamental solutions into heat part and wave part,
respectively. If we have enough time, we hope to also discuss an application of this decomposition result to an L^p-L^q evaluation of dissipative wave equations in higher dimensions. This talk is based on
joint research done with Shigehiro Sakata (Waseda University).

Speaker: Ayato Mitsuishi (Tohoku University)

Title: Current and measure homologies

Date & Time: Friday, January 24th, 16:30

Place: Room 8-618

Abstract: De Rham defined a "current" to be an element of the continuous dual of the space of differential forms on a differentiable manifold. Using a formal space of differential forms, Ambrosio and Kirchheim (in 2000)
extended the notion of "current" to metric spaces. In particular, the set of all normal currents with compact support were shown to constitute a chain complex. The speaker proved that, in a certain "wide" category of
metric spaces, the homology of this chain complex is naturally isomorphic to "measure homology" (as defined by Thurston). In particular, complete Riemannian manifolds, proper CAT spaces, and
finite-dimensional Alexandrov spaces (among others) satisfy the conditions of this assertion. In this talk, we shall introduce and discuss these ideas.

Speaker: Naoki Kato (The University of Tokyo)

Title: Lie foliations transversely modeled on nilpotent Lie algebras

Date & Time: Friday, January 10th, 16:30

Place: Room 8-618

Speaker: Tatsuro Shimizu (The University of Tokyo)

Title: An invariant of rational homology 3-spheres via vector fields

Date & Time: Friday, December 20th, 16:30

Place: Room 8-618

Abstract: In this talk, we define an invariant of rational homology 3-spheres by using vector fields. The construction of our invariant is a generalization of both that of the Kontsevich-Kuperberg-Thurston
invariant $z^{KKT}$ and that of Fukaya and Watanabe's Morse homotopy invariant $z^{FW}$. As an application of our invariant, we prove that $z^{KKT}=z^{FW}$ for rational homology 3-spheres.

Speaker: Joshua Capel (University of New South Wales)

Title: Invariant Classification of Superintegrable Systems

Date & Time: Friday, December 13th, 16:30

Place: Room 8-618

Abstract: This talk discusses the classification of second-order superintegrable classical systems over two and three-dimensional conformally-flat complex spaces. Of such systems, the so-called nondegenerate (maximum parameter)
systems can be put into correspondence with points in an algebraic variety and a complete classification can be obtained by determining subvarieties closed under the non-linear action of the conformal group.

Speaker: Kazunaga Tanaka (Waseda University)

Title: Multiple positive solutions for nonlinear elliptic equations in expanding annular type domains

Date & Time: Friday, December 6th, 16:30

Place: Room 8-618

Speaker: Michiaki Onodera (Kyushu University)

Title: On the uniqueness of quadrature surfaces

Date & Time: Friday, November 29th, 16:30

Place: Room 8-618

ABSTRACT: A new geometric flow describing the motion of quadrature surfaces is introduced. This characterization enables us to study quadrature surfaces through the
investigation of the flow. It is proved that the flow is uniquely solvable under the geometric condition that the initial surface has positive mean curvature. As a consequence,
a bifurcation criterion for quadrature surfaces is obtained.

Speaker: Akira Tanaka (Tokyo Metropolitan University)

Title: Complex contact structures on nilmanifolds

Date & Time: Friday, November 15th, 16:30

Place: Room 8-618

ABSTRACT：We shall construct complex contact similarity manifolds. Among them there exists a complex contact infranil-manifold which is a holomorphic torus fiber bundle over a quaternionic euclidean space form.
Our examples are different from previously known complex contact manifolds such as the complex Boothby-Wang fibration or the twistor fibration.

Speaker: Shu-Cheng Chang (National Taiwan University)

Title: Finite-Time Blow Up for the Heat Flow of Pseudoharmonic Maps

Date & Time: Friday, November 8th, 17:45-18:45

Place: Room 8-618

ABSTRACT： We consider the heat flow for pseudoharmonic maps from a closed pseudohermitian manifold into a compact Riemannian manifold. In our pervious work, we proved global existence
of the solution for the pseudoharmonic map heat flow, provided that the sectional curvature of the target manifold is nonpositive. In this present talk, we show that the solution of the
pseudoharmonic map heat flow blows up in finite time if the initial map belongs to a nontrivial homotopy class and its initial energy is sufficiently small. As a consequence, we obtain global
existence for the pseudoharmonic map heat flow without the curvature assumption on the target manifold. This is a jointed work with Ting-Hui Chang.

Speaker: Ting-Jung Kuo (Taida Institute for Mathematical Sciences)

Title: Estimates of the mean field equations with integral singular sources

Date & Time: Friday, November 8th, 16:30-17:30

Place: Room 8-618

ABSTRACT: http://tmugs.math.se.tmu.ac.jp/geometry_seminar/20131108_Kuo.pdf

Speaker: Hiroshi Sawai (Numazu National College of Technology)

Title: Necessary conditions for LCK structures on compact solvmanifolds

Date & Time: Friday, November 1st, 16:30

Place: Room 8-618

Abstract: It is known that, when the Lee form of a compact manifold, which has a locally conformal Kahler structure, is parallel with respect to the metric, then the manifold has an S^1 principal fibre structure
on a compact Sasaki manifold. In this talk, restricting to compact solvmanifolds, we consider the necessary and sufficient conditions on the locally conformal Kahler structure for which the Lee form is non-parallel.

Speaker: Armin Schikorra (Max Planck Institute for Mathematics in the Sciences)

Title: Fractional Harmonic Maps and Applications

Date & Time: Friday, October 25th, 16:30

Place: Room 8-618

ABSTRACT: Fractional harmonic mappings are critical points of a generalized
Dirichlet energy, where the gradient is replaced with a (non-local)
differential operator of possibly non-integer order.
I will present aspects of the regularity theory of (non-local)
fractional harmonic maps into manifolds, which extends (and contains)
the theory of (poly-)harmonic mappings.
I will also show how these methods can be extended to the regularity
theory for critical points of the Moebius energy.

Speaker: Ping Li (Tongji University/Waseda University)

Title: Apte's inequality, its generalization and application

Date & Time: Friday, October 11th, 16:30-

Place: Room 8-618

ABSTRACT: In this talk, I firstly recall a classical inequality on a compact Kaehler manifold, which is due to Apte around sixty years ago.
My talk consists of two parts. In the first part, I will present a generalization of this inequality and obtain some Chern number inequalities
when the first Chern class and Hodge numbers of the underlying Kaehler manifolds satisfy some restrictions. In the second part, I will discuss
the spectrum of the Laplacian on compact Riemannian manifolds and its rigidity problem, which has a famously affirmative answer to the complex
projective spaces. I will present some new results on this fascinating probem and particularly show that for hyperquadrics the answer is also affirmative.
Apte's inequality also plays an important role in this problem. All the above-mentioned results were initiated during my stay at TMU from
2011-10-25 to 2012-08-31 with the help of Professor Martin Guest. I would like to dedicate this talk to the Mathematics Department of TMU and to Martin.

Speaker: Yohsuke Imagi (Kyoto University)

Title: Some Uniqueness Theorems for Smoothing Singularities in Special Lagrangian Geometry

Date & Time: Friday, October 4th, 16:30-

Place: Room 8-618

ABSTRACT: Harvey and Lawson defined the notion of special Lagrangian
submanifolds, which are area-minimizing Lagrangian submanifolds of
Calabi--Yau manifolds. One can define the moduli space of compact special Lagrangian submanifolds
of a Calabi--Yau manifold. Mclean proves that it is a smooth manifold.
By using geometric measure theory one can compactify the moduli space.
Special Lagrangian submanifolds should be `mirror' to Holomorphic vector
bundles. Thomas has constructed a nice structure on the moduli space of
homolorphic vector bundles, and used it for the definition of
Donaldson--Thomas invariants. I wish to find such a nice structure on the
compactified moduli space of special Lagrangian submanifolds.
I have determined a neighbourhood of a certain boundary-point in the
compactified moduli space. The boundary point is a compact special
Lagrangian submanifold with singularity only at one point modelled on
a stable $T^2$-cone. One important point is that stable $T^2$-cones have
a symmetry which may be used for determining all the smoothing models.
As another kind of singularities I'll consider two special Lagrangian
planes intersecting transversely at one point. The union of the two planes
(in a general position). has no such symmetry as the stable $T^2$-cones.
It's an open problem to determine all the smoothing models for the union
of the two planes. I'll do it under certain topological conditions on the smoothing models.
I apply the one-point compactification to the two planes, and take the
plumbing of the compactified planes. The plumbing is a compact exact
symplectic manifold with contact-type boundary. In the plumbing the
smoothing models may be compactified, and made into objects of a Fukaya
category. From some reaults of Abouzaid and Smith one gets the uniqueness
of the quasi-isomorphism class of the compactified models in the Fukaya
category. Thomas and Yau prove a uniqueness theorem for special Lagrangian submanifolds
in a fixed quasi-isomorphism class in the Fukaya category. The compactified
models however are not special at the `infinity' points added for the
compactification. I suppose a topological condition on the asymptotic behaviour of the
smoothing models. By using the condition I can prove a maximum principle,
and so I'll be able to apply the technique of Thomas and Yau. Thus one gets
the uniqueness of the smoothing models under the topological condition.

Speaker: Tatsuya Horiguchi (Osaka City University)

Title: The equivariant cohomology of (n-k,k) Springer variety

Date & Time: Friday, July 12th, 16:30

Place: Room 8-618

Speaker: Yasuhito Miyamoto (University of Tokyo)

Title: The nonlinear "hot spots" conjecture and pattern formation

Date & Time: Monday, June 10th, 15:30

Place: Room 8-610

Speaker: Hiraku Abe (Tokyo Metropolitan University)

Title: Schubert calculus for weighted Grassmannians

Date & Time: Friday, June 7th, 16:30

Place: Room 8-618

Abstract: In this talk, we give a description of the Schubert calculus for weighted Grassmannians, starting with the definition of the Schubert class and its structure constants. We also recall that it is a well-known fact that, in the case of Grassmannian
manifolds, the Schubert class is represented by Schur polynomials, and discuss how this generalizes to the weighted Grassmannian case. This research was (and still is being) done in collaboration with Tomoo Matsumura of KAIST (Korea).

Speaker: Nobuhiko Otoba (Keio University)

Title: Constant scalar curvature metrics on S^2-bundles with structure group S^1

Date & Time: Friday, May 31st, 16:30
Place: Room 8-618

ABSTRACT: We exhibit a method for constructing a family of constant scalar curvature (abbreviated as csc) metrics on S^2-bundles with structure group S^1.
Out of any constant scalar curvature metric and any integral closed 2-form on the base space, a one-parameter family of csc metrics on the corresponding S^2-bundle is constructed.
These metrics are quite explicit and respect the fiber bundle structure on the total space as well. As an application, we construct on each Hirzebruch surface a one-parameter family of
csc metrics which are Hermitian with respect to the complex structure. These metrics are certain generalizations of the product metrics on the zeroth Hirzebruch surface
(namely, CP^1 \times CP^1). Relations with the Einstein metric obtained by Don Page (1978) and the B^t-flat metric constructed by Gursky and Viaclovsky (2013) will also be mentioned.

Speaker: Toru Yoshiyasu (The University of Tokyo)

Title: On Lagrangian embeddings of parallelizable manifolds

Date & Time: Friday, May 10th, 16:30

Place: Room 8-618

ABSTRACT: The topology of a closed Lagrangian submanifold of the Euclidean space
with the standard symplectic structure is restricted in a certain
condition. In this talk, we explain that almost all the closed
parallelizable manifolds can be embedded in the Euclidean space with a
certain symplectic structure as Lagrangian submanifolds. This is a joint
work with Naohiko Kasuya (University of Tokyo).

Speaker: Hiroyuki Tasaki (Tsukuba University)

Title: Antipodal sets in oriented real Grassmann manifolds

Date & Time: Friday, April 26th, 16:30

Place: Room 8-618

Speaker: Morimichi Kawasaki (University of Tokyo)

Title: Superheavy Lagrangian immersions and noncontractible Hamiltonian circle actions

Date & Time: Friday, April 19th, 16:30

Place: Room 8-618

ABSTRACT: M. Entov and L. Polterovich defined heaviness and superheaviness of closed subsets in closed symplectic manifolds to solve the problem of displaceability of Lagrangian submanifolds.
To define heaviness and superheaviness, they used the Oh-Schwarz spectral invariants which are from the Hamitonian Floer theory. We explain the theory of Entov and Polterovich and our method
to give superheavy subsets by using noncontractible Hamitonian circle actions.

2012

Speaker: Hirofumi Sasahira (Nagoya University)

Title: Gluing of Bauer-Furuta invariants along 3-manifolds with first Betti number b_1 = 1

Date & Time: Friday, December 21st, 16:30

Place: Room 8-618

Speaker: Hiroyasu Satoh (Tokyo Denki University)

Title: Rigidity, volume entropy and asymptotically harmonic Hadamard manifolds

Date & Time: Friday, December 14th, 16:30

Place: Room 8-618

ABSTRACT: An n-dimensional Hadamard manifold (X, g) is asymptotically harmonic if all horospheres in X have constant mean curvature -c/(n-1). In this talk, we show that the constant c coincides with the volume entropy of X. Moreover, as an application of this result,
we show the rigidity theorems which characterize real, complex and quaternionic hyperbolic spaces. This talk is based on joint work with Mitsuhiro Itoh (University of Tsukuba).

Speaker: Fumihiko Sanda (University of Tokyo)

Title: Non-displaceable torus fibers in toric manifolds and tropical geometry

Date & Time: Friday, November 30th, 16:30

Place: Room 8-618

Speaker: Kengo Hirachi (University of Tokyo)

Title: Q and Q prime curvatures in CR geometry

Date & Time: Friday, November 16th, 16:30

ABSTRACT： Q-curvature has been a main object of study in conformal geometry for more than 10 years. While Q-curvature has a natural analogue in CR geometry, it is less interesting since CR Q-curvature vanishes on the boundaries of domains in C^n, which are the standard examples of CR manifolds.
In this talk, we introduce Q prime curvature (a variant of Q-curvature) that gives a new global invariant of strictly pseudo-convex domains.

Speaker: Yuichiro Tanaka (University of Tokyo)

Title: A classification of visible actions on flag varieties and a generalization of the Cartan decomposition

Date & Time: Friday, November 9th, 16:30

Speaker: Masataka Shibata (Tokyo Institute of Technology)

Title: A construction of Hofer's distance on a certain Hamiltonian diffeomorphism group of a symplectic Hilbert space

Date & Time: Friday, October 26th, 16:30

Speaker: Takashi Sakai (Tokyo Metropolitan University)

Title: On the structure of the intersection of real flag manifolds in a complex flag manifold

Date & Time: Friday, October 12th, 16:30

Speaker: Shigeru Sakaguchi (Tohoku University)

Title: Stationary isothermic surfaces in Euclidean 3-space

Date & Time: Friday, July 27th, 16:30

Abstract: In Euclidean 3-space, we consider solutions of the Cauchy problem for the heat equation, where initial data are given by characteristic functions of domains. The problem we consider is to characterize the domain in such a way that
there exists a stationary isothermic surface. The characterizations of hyperplanes and spherical cylinders are given. We use the structure theorem of embedded surfaces with constant mean curvature by Korevaar-Kusner-Solomon (1989) and
that of embedded minimal surfaces of finite total curvature.

Speaker: Futoshi Takahashi (Osaka City University)

Title: Multi-bubble solutions and the geometry of the domain: some simple cases

Date & Time: Friday, July 13th, 16:30

ABSTRACT: It is known that the blow-up set of multi-bubble solutions of certain PDEs, such as the 2-dimensional Liouville equation, is, in fact, the set of critical points of
a certain finite-dimensional function determined by the Green's function of the equation's domain. (This function is called the ``Hamiltonian'' in the language of
2-dimensional turbulence theory.) However, using this fact when the domain is convex, we show that there are no multi-bubble solutions that blow up at two or more points within
this domain. Additionally, we will describe how to position the blow-up points of 2-bubble solutions on a two-dimensional annular domain. This talk is based on joint research
with M. Grossi (Sapienza University of Rome).

Speaker: Alexander Its (Indiana University - Purdue University Indianapolis)

Title: Special Functions and Integrable Systems

Date & Time: Friday, July 6th, 16:30

ABSTRACT: Recent developments in the theory of integrable systems have revealed its intrinsic relation to the theory of special functions. Perhaps the most
generally known aspects of this relation are the group-theoretical, especially the quantum-group theoretical, and the algebra-geometrical ones. In the talk, we will
discuss the analytic side of the Special Functions-Integrable Systems connection: this aspect of the relation between the two theories is less known to the general
mathematical community, although it goes back to the classical works of Fuchs, Garnier and Schlesinger on the isomonodrony deformations of systems of linear
differential equations with rational coefficients. Indeed, the monodromy theory of linear systems provides a unified framework for the linear (hypergeometric type) and
nonlinear (Painleve type) special functions, and, simultaneously, builds a base for a new powerful technique of asymptotic analysis - the Riemann-Hilbert method.
In addition to the above topics, which are based on the work of many authors spanning more than two decades, the isomonodromy point of view on special functions will be outlined,
and we will also review the history of the Riemann-Hilbert method, as well as its most recent applications in the theory of orthogonal polynomials and random matrices.

Speaker: Elizabeth Its (Indiana University - Purdue University Indianapolis)

Title: A Riemann-Hilbert approach to the boundary problems for linear PDEs - The elastodynamic equation in the quarter-plane: a case study

Date & Time: Friday, July 6th, 15:00

ABSTRACT: The Riemann-Hilbert method originated in the theory of integrable nonlinear PDEs. In the 90s, the method was extended to a number of new
areas, and since then, it has played an important role in solving a number of long-standing problems in analysis and mathematical physics. In the talk,
we will present some recent developments in the Riemann-Hilbert approach obtained back in the PDE theory. This time, the Riemann-Hilbert techniques are
applied to linear problems, but in domains which do not allow a direct separation of variables. We will focus on the solution of the boundary value problem for the
elastodynamic equation in the quarter-plane. We shall show that the problem is reduced to a matrix Riemann-Hilbert problem with a shift posed on a torus. This talk is
based on joint work with Alexander Its and Julius Kaplunov.

Speaker: Hiroaki Ishida (OCAMI, Osaka City University)

Title: Complex manifolds with ``maximal" torus actions

Date: Time: Friday, June 22nd, 16:30

ABSTRACT:
Whenever a compact torus $T^k$ acts on a connected manifold $M^n$ of dimension $n$ effectively, the transformation group theory tells us that the dimension of each orbit should be
greater than or equal to $2k-n$. In case there is an orbit of dimension $2k-n$, we can say that the action of $T^k$ on $M$ is ``maximal" in some sense. In this talk, we describe
compact connected complex manifolds with ``maximal" torus actions.

Speaker: Aya Ishizeki (Saitama University)

Title: The absolute integrability of variational formulae for Mobius energy

Date: Time: Friday, June 15th, 16:30

ABSTRACT:
Since the Mobius energy is defined so that its value diverges when a knot has a self-intersection, its energy density has singularity.
In addition to the self-intersection, ``diagonal part" induces the singularity. In this talk the removability of the singularity at diagonal part is shown. This yields the
absolute integrability of the first and second variational formulae. This is joint work with Nagasawa, Saitama University.

Speaker: Hirokazu Maruhashi (Kyoto University)

Title: Parameter rigidity of actions of nilpotent Lie groups

Date & Time: Friday, May 18th, 16:30

ABSTRACT: A locally free smooth action $\rho$ of a connected Lie group on a closed manifold is said to be parameter rigid if each action which has the same orbits as $\rho$ is conjugate
to $\rho$. There are not so many known parameter rigid actions of noncommutative groups. In this talk we give a criterion for parameter rigidity of nilpotent group actions and construct
parameter rigid actions of nilpotent groups.

Speaker: Fumitoshi Sato (Kagawa National College of Technology)

Title: Are new topological recursion relations really new?

Date: Time: Tuesday, May 15th, 15:00-16:30

ABSTRACT: New topological recursion relations are found by X. Liu and R. Pandharipande in "New topological recursion relations". We will
explain that they are new in some sense, but they are not new in some sense.

Speaker: Kota Hattori (Tokyo Institute of Technology)

Title: On hyper-Kahler manifolds of type A_{infty}

Date & Time: Friday, April 20th, 16:30

ABSTRACT: Hyper-Kahler manifolds of type A_{infty} were introduced by Anderson, Kronheimer and LeBrun and known as noncompact complete hyper-Kahler manifolds whose homology
groups are infinitely generated. Hyper-Kahler manifolds are attractive objects from the point of view of both Riemannian geometry and complex geometry, since they have Ricci-flat
Kahler metrics and holomorphic symplectic forms. I will talk about both aspects of hyper-Kahler manifolds of type A_{infty}.

Speaker: Manuel Cruz Lopez (University of Guanajuato)

Title: A compact model for real time

Date & Time: Tuesday, Feb. 21th, 16:30-

Abstract: One of the biggest tragedies for mankind is the
irreversibility of real time. In this general talk we will analyze the
possibility of defining a compact model for real time made by cycles.
The mathematical objects involved are related to geometry, topology
and Fourier analysis.

Speaker: Ramiro Carrillo Catalan (University of Guanajuato)

Title: On the basic algebraic topology of the S_1 invariant

Date & Time: Friday, Feb. 21st, 15:00-

[Intensive Course]

Lecturer: Hiroyuki Tasaki (University of Tsukuba)

Title: The Integral Geometry of Homogeneous Spaces

Dates & Times: Tuesday, Jan. 17th - Thursday, Jan. 19th, 13:00-16:10; Friday, Jan. 20th, 14:40-17:50

Course Outline: After discussing integration over manifolds, I will explain Howard's formularization of the Poincare' formula in Riemannian homogeneous spaces. I will then describe the
Poincare' formula in greater detail for real space forms and complex space forms.

Speaker: Masahiko Kanai (University of Tokyo)

Title: On the Cross-ratio

Date & Time: Friday, Jan. 13th, 16:30 -

Abstract: It is said that the cross-ratio has a history extending over two millenia, yet in only the past twenty years,
there has been a considerable number of novel and important discoveries made concerning the cross-ratio. It would, indeed,
appear that our understanding of the cross-ratio has been quite limited in its scope, until now. In this talk, I would like to
give a broad overview of the present state of research on the cross-ratio, as well as discuss various aspects related to my
own research.

2011

Speaker: Claus Hertling (Mannheim University)

Title: mu-constant monodromy groups and marked singularities

Date & Time: Friday, Dec. 16th, 16:45-17:45

Speaker: Martin Guest (Tokyo Metropolitan University)

Title: The tt*-Toda equations

Date & Time: Friday, Dec. 16th, 15:30-16:30

Speaker: Re'mi Langevin (Universite' de Bourgogne)

Title: Finding a cyclide that satisfies three contact conditions

Date & Time: Friday, Dec. 9th, 16:00 -

Abstract: Dupin cyclides form a 9-dimensional set of surfaces which are, from the viewpoint of differential geometry,
the simplest after planes and spheres. We prove here that, given three oriented contact conditions, there is in general
no Dupin cyclide satisfying them, but if the contact conditions belongs to a codimension one subset, then there is a
one-parameter family of solutions, which are all tangent along a curve determined by the three contact conditions.
[Dr. Langevin's talk will be accompanied by slides on the overhead projector.]

[Cross-listed from the Complex Geometry group's homepage]

Speaker: Hisanori Ohashi (Nagoya University)

Title: Classification of involutions of Enriques surfaces

Date & Time: Friday, Dec. 9th, 14:30-15:30

Speaker: Tomoo Matsumura (KAIST)

Title: Moment complexes and the integral cohomology of toric orbifolds

Date & Time: Wednesday, Dec. 7th, 14:40 -

Abstract: When there is a hamiltonian torus action on a symplectic manifold, the
injectivity theorem shows that the equivariant cohomology injects to
the equivariant cohomology of the fixed points and the GKM theorem
allows us to describe the image with only the data of the action
around fixed points. Then once we compute the equivariant cohomology,
we hope that the ordinary cohomology is computed from the equivariant
cohomology. In the first part of the talk, I will explain a
generalization of the injectivity theorem and the GKM theorem to
orbifolds (joint work with T. Holm). In the second part, we look at
the case of toric orbifolds. I describe their integral cohomology in
terms of equivariant cohomology of moment angle complexes and discuss
the conditions when the integral cohomology is the quotient of the
Stanley-Reisner ring.

Speaker: Siu Cheong Lau (IPMU)

Title: Quantum corrections in SYZ mirror symmetry

Date & Time: Friday, Nov. 25th, 16:30

Abstract: Mirror symmetry is a duality between symplectic and complex geometries
discovered by string theorists in the '90s, which surprised mathematicians in its ability to (correctly)
compute the number of rational curves in Calabi-Yau manifolds. Strominger-Yau-Zaslow proposed a
mathematical reason for the mirror phenomenon, which they called
"T-duality". T-duality works nicely for Lagrangian fibrations without
singularities, but in reality, most Lagrangian fibrations have
singularities, and "quantum corrections" are needed in the SYZ
picture. We will discuss what these "quantum corrections" are,
and how they lead to interesting consequences concerning the mirror
maps.

Speaker: Chang-Shou Lin (Taiwan National University)

Title: Classification and non-degeneracy of solutions of the SU(n+1) Toda system

Date & Time: Friday, Nov. 18th, 16:30 -

Abstract: In this talk, I will talk about the SU(n+1) Toda system,
which is well known as a completely integrable system. The
integrability condition enables us to connect this nonlinear PDE with
holomorphic maps into CP^n. In our study,
we want to consider the equation with singular sources. In particular,
we will show the classification of entire solutions
of the Toda system with one single singular source.

Speaker: Masao Jinzenji (Hokkaido University)

Title: Open Virtual Structure Constants and Mirror Computation of Open Gromov-Witten Invariants of Projective Hypersurfaces

Date & Time: Friday, Nov. 11th, 16:30 -

Speaker: Jose Seade (National Autonomous University of Mexico)

Title: "Introduction to the topology of complex singularities"

Date & Time: Friday, Oct. 21st, 14:00-15:30 and 16:30-17:30

Abstract: Professor Seade will give an introductory mini-course,
based on his book, "On the topology of isolated singularities in analytic spaces"
(Progress in Mathematics 241, Birkhauser), which was awarded the 2005
Ferran Sunyer i Balaguer Prize.

Speaker: Hironao Kato (Osaka City University)

Title: "Invariant flat projective structures and prehomogeneous vector spaces"

Date & Time: Friday 29 July, 16:30

Abstract: A flat projective structure on a manifold M is given by a projectively
flat affine connection, or equivalently an atlas of charts by which we
can identify M with projective space locally. On the other hand,
a prehomogeneous vector space is a rational representation of a complex
algebraic group admitting a Zariski open orbit. We establish a one to
one correspondence between invariant flat complex projective structures
on complex homogeneous spaces and infinitesimal prehomogeneous vector
spaces. In fact any pｒehomogeneous vector space induces a invariant
flat complex projective structure. By using this correspondence and
a result of M.Sato and T.Kimura, we can classify complex Lie groups
admitting an irreducible invariant flat complex projective structure.

6th Akihabara Differential Geometry Seminar

Speakers: Masaaki Umehara (Tokyo Institute of Technology Graduate School of Information Science and Engineering)

Koutarou Yamada (Tokyo Institute of Technology Graduate School of Science and Engineering)

Title: "Completeness and Weak Completeness of Surfaces with Singularity Points"

Date & Time: Saturday, July 16th, 11:00

Place: Akihabara Dai Building, 12th Floor, Tokyo Metropolitan University Akihabara Satellite Campus, Conference Room DE

Program Overview:

11:00 - 12:00

Osserman's Lemma and Minimal Surfaces (Umehara)

13:30-14:30

Maximal Surfaces of Spacetime and an Introduction to Singularity Points (Yamada)

15:00-16:00

Applications of Osserman's Lemma towards completeness of various surfaces (Umehara)

16:30-17:30

Weak Completeness and Bounded Maximal Surfaces (Yamada)

Speaker: Li Yu (Osaka City University/Nanjing University)

Title: Crystallographic groups with cubic normal fundamental domain --- some generalization of real Bott manifolds

Date & Time: Friday, July 8th, 16:30

Speaker: Hisashi Kasuya (University of Tokyo)

Title: "Minimal models of solvmanifolds with local systems"

Date & Time: Friday, July 1st, 16:30

Speaker: Atsufumi Honda (Tokyo Institute of Technology)

Title: "Extrinsically flat surfaces of Space Forms and the geometric structure on the space of oriented geodesics"

Date & Time: Friday, June 17th, 16:30

Speaker: Mayumi Nakayama (Tokyo Metropolitan University)

Title: "On the nil S^1-Bott tower of aspherical manifolds"

Date & Time: Friday, June 10th, 16:30

Speaker: Shigehiro Sakata (Tokyo Metropolitan University)

Title: "Extremal problems for the solid angle and the central projection"

Date & Time: Friday, May 27th, 16:30

Abstract: In this seminar, we will consider extremal problems that make use of two particular functionals. One of them will be the solid angle subtended by a domain in the plane when viewed from a point at height h > 0 above the domain; the other will be the central projection from the sphere to the tangent plane.
For the given domains, I will explain several properties of the extremal points of the functionals. Additionally, for a given circle and a domain with area equal to the circle's, I will show that the solution to the variational problem, which makes use of the maximal or minimal values, is a circle.

Friday, Apr. 22nd, 2011 [16:30-18:00]
Yukiko Fukugawa (Osaka City University)
"The cohomology ring of GKM graph of a flag manifold"

Abstract: When one places several conditions on closed manifolds with torus actions,
it is known that the equivariant cohomology of that manifold is determined by only the set
of fixed points of a 1-codimensional sub-torus of a torus. Moreover, we are able to consider
the cohomology ring of the labelled graph that corresponds to the set of fixed points of a
1-codimensional sub-torus of a torus, and in particular, when the manifold is a flag manifold,
it is also known that a flag manifold's equivariant cohomology and the cohomology of its
labelled graph are isomorphic. In this talk, using the example of type A flag manifolds, we
will define the cohomology ring of a labelled graph, and give the ring structure of the
cohomology ring using only the information in the graph. Additionally, we would also like to
present the results on types B, C, D.

Friday, Apr. 15th, 2011 [16:30-18:30] Mathieu Molitor (Keio University) "Information geometry and quantum mechanics" Abstract

2010

Friday 10 December

(1) 15:30: Sorin Sabau (Tokai University, Sapporo), "Remarks on the Generalized Finsler structures on 3-manifolds"

(2) 17:00: River Chiang (National Cheng Kung University, Tainan), "Convexity package for moment maps on contact manifolds"

ABSTRACT: Let a torus T act effectively on a compact connected cooriented contact manifold, and consider the natural moment map on the symplectization. We prove that, if dim T > 2, the union of the origin and the moment image is a convex polyhedral cone, the nonzero level sets of the moment map are connected (while the zero level set can be disconnected), and the moment map is open as a map to its image. This is a joint work with Yael Karshon.

Friday 26 November, Part 1: 16:00-17:00, Part 2: 17:15-18:15: Todor Milanov (IPMU), "Simple singularities and representations of affine Lie algebras"

ABSTRACT: I am planning to explain Givental's Fock space formalism in the settings of simple singularities. This formalism provides an element in the Fock space that containsvery important topological information. Namely, it is a generating function for the W-spin invariants of Fan-Jarvis-Ruan. Then I would like to explain my old work with Givental, but from the point of view of vertex algebras. More precisely, the Gelfand-Lerey periods of a simple singularity provide a realization of the so called basic representation of the corresponding affine Lie/vertex algebra. This leads naturally to an integrable hierarchy characterization of the generating function. I will try to make my talk accessible to a general audience, especially the part about Givental's formalism.

Friday 19 November, 17:00: Louis Boutet de Monvel (Universite Pierre et Marie Curie, Jussieu), "Asymptotics for Toeplitz operators"

ABSTRACT:Toeplitz operators live on arbitrary contact manifolds, generalizing pseudodifferential operators (and Fourier integral operators). They constitute also an important paradigm of "star" algebra (the deformed noncommutative product of which can be written as a "star product" of deformation quantization). Especially useful constructions are the residual trace (= Wodzicki residue), and in presence of a compact group action, the asymptotic equivariant trace (Atiyah's equivariant trace takes its values in the vector space of central distributions on the group; the asymptotic trace, better suited for Toeplitz operators, takes its values in the same mod smooth functions - i.e. the space of singularities of central distributions).

Friday 29 October, 15:00 (Lecture 1)and 17:00 (Lecture 2): David Blazquez-Sanz (Niigata University & Universidad Sergio Arboleda). Short course on "Differential Galois Theory and Complete Integrability". See "Conferences" for more details.

ABSTRACT: In this talk we will give an overview of the Morales-Ramis approach to complete integrability of Hamiltonian systems, and give the details of a concrete application recently developed by the speaker. This application is chosen because it gives a nice interpretation of the algebraic structure of complete integrability that can be captured by means of linear differential Galois theory. If we have enough time, we will discuss some ideas for the general case based on non-linear differential Galois theory.

Friday 8 October, 17:00: Jun O'Hara (TMU), "Renormalization of potentials and its applications"

ABSTRACT: I will introduce renormalization of r^{\alpha-m}-potential for compact domains in R^m for alpha nonpositive, which produces generalization of barycenters. When m=2 and alpha=-4, renormalization of the integration of the potential thus obtained gives a Mobius invariant energy of knots which is average linking with random circles. The second half is a joint work with Gil Solanes (Barcelona).

Friday 13 August, 17:00: Claus Hertling (Mannheim), "A generalization of Hodge structures and oscillating integrals"

Friday 23 July, 17:00: David Blazquez-Sanz (Niigata), "A survey on applications of differential Galois theory to dynamical systems"

Wednesday 14 July, 13:00: Claus Hertling (Mannheim), "Catastrophe theory"

Friday 28 May, 17:00: Sanae Kurosu (Tokyo Univ. of Science), "A construction of a tt*-bundle from a harmonic map to S^N"

Friday 16 April, 17:00: Hiroyuki Tasaki (Tsukuba), "The intersection of two real forms in Hermitian symmetric spaces of compact type"

Wednesday 17 February, 14:40: Chris Budd (University of Bath), "Symplectic methods in numerical analysis" (joint with Mathematical Analysis Seminar; followed by Workshop and Symposium on "Mathematics in the Real World", 18-19 February) (see conference listings)

2009

Friday 25 December, 17:00: Andreas Arvanitoyeorgos (University of Patras), "Invariant Einstein metrics on compact Lie groups and generalized flag manifolds"

Friday ４December:

15:30-16:30: Naoki Kato (Tokyo University), "Transversely affine foliations of torus bundles over the circle"

17:00-18:00 Remi Langevin (Dijon), "Foliations of S^3 by canal surfaces" ABSTRACT: There exist no (non-singular) foliation of $S^3$ endowed with the round metric with only totally geodesic or totally umbilical leaves. Even foliations with all leaves {\it Dupin} (principal curvatures constant along the lines of curvature) do not exist. The next most natural extrinsic condition is to impose that only one of the principal curvature of leaves is constant along the corresponding lines of curvature. The leaves are therefore canal surfaces, that is envelopes of one-parameter families of spheres. With Pawel Walczak, we have described all such foliations.

Friday 27 November, 17:00: Sergey Galkin (IPMU), "Mirror symmetry of del Pezzo surfaces" (preceded by informal seminar 14:30-16:00)

Friday 20 November, 17:00: Dusan Repovs (University of Ljubljana), "Topology of Busemann G-spaces" ABSTRACT: We shall present a survey of the classical Busemann Conjecture, which asserts that every n-dimensional Busemann G-space, n>4, is a topological n-manifold. We shall also present the status of the related, also classical, conjecture concerning the characterization of topological n-manifolds, the Bing-Borsuk Conjecture, which asserts that every n-dimensional homogeneous absolute neighborhood retract (ANR), n>2, is a topological n-manifold. The key object in both cases are so-called generalized n-manifolds, i.e. Euclidean neighborhood retracts (ENR) which are also Z-homology n-manifolds. We shall look at their history, from the early beginnings to the present day, concentrating on those geometric properties of these spaces which are particular for dimensions 3and 4, in comparison with generalized (n>4)-manifolds. In the second part of the talk we shall present the current state of the two conjectures. We shall also discuss the latest results, examples, conjectures and open problems concerning the class of Busemann G-spaces.

Friday 13 November, 17:00: Yusuke Nishizawa (TMU), "Dynamical systems of diffeomorphisms exhibiting a homoclinic or heterodimensional tangency"

Friday 30 October, 17:00: Ralph Willox (Tokyo University), "Geometric crystals and local Darboux transformations"

Friday 23 October, 17:00: Sanae Kurosu (Tokyo University of Science), "A characterization of a pluriharmonic affine immersion of low codimension with respect to its index of relative nullity"

Friday 16 October, 17:00: Pei-Wen Kao (Keio), "T-duality and Generalized Geometry"

Friday 2 October, 17:00: Yoshihiro Ohnita (Osaka City University), "Hamiltonian stability of the Gauss images of homogeneous isoparametric hypersurfaces" ABSTRACT: In this talk we shall give attention to Lagrangian submanifolds in the complex hyperquadric, which is a compact Hermitian symmetric spaces of rank 2. For any compact isoparametric hypersurface in the standard sphere, the image of its Gauss map is a compact minimal Lagrangian submanifold embedded in a complex hyperquadric. The relationship between Lagrangian submanifolds in complex hyperquadrics and isoparametric hypersurfaces in spheres will be emphasized. Recently we gave a complete classification of compact homogeneous Lagrangian submanifolds in complex hyperquadrics and we determined the Hamilitonian stability of ALL compact minimal Lagrangian submanifold embedded in complex hyperquadrics which are obtained as the Gauss images of homogeneous isoparametric hypersurfaces in spheres. This talk is based on my joint work with Hui Ma (Tsinghua University, Bejing).

Tuesday 29 September, 14:00-16:00: Sorin Dragomir (Basilicata), TBA

Friday June 26, 16:15: Hui Ma (Tsinghua University/Osaka City University),
"On Lagrangian submanifolds in complex hyperquadrics and related variational
problems" ABSTRACT: It is interesting to study volume minimizing
problem of Lagrangian submanifolds in Kaehler manifolds under Hamiltonian deformations.
In this talk, we focus on Lagrangian submanifolds in complex hyperquadrics,
obtained from Gauss images of isoparametric hypersurfaces in unit spheres. We
shall discuss our recent results on properties of such Lagrangian submanifolds
and their Hamiltonian stability and Hamiltonian instability in the homogenous
case. This

talk is based on joint work with Prof. Yoshihiro Ohnita.

Friday June 12, 16:15: Hiroshi Irieh (Tokyo Denki University), "Global tightness of real forms in complex hyperquadrics and special functions" (joint work with Takashi Sakai)

Friday June 5, 16:15: Ayumu Inoue (Tokyo Institute of Technology), "Quandles and hyperbolic volume"

Friday May 29, 16:15: Oliver Baues (Karlsruhe), "Virtually abelian Kaehler and projective groups"

Friday April 24, 16:15: Florent Schaffhauser (Keio), "Stable bundles and anti-holomorphic involutions on compact Riemann surfaces"

Friday April 17, 16:15: Manabu Akaho (TMU), "Lagrangian mean curvature flow and symplectic area"

Friday January 23, 16:15: Makiko Tanaka (Tokyo University of Science) "Totally geodesic submanifolds in compact symmetric spaces"

Friday January 16, 13:00-14:00, Liviu Ornea (University of Bucharest/IPMU), "Recent results in locally conformally Kaehler geometry"; 14:30-15:30, Misha Verbitsky (ITEP/IPMU), "Topology of lck manifolds with potential"

2008

Friday December 5, 17:15: Jun-ichi Inoguchi (Utsunomiya) "Affine spheres via loop groups"

Friday November 28, 16:15: Jun Imai( (TMU) "The configuration space of equilateral and equiangular polygons"

Friday November 14, 16:15: Udo Jeromin (Bath/Kyushu) "Models in Moebius differential geometry"

Friday November 7, 16:15: Andreas Kollross (Augsburg) "Manifolds with large isotropy groups" ABSTRACT: It is a well known classical result that two-point homogeneous spaces, i.e. Riemannian manifolds where any ordered pair of equidistant points can be mapped to any other such pair by an isometry, are exactly the rank-one symmetric and Euclidean spaces. Two-point homogeneity is equivalent to the condition that the isotropy action at any point is of cohomogeneity one. Thus, Riemannian manifolds whose isotropy actions are of cohomogeneity one are well known and it is a natural generalization to ask which Riemannian manifolds have isotropy actions of cohomogeneity two. We present a classification of such Riemannian manifolds. (Joint work with Evangelia Samiou.)

Friday October 24, 16:15: Shinichi Oguni (Keio) "How to use pseudogroups in geometric group theory"

Friday October 10, 16:15: Michihiko Fujii (Kyoto) TBA

Friday October 3, 16:15: Martin Guest (TMU), "A differential geometric interpretation of the quantum cohomology of S^2"

Friday May 23 (following the workshop on mathematics and computers, see CONFERENCE NEWS on the previous page)

14:00-15:00 Robert Sinclair (OIST), "Doing Mathematical Research with Computational Tools: Closed Asymptotic Curves"

15:30-16:30: Daisuke Nakajo (Kyushu), "A representation formula for indefinite improper affine spheres"

16:45-17:45: David Brander (Kobe), "CMC surfaces in Minkowski 3-space via loop group methods"

Friday May 16, 16:00: Admi Nazra (TMU), "Seifert fibred structure and rigidity on real Bott towers"

Friday May 9, 16:00: Sorin Sabau (Tokai University), "Some remarks on the Gauss-Bonnet theorem in Riemannian and Finslerian geometries"

Monday April 21, 16:00: Motohico Mulase (University of California, Davis), "Hitchin's integrable systems and mirror symmetry"

Friday April 18, 16:00 : Alan Huckleberry (Ruhr University, Bochum), "Surface Symmetry"

SHORT COURSES

11/9, 11/16, 11/30, 12/7 1400-1600

**Hitoshi Murakami (Tokyo Inst Tech)
Introduction to the volume conjecture of knots**

11/28, 11/29, 12/5, 12/6 1500-1700

**Yuichi Yamada （The University of Electro-Communications)
Plane curves, and surgeries on 3-dimensional manifolds**

ABSTRACT: In contrast to the case of 2-dimensional manifolds(surfaces), there are very many 3-dimensional manifolds. They are related by surgery (cut and paste) along tori. There are some "exceptional" or "unexpected" strange surgeries, such as a complicated knot in the 3-dimensional sphere which yields a simple manifold. Such surgeries are rare, and we would like to know "the rule of exceptional surgeries.

12/10, 12/17 1300-1500

**Takashi Otofuji (Nihon Univ.)
Introduction to Frobenius manifolds**

ABSTRACT: Frobenius manifolds are differential geometric objects, which have an origin in physics. I will explain some general features of Frobenius

manifolds, and give a few examples, including quantum cohomology.

12/13, 12/20, 1/17, 1/24, 1/31 13:00-15:00

**Akishi Kato (Univ. of Tokyo)**

Friday February 29, 16:00: Gleb Novitchkov (Keio/TMU), "Coupled dynamical r-matrices and WZNW model"

Friday February 22, 17:30: Rolando Jimenez (UNAM, Oaxaca), "Equivariant Fibrations between manifolds" (postponed to Feb 28)

Thursday February 7, 14:00: Claus Hertling (Mannheim), "Frobenius manifolds"

Friday January 25, 16:00: Tetsuya Taniguchi (Kitasato University), "The spectral curve of the Clifford torus"

Friday February 1, 16:00: Yoshihiro Sawano (TMU), "An introduction to function spaces suitable for analysis connected with differential geometry"

2007

Friday December 21:

(1) 16:00-17:00:Katsuhiro Moriya (University of Tsukuba),"Flat connections for Hamiltonian stationary Lagrangian tori in the complex Euclidean plane"

(2) 17:30-18:30: Alexander Cardona (Univ. Los Andes, Bogota),"Geometric Quantization of Dirac Structures and Gerbes". ABSTRACT: Geometric prequantization of Dirac structures has been defined by Weinstein and Zambon in the case of structures defined by non twisted Courant brackets, through the use of line bundles, generalizing the usual setting of geometric quantization for symplectic and Poisson manifolds. In this talk we go on to define such a prequantization for twisted Courant brackets using gerbes, and we consider the problem of reduction associated to the action of compact Lie groups on Dirac manifolds.

(then Christmas Party)

Friday December 14:

(1) 16:00-17:00: Rolando Jimenez (UNAM, Oaxaca),"On fundamental algebras of unions of H-spaces"

(2) 17:30-18:30: Ernesto Lupercio (CINVESTAV, Mexico City), "Orbifolds and topological quantum field theories"

Friday December 7, 16:00: Daisuke Yamakawa (Kyoto), "Simpson's Riemann-Hilbert and multiplicative quiver variety"

Friday November 30 (1) 16:00-17:00: Jose-Luis Cisneros (UNAM, Cuernavaca),"A refinement of the Milnor Fibration Theorem" ABSTRACT (2) 17:30-: Masahiro Futaki (Tokyo University), On the stabilization of the Fukaya-Seidel category

Thursday November 22, 14:00: Ayako Tanaka (Yokohama City University) , "Surfaces in the Euclidean unit n-sphere with prescribed Gauss map and mean curvature vector field"

Friday November 16, 16:00: Ken-ichi Sugiyama (Chiba University), "Similarities between 3-dimensional hyperbolic geometry and number theory"

Friday November 9, 16:00: Takafumi Akahori (Ehime University, "Global solutions of the nonlinear Schroedinger equation on closed manifolds"

October 29-31: JAVA AND VISUALIZATION TUTORIAL by Richard Palais (University of California) and Takashi Sakai (Osaka City University). Financial support may be available for students - please contact Martin Guest (martin@comp.metro-u.ac.jp) or Takashi Sakai (tsakai@sci.osaka-cu.ac.jp).

October 20, 23, 27: Horatiu Nastase (Tokyo Inst. Tech.), "AdS/CFT Correspondence: relations between gauge theories and strings (in celebration of 10 years of AdS/CFT)". (Lecture series in the Department of Physics, TMU. October 20: 8-301, 13:00-, October 23: 8-499, 13:00-, October 27: 8-301, 13:00-.) LECTURE NOTES AVAILABLE HERE

Friday October 19, 16:00: Jun Imai (TMU), "Indefinite Grassmannian manifolds and their applications" Abstract: The set of q-dimensional subspheres in S^n is a Grassmann manifold which has a natural pseudo-Riemannian structure, and, in some cases, a symplectic structure as well. Both of them are conformally invariant. I will explain some examples of their applications to knots and links. SLIDES OF THE LECTURES (smaller version for printing )

Friday October 12, 16:00: Ernst Heintze (Augsburg), "Involutions of Kac-Moody
algebras, hyperpolar actions and infinite

dimensional symmetric space" Abstract: We describe a classification
of involutions of affine Kac-Moody algebras, point out their relation to hyperpolar
actions on compact Lie groups, and consider the infinite dimensional symmetric
spaces corresponding to these involutions.

Thursday September 27, 14:00: Sorin Dragomir (Basilicata), "Subelliptic harmonic morphisms"

Wednesday July 4 [please note special day/time] Megumi Harada (McMaster University):

16:30-17:30 "The topology of symplectic and hyperkahler quotients"

Abstract: Symplectic and hyperkahler geometry lie at the crossroads
of many exciting areas of research due to their relations to geometric representation
theory, combinatorics, and certain areas of physics such as string theory and
mirror symmetry. As often happens in mathematics, the presence of symmetry in
these geometric structures -- in this context, a Hamiltonian $G$-action for
$G$ a Lie group -- turns out to be crucial in the computation of topological
invariants, such as the Betti numbers or the cohomology ring, of symplectic
and hyperkahler manifolds. I will give a bird's-eye, motivating overview of
the subject and then give a survey of my recent results on the topic.

17:40-18:40 "The K-theory of symplectic quotients"

Abstract: Let G be a compact connected Lie group, and (M, omega)
a Hamiltonian G-space with proper moment map mu. A classical theorem of Kirwan
states that there is a surjective ring map kappa from the G-equivariant rational
cohomology of M surjects onto the ordinary rational cohomology ring of the symplectic
quotient M//G. The Kirwan surjectivity theorem, in addition to computations
of the kernel of kappa, give powerful methods for explicit computations of the
cohomology rings of symplectic quotients. We present integral K-theoretic analogues
of this theory which therefore gives methods for computing the integral K-theory
of symplectic quotients. More specifically: (1) we prove a K-theoretic Kirwan
surjectivity theorem; (2) give a relationship between the kernel of the Kirwan
map kappa_G for a nonabelian Lie group and the kernel of the Kirwan map kappa_T
for its maximal torus (thus allowing us to reduce computations to the abelian
case; and (3) in the abelian case, give methods for explicit computations of
the kernel of kappa_T. Our results are K-theoretic analogues of the rational-cohomological
theory developed by Kirwan, Martin, Tolman-Weitsman, and others.

Friday June 29, 16:00: Takashi Sakai (Osaka City University), "Some geometric properties of the orbits of s-representations"

Wednesday June 27, 16:30: Hiro-o Tokunaga (TMU), "On local trigonal fibrations"

Friday June 22, 16:00: Masahiko Saito (Kobe), "The Painleve properties
of algebraic

differential equations and minimal models"

Friday June 15, 16:00: Yoshinobu Kamishima (TMU), "Preliminary report -- Conformally flat Lorentz manifold and Fefferman Lorentz metric"

Friday June 1, 16:00: Ayako Tanaka (Yokohama City University), "Surfaces in the Euclidean unit n-sphere with prescribed Gauss map and mean curvature vector field" CANCELLED DUE TO MEASLES OUTBREAK AT TMU

Friday June 8, 16:00: Jun Imai (TMU), "Indefinite Grassmannian manifolds and their applications"CANCELLED DUE TO MEASLES OUTBREAK AT TMU

Friday May 25, 16:00: Florent Schaffhauser (Keio), "Decomposable representations of surface groups"

Friday May 18, 16:00: Jun-ichi Inoguchi (Utsunomiya University), "Integrable systems in Moebius geometry"

Friday April 27, 16:00: Alfonso Gracia-Saz (Keio), "The symbol of a function of an operator"

Friday April 20, 16:00: Teruhiko Soma (TMU), "Ends of open hyperbolic 3-manifolds"

Wednesday January 31, 16:30: Yasunari Nagai (KIAS), "On degeneration of irreducible symplectic manifolds and monodromy"

Friday January 26, 16:00: Nariya Kawazumi (Tokyo University), "A higher analogue of the classical period matrix for a Riemann surface"

Thursday January18, 16:30 [Topology Festival]: Dusan Repovs (University of Ljubljana), "Constructing exotic continua using the Topologist sine curve"

Thursday January18, 15:00 [Topology Festival]: Mikiya Masuda (Osaka City University), "Toric Topology"

January 17-19: Mikiya Masuda (Osaka City University), Short course on toric varieties (January 17 (15:30-16:30), January 18 (10:30-12:00, 15:00-16:00 [Topology Festival]), January 19 (15:00-16:00))

January 16, 22: Kiyoshi Oba (Ochanomizu University), Short course "On Haefliger's (6,3) knots"

Friday January 12, 16:00: Masaharu Ishikawa (Tokyo Inst. of Tech.), "Legendre graphs and quasipositive diagrams"

2006

Friday December 22, 16:00: Takashi Otofuji (Nihon University), "Geodesics of Hofer's metric on the space of Lagrangian submanifolds"

Friday December 15, 16:00: Ben MacReynolds (Caltech), "Length and eigenvalue equivalent manifolds"

November 24, December 8,22, January 12,26 (all 10:30-12:00): Atsushi Noma (Yokohama National University), Short course on "Applications of Castelnuovo-Mumford regularity for projective varieties"

November 28 - December 1: Mutsuo Oka (Tokyo University of Science), Short course on "Fundamental groups of plane curves and Alexander polynomials" (November 28 (15:00-17:00), November 29 (15:00-17:00), November 30 (13:00-15:00), December 1 (15:00-17:00)

Friday November 24, 16:00: Shinzo Bannai (TMU) "On embeddings of $S_4$ and $A_5$ into the Cremona group and versal Galois covers"

Friday November 10, 16:00: Andreas Arvanitoyeorgos (University of Patras, Greece) "Biharmonic hypersurfaces in pseudo-Euclidean spaces"

Friday November 3, 13:30-17:00: Sumio Yamada (Tohoku University) "Geometrical variational principle for a minimal subset with singularities"

Friday October 27, 16:00: Wayne Rossman (Kobe University) "Using monodromy to close constant mean curvature surfaces"

Friday October 20, 16:00: Yoshiyuki Yokota (Tokyo Metropolitan University) "On the limit of the colored Jones polynomial of knots"

Friday October 13, 16:00: Masatoshi Kokubu (Tokyo Denki University) "Differential geometry of linear Weingarten surfaces in H^3"

Friday October 6, 16:00: Martin Guest (Tokyo Metropolitan University) "Differential equations from the D-module point of view"

Wednesday October 4, 16:30: Qihong Xie (Tokyo Inst. Tech.), "Counterexamples for the Kawamata-Viehweg vanishing on ruled surfaces in positive characteristic"

Friday 21July, 16:00: S. Kiriki (Kyoto University of Education) , "Coexistence of invariant sets with and without SRB measures in the Henon famiy"

Friday 14 July, 16:00: Kokoro Tanaka (Tokyo University) , "A note on C1-moves"

Wednesday 12 July, 16:30: Shigeru Kuroda (Kyoto University) , "Construction of finitely generated algebras and Hilbert's 14th Problem"

Friday 7July, 16:00: Sugiyama (Kyoto University) , "Moduli spaces of polynomial maps "

Friday 23 June, 16:00: Kohei Honda (Kyoto University), "Positive Ricci curvature"

Friday 16 June, 16:00: Kazushi Ueda (Kyoto University), "Mirror Symmetry and Stability Conditions on A_n Singularities"

Wednesday 14 June, 16:30: Yukinobu Toda (Tokyo University) , "Stability conditions and Calabi-Yau fibrations"

Monday 12 June, 14:00-15:00 and 15:30-16:30; Tuesday 13 June, 14:00-15:00 and 15:30-16:30, "Floer theory and its applications". Introductory lecture series by Paul Biran (Tel-Aviv University). Abstract: The speaker will explain Floer theory for Lagrangian submanifolds and describevarious recent applications to symplectic topology as well as to algebraic geometry and singularity theory.

Wednesday 31 May, 16:30: Hokuto Uehara (TMU), "Stability conditions and $A_n$-singularities on surfaces"

Friday 26 May, 16:00: Augustin-Liviu Mare (University of Regina), "Connectivity of preimages for moment maps on loop groups"

Friday 19 May, 16:00: Kazunori Nakamoto (Yamanashi University), "Topology of the representation varieties with Borel mold for unstable cases"

Friday 12 May, 16:00: Yoko Takane (UNAM, Mexico City), "Equilibria of pairs of nonlinear maps associated with cones"

Friday 28 April, 16:00: Florent Schaffhauser (Keio), "Introduction to quasi-Hamiltonian geometry (after Alekseev, Malkin and Meinrenken)"

Friday 21 April, 16:00: Shinichirou Matsuo (Tokyo University), "Removable singularities for harmonic maps in higher dimensions"

Friday 14 April, 16:00: Jun Imai (TMU), "Morse Theory applied to configuration spaces"

Friday 17 February, 16:00: Brian Forbes (Hokkaido), "Quantum cohomology and J functions of non-nef toric varieties"

6-8 February 2006: Lecture series by Takao Yamaguchi (Tsukuba) on the Poincare Conjecture. 6 February: 13:00-14:30, 7 February: 13:00-14:30, 8 February 10:30-12:30 and 14:00-15:30.

Monday 6 February, 16:00: Takao Yamaguchi (Tsukuba), "Flows on Riemannian manifolds"

3 February 2006 special seminars on geometry:

11:00-12:00 John Sullivan (TU Berlin), "Nondegeneracy of CMC triunduloids"

14:00-15:00 Christoph Bohle (TU Berlin), "Discrete holomorphic geometry"

15:15-16:15 Mark Haskins (Imperial College, London), "Smoothing isolated conical singularities of special Lagrangian n-folds"

16:30-17:30 Markus Schmies (TU Berlin), "Computational methods for Riemann surfaces and helicoids with handles"

Wednesday 25 January, 16:30: Noboru Nakayama (RIMS, Kyoto), "Classification of log del Pezzo surface of index two"

Friday 20 January, 16:00: Ben MacReynolds (University of Texas), "Constructing isospectral manifolds"

Friday 13 January, 16:00 : Dusan Repovs (University of Ljubljana) "Approximating maps of codimension one spheres by embeddings"

2005

Thursday 22 December, 13:00 : Rama Mishra (Indian Inst. Tech. Delhi), "Polynomial knots and a nice energy function"

Friday 16 December, 16:00 : Kouki Itoh (Kyoto), "A naive extension of Aomoto's twisted homology and de Rham cohomology theory"

Friday 9 December, 16:00 : Sergei Ketov (TMU), "Non-anticommutative deformation of complex geometry"

Wednesday 7 December, 16:30 : Takeshi Kajiwara (Tohoku University), "Tropical geometry and toric geometry"

Friday 2 December, 16:00 : Keiichi Sakai (Tokyo University), "Bott-Taubes construction for the space of framed embeddings R^1 to R^n "

Wednesday 30 November, 16:30 : Yasuharu Amitani (Waseda), "Projective manifolds containing 5-sheeted covers of projective space as hyperplane sections"

Friday 25 November, 16:00 : Yuichi Kabaya (Tokyo Institute of Technology), "Hyperbolic manifolds and the pre-Bloch group"

Friday 18 November, 16:00 : G. Fujita (Tokyo University), "Some properties of real conformal blocks"

Friday 11 November, 16:00 : Atsushi Fujioka (Hitotsubashi), "Motions of curves and their discretization"

Thursday 10 November, 16:00: John Rawnsley (Warwick), "Compact homogeneous symplectic manifolds"

Thursday 10 November, 14:00 : Toshiaki Kori (Waseda), "Prequantization of the moduli spaces of flat connections on four manifolds" (Mathematical Analysis Seminar)

Wednesday 2 November, 16:30: Takuro Abe (Kyoto), "The Stability of A_2-type arrangements"

Friday 28 October, 16:00 : Max Neumann (UNAM, Mexico and TMU), "Lengths and intersections of geodesics on surfaces"

Thursday 20 October, 14:00 : H. Sasahira (Tokyo University), "The spin structure of instanton moduli space" (Mathematical Analysis Seminar)

Friday 14 October, 16:00 : Satoru Saito (TMU), "The nature of manifolds of periodic points for higher dimensional integrable maps"

Thursday 13 October, 14:00 : Hideki Omori (Tokyo University of Science), "Deformation theory of algebraic representations" (Mathematical Analysis Seminar)

Tuesday 11 October, 11:00 : Robert Sinclair (Ryukyu University), "Experimental Mathematics" (talk given in conjunction with Computing Geodesic Curves: Computational Geometry with Maple, see below)

Friday 7 October, 16:00 : Masaki Tsukamoto (Kyoto University), "Infinite energy gauge theory"

Friday 15 July, 16:00 : Takashi Sakai (TMU), "Transfer principle in integral geometry"

Friday 17 June, 16:00 : Ser Peow Tan (National University of Singapore), "SL(2,C) characters of the one-holed torus"

Friday 10 June, 16:00 : Atsushi Tomoda (Keio), "On the splitting principle for bundle gerbe modules"

Friday 3 June, 16:00 : Hiroo Tokunaga (TMU), "Introduction to Galois coverings"

26-27 May: Conference on Integrable Systems, Geometry, and Abelian functions

Friday 20 May, 16:00: Emma Previato (Boston University), "Differential equations integrable by algebraic geometry: a survey of methods and problems"

Friday 13 May, 16:00 : Yoshinobu Kamishima (TMU), "Cusp cross-sections of hyperbolic orbifolds by Heisenberg nilmanifolds "

Friday 6 May, 16:15 : Jun Ohara (TMU), "Conformal geometry for knots and links (joint work with R. Langevin)"

Friday 22 April, 16:15: Kokoro Tanaka (Tokyo University), "Khovanov-Jacobsson numbers of surface-knots and their extension"

Wednesday 13 April, 16:00: Masumi Odagiri (TMU), "Tropical algebraic geometry(after Speyer and Sturmfels)"

Saturday 19 March, 14:00: Hiroshi Takai (TMU), "Moduli spaces of Yang-Mills connections on noncommutative manifolds" (NLYH meeting, joint with Department of Physics)

Friday 18 March, 15:00: Yoshihiro Ohnita (TMU), "Stability-index of certain special Lagrangian cones"

Wednesday 9 March, 16:00: Alan Huckleberry (Bochum), "Examples of Chow varieties"

Wednesday 19 January, 16:00: Le Dung Trang (ICTP), "Combinatorics of rational singularities"

Wednesday 19 January, 14:00: Bernard Teissier (Paris VII), "Polar invariants, conormal bundles and characteristic classes"

2004

Friday 24 June, 16:00 : Manabu Akaho (TMU), "Introduction to Polyfolds: a review of Hofer-Wysocki-Zehnder "Polyfolds and Fredholm Theory Part I", Chapter 1-3 "

Wednesday 22 December, 15:30: Susumu Tanabe (Independent University of Moscow), "A duality between monodromy and Poincare polynomial for multi-quasihomogeneous complete intersections"

Friday 10 December, 15:00: Masahito Toda, (Ochanomizu University), "Ricci flow and the work of Perelman-2"

Thursday 9 December, 15:00: Masahito Toda, (Ochanomizu University), "Ricci flow and the work of Perelman-1"

Friday 3 December, 15:00: K. Yamada (Sophia University), "Moduli spaces and polarization change problems of algebraic vector bundles"

Monday 22 November, 15:30: Yuichi Yamada (Electro-Communications University) "Some graph surgeries along A'Campo's divide knots"

Monday 15 November, 16:00: Vu The Khoi (Hanoi Inst. Math.) "Computing Godbillon-Vey invariant of SL(2,R) representations and applications"

Friday 12 November, 15:00: H. Ono (TMU), "Hamiltonian stability of Lagrangian tori in toric Kahler manifolds"

Friday 29 October, 15:00: F. Nakata (Tokyo University), "On the twistor correspondence for instantons of an indefinite metric"

Friday 22 October, 15:00: H. Satou (Tsukuba University), "Integrability of almost Kahler structures with divergence-free Weyl conformal tensor"

Friday 15 October, 15:00: Motoko Kotani (Tohoku University), "Magnetic transition operators on a crystal lattice"

Monday 18 October, 16:00: Yutaka Matsui (Tokyo University), "Radon transforms of construcutible functions on Grassmann manifolds"

Friday 8 October, 15:00: Jacob Mostovoy (UNAM Cuernavaca), "Sabinin algebras"

Wednesday 6 October, 15:30: Qihong Xie (University of Tokyo), "On pseudo-effectivity of the second Chern classes for smooth threefolds"

Friday 1 October, 15:00: Dusan Repovs (University of Ljubljana), "Fifty Years of the Recognition Problem for Topological Manifolds"

Friday 1 October, 16:30: Paul Biran (Tel-Aviv University), "Symplectic geometry of algebraic singularities"

Wednesday 8 September, 15:30: O. Riemenschneider (Hamburg University), "Searching for a more concrete form of the McKay correspondence for surfaces"

Tuesday 7 September, 15:00: Udo Hertrich-Jeromin (University of Bath), "Ribaucour transformation: A Bianchi permutability theorem"

Monday 26July, 15:30: Y. Kawahara (TMU) "Decomposability of resonance varieties and non-trivial components"

Friday 16 July, 1300-1400: A. Corti (University of Cambridge) "Fano 3-folds, K3 surfaces, mirrors etc."

Friday 9 July, 15:00 Alexander Cardona (Keio University) "Regularized traces in commutative and noncommutative geometry"

Monday 5 July, 15:30: Elizabeth Gasparim (New Mexico State University) "Moduli of vector bundles on surfaces"

Friday 2 July, 15:00: H. Sasahira (Tokyo University) "Spin structure on the Seiberg-Witten moduli space"

Wednesday 30 June, 15:30: Hiroyasu Tsuchihashi (Tohoku Gakuin University) "On irreducible curves in projective plane which can be the branch locus of a dihedral cover"

Monday 28 June, 15:30: M. Kobayashi (TMU) "Real blow-ups of embedded curves"

Friday 25 June, 15:00: Andreas Arvanitoyeorgos (American College of Greece) "Flag manifolds with homogeneous geodesics"

June 15-17: Lecture series by T. Yoshida (Tokyo Institute of Technology) "Conformal blocks and invariants of 3-manifolds" [June 14 16:00-18:00, June 15 14:00-16:00, June 16 16:00-18:00, June 17 13:00-15:00]

Friday 4 June, 16:00: S. Yamaguchi (Tokyo University) "Reidemeister-Turaev torsion from unitary representations of the fundamental group"

Friday 4 June, 14:30-15:30: Fumitoshi Sato (University of Utah) "On a conjecture of Faber and Pandharipande"

Monday 31May, 15:30: H. Terao (TMU) "Ranking Patterns and Arrangements "

Friday 28 May, 15:00: H. Murakami (Tokyo Institue of Technology) "On Khovanov homology"

Monday 24 May, 15:30: Do Duc Thai (Hanoi University of Education) "Unicity problems with truncated multiplicities of meromorphic mappings in several complex variables"

Friday 21 May, 15:00: H. Ishi (Yokohama City University) "The CR cohomology and Laplacian of the Shilov boundary of certain domains"

Monday 17 May, 16:20: M. Akaho (TMU) "Morse homology for manifolds with boundary"

Friday 14 May, 16:30: Augustin-Liviu Mare (University of Toronto) "Quantum cohomology of flag manifolds: the role of the Dubrovin connection"

Friday 14 May, 15:00: A. Tomoda (Keio University) "Homology handles obtained from Seifert homology spheres by surgery, and Floer homology"

Wednesday 12 May, 15:30: S. Bannai (TMU) "Construction of versal Galois coverings using toric varieties"

SPECIAL LECTURE: Monday 10 May, 15:30: Heisuke Hironaka (Japan Association for Mathematical Sciences) "Plane curve singularities from a higher dimensional view"

Friday 7 May, 15:00: A. Tanaka (Yokohama City University) "Surfaces in the sphere with given Gauss map and mean curvature vector field"

Wednesday 28 April, 16:00: S. Odagiri (TMU) "The shape of matroids corresponding to fine Schubert cells"

Monday 26 April, 15:30: Mutsuo Oka (TMU) "Fermat curves and maximal rational curves "

Friday 23 April, 15:00: D. Alekseevsky (University of Hull) "Normal holonomy groups and Kaehler submanifolds"

Wednesday 21 April, 15:30: Pho Duc Tai (Hokkaido University) "Duals of smooth curves"

Saturday 20 March, 10:30-12:00: Takashi Otofuji (Nihon university) "J-functions in quantum cohomology", 13:30-15:00 Quantum cohomology of infinite dimensional manifolds"

Friday 19 March, 15:00: Takashi Otofuji (Nihon university) "Introduction to quantum cohomology" (first of a series of three lectures)

Tuesday 16 March, 15:00: River Chiang (Academia Sinica - Taiwan, Hokkaido University) "A construction of Lagrangian embeddings using Hamiltonian actions"

SPECIAL ANNOUNCEMENT: Prof. Spivak will give a series of lectures on Thursdays and Fridays in March, at Keio University.

Wednesday 10 March, 16:30: Michael Spivak (Publish or Perish Inc) "Rigid bodies"

Tuesday 2 March, 15:00: Jose Seade (National Autonomous University of Mexico) "Orthogonal actions on complex projective spaces and the theorem of Arnold-Kuiper-Massey"

Friday 27 February, 15:00: Y. Sanno (Tokyo Institute of Technology) "On the Chow normal form and Chow stability"

Friday 20 February, 15:00: Susumu Tanabe (Independent University of Moscow) "The period integrals associated to affine complete intersections as generalized hypergeometric functions"

Friday 13 February, 15:00: Michael Spivak (Publish or Perish Inc) "How Newton really analysed the motion of planets. (The dangers of being smarter than every one else.)"

Monday 26 January, 15:30: Laurentiu Paunescu (University of Sydney) "On blow-analytic equivalence"

Monday 19 January, 15:30: Martin Guest (TMU) "An artificial version of mirror symmetry for hypersurfaces"

2003

Friday 19 December, 15:00: Fumitoshi Sato (University of Utah), "Relations in tautological rings by localization"

Monday 15 December, 15:30: Hiroo Tokunaga (TMU) "Zariski k-plets of rational curve arrangements and dihedral covers"

Monday 8 December, 15:30: Chris Macmeikan (TMU) "Modules of derivatons for semi-simple groups"

Friday 21 November, 15:00: Takefumi Kondo (Kyoto University) "Probability distributions on measured metric spaces"

Monday 17 November, 15:30: Philibert Nang (Tsukuba University) "D-modules associated to invertible matrices"

Friday 14 November, 15:00: Toshiake Kori (Waseda University) "Pre-quantum line bundles in Chern-Simons gauge theory on four-manifolds"

Monday 10 November, 15:30: Yacoub Ould Mohamed Abderrahmane (Saitama University) "Stratification theory from the Newton polyhedron point of view"

Friday 24 October, 15:00: Yumiko Kitagawa (Nara Women's University) "On isomorphism groups of homogeneous sub-Riemannian contact structures"

Wednesday 22 October, 1500: J. Wolf (UC Berkeley) "Quaternionic symmetric spaces"

Friday 10 October, 15:00 H. Iriyeh, informal seminar

Wednesday 8 October 2003, 16:00: Y. Maeda (Keio) "Z_2 gerbes and deformation quantization"

Monday 6 October 2003, 15:30: R. Langevin （Univ. Dijon) "Conformal invariants of knots and links, and what does not work in the complex algebraic case"