## Colloquium

Title

**
Moore-Tachikawa 2d TQFTs whose values are holomorphic symplectic varieties
**

Date

2018.2.14 (Wed) 16:30～17:30 (16:00- tea)

Place

Rm110, Building No.3, Faculty of Science, Kyoto University

Speaker

Hiraku Nakajima (RIMS, Kyoto University)

Title

**
Mod $p$ representation theory of $p$-adic reductive groups
**

Date

2018.1.24 (Wed) 15:00～16:00 (16:00- tea)

Place

Rm110, Building No.3, Faculty of Science, Kyoto University

Speaker

Noriyuki Abe (Hokkaido University)

Title

**
see the Japanese page
**

Date

2018.1.24 (Wed) 16:30～17:30 (16:00- tea)

Place

Rm110, Building No.3, Faculty of Science, Kyoto University

Speaker

Atsushi Yamaguchi (Osaka Prefecture University)

Title

**
See the Japanese page
**

Date

2018.1.17 (Wed) 16:30～17:30 (16:00- tea)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Hiromichi Takagi (The University of Tokyo)

Title

**
Potential geometry in the moduli of complex dynamics
**

Date

2018.1.10 (Wed) 16:30～17:30 (16:00- tea)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Yûsuke Okuyama (Kyoto Institute of Technology)

Title

**
Combinatorial reciprocity and Euler characteristic
**

Date

2017.12.27 (Wed) 14:45～15:45

Place

Rm110, Building No.3, Faculty of Science, Kyoto University

Speaker

Masahiko Yoshinaga (Hokkaido University)

Title

**
see the Japanese page
**

Date

2017.12.27 (Wed) 16:30～17:30

Place

Rm110, Building No.3, Faculty of Science, Kyoto University

Speaker

Kenji Fukaya (Stony Brook University)

Title

**
On some existence theorem for unstable minimal hypersurface
**

Date

2017.12.20 (Wed) 16:30～17:30 (16:00- tea)

Place

Rm110, Building No.3, Faculty of Science, Kyoto University

Speaker

Yoshihiro Tonegawa (Tokyo Institute of Technology)

Title

**
Applications of gauge theory to low dimensional topology
**

Date

2017.12.13 (Wed) 16:30～17:30 (16:00- tea)

Place

Rm110, Building No.3, Faculty of Science, Kyoto University

Speaker

Hirofumi Sasahira (Kyushu University)

Title

**
The Ricci flow on four-manifolds and the Seiberg-Witten equations
**

Date

2017.12.6 (Wed) 16:30～17:30 (16:00- tea)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Masashi Ishida (Tohoku University)

Abstract

A solution to the normalized Ricci flow is called non-singular if the solution exists for all time and the Riemannian curvature tensor is uniformly bounded. In 1999, Richard Hamilton introduced it as an important special class of solutions and classified 3-dimensional non-singular solutions. In particular, it was proved that the underlying 3-manifold is geometrizable in the sense of Thurston. On the other hand, in 1994, new invariants of smooth 4-manifolds were introduced by Edward Witten. The invariants are constructed from nonlinear partial differential equations which are called the Seiberg-Witten equations. In this talk, the Seiberg-Witten equations are used to study the properties of 4-dimensional non-singular solutions. In particular, we would like to explain that gauge theoretical invariants associated with the Seiberg-Witten equations give rise to obstructions to the existence of 4-dimensional non-singular solutions and we will also discuss its application.

Title

**
A trace formula on $SL(3,Z)\backslash SL(3,R)/SO(3)$
**

Date

2017.11.29 (Wed) 16:30～17:30 (16:00- tea)

Place

Rm110, Building No.3, Faculty of Science, Kyoto University

Speaker

Satoshi Wakatsuki (Kanazawa University)

Abstract

In this talk, we give a trace formula on $SL(3,Z)\backslash SL(3,R)/SO(3)$, whose spectral side and geometric side are explicitly described by the spherical transform of any bi-invariant test function. We will also discuss its application to Weyl's law. This is a joint work with Werner Hoffmann and Masao Tsuzuki.

Title

**
Monodromy and derived equivalences
**

Date

2017.11.22 (Wed) 16:30～17:30 (16:00- tea)

Place

Rm110, Building No.3, Faculty of Science, Kyoto University

Speaker

Andrei Okounkov (Kyoto University & Columbia University)

Abstract

Monodromy of linear differential equations is a very old and classical object, which for certain very special equations of geometric origin has been the subject of challenging conjectures of more modern flavor. One such conjecture, proposed by Bezrukavnikov and myself, identifies the monodromy of certain quantum differential equations with a generalization of the Hecke algebra that is important for representation theory in large prime characteristic. I will explain what this conjecture says and how we prove it for Nakajima quiver varieties.

Title

**
Extremal length geometry on Teichmuller space
**

Date

2017.11.15 (Wed) 17:00～18:00 (16:30- tea)

Place

Rm110, Building No.3, Faculty of Science, Kyoto University

Speaker

Hideki Miyachi (Osaka University)

Abstract

In this talk, I would like to give a recent progress of my study on Extremal length geometry on Teichmueller space. This research is aimed for unifying (or understanding the relation between) the complex analytical aspect and the topological aspect of Teichmueller theory in the framework of the Thurston theory. Extremal length geometry is expected to act as a mediator at the unification. If time permits, I will explain my program for the unification.

Title

**
Nonlinear stochastic integration and hedging in nonlinear markets
**

Date

2017.10.25 (Wed) 16:30～17:30 (16:00- tea)

Place

Rm110, Building No.3, Faculty of Science, Kyoto University

Speaker

Masaaki Fukasawa (Osaka University)

Title

**
Nonpositive curvature and operator algebras
**

Date

2017.10.11 (Wed) 16:30～17:30 (16:00- tea)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Mikael Pichot (RIMS & McGill University)

Abstract

The field of operator algebras was begun in the late 1920’s by J. von Neumann, through his work on abstract Hilbert spaces and the foundation of quantum mechanics. The subject developed steadily for nearly a century, and found deep connections with many branches of mathematics. The talk will discuss, using concrete examples, some of these connections, in particular with group theory and geometry of nonpositive curvature. The main focus will be the recent work of Sylvain Barré and myself on intermediate rank geometry. I will give some motivation for this work, and explain some of the leading ideas in the study of discrete groups of intermediate rank.

Title

**
Two Proofs of Fermat's Last Theorem
**

Date

2017.7.19 (Wed) 16:30～17:30 (16:00- tea)

Place

Rm110, Building No.3, Faculty of Science, Kyoto University

Speaker

Fucheng Tan (RIMS, Kyoto University)

Abstract

In this talk, we start with the basics on Galois representations and modular forms. It is well-known that to a modular form one can attach a Galois representation satisfying several natural properties. On the other hand, the modularity conjectures, started by Taniyama and Shimura, assert that a Galois representation, which satisfies such properties as above, necessarily arises from a modular form. Andrew Wiles' milestone work on modularity in addition provided us the first proof of Fermat's Last Theorem. Several years ago, Shinichi Mochizuki presented an entirely new theory, called Inter-universal Teichmuller theory, which has a remarkable application, namely the ABC conjecture. Certain effective version of ABC conjecture will in turn imply Fermat's Last Theorem. We shall give an introduction to both proofs of FLT. Time permitting, we will make some brief remarks on Inter-universal Teichmuller theory.

Title

**
Data compression and communication in topological dynamics.
**

Date

2017.7.12 (Wed) 14:40～15:40

Place

Rm420, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Masaki Tsukamoto (Kyoto University)

Abstract

Data compression and communication are the most basic themes of information theory.
We explain some problems of topological dynamics from this viewpoint.
Given a dynamical system $X$, we consider the following three problems:

(1) Take two points in $X$. We want to collapse $X$ into a smaller dynamical system $Y$ while
distinguishing the given two points. When is this possible?

(2) Take an invariant probability measure $m$ on $X$, which determines a stochastic process taking values in $X$.
The rate distortion function gives how many bits we need to describe this process under a distortion constraint.
What determines the asymptotic (as the distortion goes to zero)
of the supremum of the rate distortion function over all invariant probability measures $m$?

(3) Consider signals whose frequencies are limited in a fixed band of length $W$.
(In the standard telephone, $W = 3400Hz$.)
We want to communicate $X$ by using these signals.
How large should $W$ be?

The answer to (2) is known (Lindenstrauss--T.).
The answers to (1) and (3) are known when $X$ is a minimal system (Lindenstrauss, Gutman--T.).

It is known that ``mean dimension theory'' is a key player in all the above three problems.
The main purpose of this talk is to give an introduction to mean dimension through the above problems.

Title

**
Double Affine Hecke Algebras and Low-Dimensional Geometry
**

Date

2017.7.12 (Wed) 16:30～17:30

Place

Rm420, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Ivan Cherednik (RIMS & UNC Chapel Hill)

Abstract

We will discuss 3 major approaches to Double Affine Hecke algebras via topology of elliptic configuration spaces, K-theory of affine flag varieties and harmonic analysis (integrable systems). These algebras are flat deformations of Heisenberg and Weyl algebras (non- commutative tori) and as such are expected to play an important role in non-commutative geometry. We will mainly focus on a new DAHA based theory of refined invariants of iterated links, including all algebraic ones, and its geometric aspects (compactified Jacobians of plane curve singularities). The case of sl_2(A_1) will be considered in detail; we will calculate the DAHA superpolynomial of trefoil and provide other examples.

Title

**
Subfactors and representation theory
**

Date

2017.7.5 (Wed) 16:30～17:30 (16:00- tea)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Yuki Arano (Kyoto University)

Title

**
Frobenius maps and abelian varieties
**

Date

2017.6.28 (Wed) 16:30～17:30 (16:00- tea)

Place

Rm110, Building No.3, Faculty of Science, Kyoto University

Speaker

Akiyoshi Sannai (RIMS, Kyoto University)

Abstract

Frobenius maps are the most basic tool in algebraic geometry in positive characteristic. The module structure of the Frobenius pushforward of the structure sheaves of algebraic varieties has great influence on both the local and the global structure of algebraic varieties, and the theory related to them is called F-singularity theory. This theory was developed by Hochster and Huneke, who are commutative ring theorists, but in recent years it has been applied to the minimal model theory in positive characteristic. In this talk, we start with an introduction to F-singularity theory, touched on the relationship with singularities appearing in birational geometry, the relationship with log Fano varities, and finally we give the characterization of abelian varieties by using the Frobenius pushforward of the structure sheaves.

Title

**
Proper actions on homogeneous spaces
**

Date

2017.6.21 (Wed) 16:30～17:30 (16:00- tea)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Yosuke Morita (Kyoto University)

Abstract

Let G/H be a homogeneous space. The quotient of G/H by a discrete subgroup of G becomes a manifold locally modelled on G/H if and only if the discrete subgroup acts properly and freely on G/H. If these conditions are satisfied, the discrete subgroup is called a discontinuous group for G/H, and the quotient manifold is called a Clifford-Klein form of G/H. Toshiyuki Kobayashi's work since the late 1980s revealed that, when G is a reductive Lie group, the properness of the action is rephrased in terms of the structure theory of reductive Lie groups (the Cartan projection). Since then, the following questions has attracted considerable attention and studied based on his results:

- Is there a discontinuous group for G/H which is isomorphic to a given discrete group?

- Is there a cocompact discontinuous group for G/H?

In this talk, I will review these studies with examples and give my recent results.

Title

**
Data analysis using persistent homology and machine learning
**

Date

2017.6.14 (Wed) 16:30～17:30 (16:00- tea)

Place

Rm110, Building No.3, Faculty of Science, Kyoto University

Speaker

Ippei Obayashi (Tohoku University)

Abstract

Persistent homology is the homology theory on a filtration, which is developed for the data analysis. By combining the scale with the filtration index, we can treat topological information of the data with scale. Persistent homology is a powerful method which can summarize quantitative geometric infromation effectively, and it is applied various kinds of data analysis such as amorphous solids, granular crystallization, glassy polymers, viral evolution, and sensor networks. Machine learning enables us to find a characteristic patterns from data statistically and widely used for data analysis.

By the combination of persistent homology and machine learning, we can find characteristic geometric patterns from data. I will show you our recent research about that combination. Some methods for that purpose are already proposed, but our method has an advantage of intuitive understanding and effective visualization of the learned results.

This research is a joint work with Y. Hiraoka (WPI-AIMR, Tohoku Univ.).

Title

**
Relative singular locus and matrix factorizations
**

Date

2017.6.7 (Wed) 16:30～17:30 (16:00- tea)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Yuki Hirano (Kyoto University)

Abstract

The theory of matrix factorizations was introduced by Eisenbud around 1980, and he applied matrix factorizations to the representation theory of Cohen-Macaulay modules over hypersurface singularities. Orlov and Buchweitz showed that the categories of matrix factorizations are equivalent to the singularity category of hypersurface singularities, and later the theory of matrix factorizations was applied to various areas of mathematics.In this talk, we give a kind introduction to matrix factorizations, and then we explain a relationship between matrix factorizations and relative singular locus introduced in this work.

Title

**
On a refinement of the reciprocity law on Stark units
**

Date

2017.5.31 (Wed) 15:00～16:00 (16:00- tea)

Place

Rm110, Building No.3, Faculty of Science, Kyoto University

Speaker

Tomokazu Kashio (Tokyo University of Science)

Title

**
Random Matrices and Operator Algebras
**

Date

2017.5.31 (Wed) 16:30～17:30 (16:00- tea)

Place

Rm110, Building No.3, Faculty of Science, Kyoto University

Speaker

Yoshimichi Ueda (Kyushu University)

Title

**
On a dynamic model for limit profiles and their Gaussian fluctuations in group-theoretical ensembles of Young diagrams
**

Date

2017.5.24 (Wed) 16:30～17:30 (16:00- tea)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Akihito Hora (Hokkaido University)

Abstract

In 1970's Vershik-Kerov and Logan-Shepp showed that a limit profile is observed in the Plancherel ensemble of Young diagrams as a law of large numbers. This concentration phenomenon in a Young diagram ensemble was extended to various models and has been studied in connection with asymptotic representation theory of symmetric groups, random matrices, free probability theory, and so on. Further more, we can see a wide range of studies on fluctuations. First we will overview static models on such limit profiles and their Gaussian fluctuations of Young diagrams. Then we will consider a continuous time Markov chain preserving the Plancherel measure on Young diagrams, and give a dynamic model for the macroscopic time evolution of limit profiles and their Gaussian fluctuations through a diffusive scaling limit in space and time. Analysis of the polynomial functions in several coordinates of Young diagrams introduced by Kerov-Olshanski in 1990's is effectively used to solve these problems. Some examples of explicit computations will be mentioned.

Title

**
Mirror symmetry and theta functions
**

Date

2017.5.17 (Wed) 16:30～17:30 (16:00- tea)

Place

Rm110, Building No.3, Faculty of Science, Kyoto University

Speaker

Atsushi Kanazawa (Kyoto University)

Abstract

I will talk about an attempt to understand and generalize classical theta functions of abelian varieties by affine geometry. Our motivation comes from mirror symmetry, which is duality between complex geometry and symplectic geometry among distinct Calabi-Yau manifolds. Recent study of mirror symmetry has revealed that affine (tropical) geometry plays an essential role in this duality. Prototypical examples are lattice polytopes and rational fans in the theory of toric manifolds. In this talk, I will review recent progress of mirror symmetry and then discuss ``theta functions'' of toric manifolds and Calabi-Yau manifolds. If time permits, I will mention their relation to geometric quantization.

Title

**
Counting BPS bound states on toric Calabi--Yau 3-folds
**

Date

2017.5.10 (Wed) 16:30～17:30 (16:00- tea)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Yutaka Yoshida (RIMS, Kyoto University)

Title

**
Introduction to deformation/rigidity theory for von Neumann algebras
**

Date

2017.4.26 (Wed) 16:30～17:30 (16:00- tea)

Place

Rm110, Building No.3, Faculty of Science, Kyoto University

Speaker

Yusuke Isono (RIMS, Kyoto University)

Title

**
The six vertex model and randomly growing interfaces in (1+1)dimensions
**

Date

2017.4.19 (Wed) 16:30～17:30 (16:00- tea)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Alexei Borodin (Massachusetts Institute of Technology)

Abstract

The goal of the talk is to explain how the six vertex model gives rise to models of (1+1)d random growth in the KPZ (Kardar-Parisi-Zhang) universality class, and how the Yang-Baxter integrability of the former leads to solvability of the latter.

Title

**
Applying physics to mathematics
**

Date

2017.4.12 (Wed) 15:00～16:00 (16:00- tea)

Place

Rm110, Building No.3, Faculty of Science, Kyoto University

Speaker

Tadashi Tokieda (University of Cambridge)

Abstract

Traditionally mathematics is expected to spawn unexpected applications to physics. We explore the reverse: to use physics to prove mathematical results. The talk should be understandable to everybody in its entirety, but I will try to present a variety of new examples---inequality, lattice points, elementary geometry, analysis of algorithms, topology, etc.

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