Title

Non-commutative amenable dynamics

Date

2025.12.17 (Wed)　16:45-17:45 (16:15- tea in 2nd floor common room)

Place

Rm111, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Yuhei Suzuki (Hokkaido University)

Abstract

　Amenability of a group action on a space is a classical concept introduced by Zimmer, which allows us to handle a non-amenable group action as an amenable group. Recently, amenability of C*-dynamics (i.e., non-commutative variant of the classical dynamical systems) is revisited and there is some drastic progress. I review some of them, notably characterizations, applications, and recipes to produce interesting examples. Partly a joint work with Narutaka Ozawa.

Title

Fluctuations and Tail Estimates in First-Passage Percolation

Date

2025.12.10 (Wed)　16:45-17:45 (16:15- tea in Rm105)

Place

Rm110, Bldg no. 3, Graduate School of Science, Kyoto University

Speaker

Shuta Nakajima (Keio University)

Abstract

　First-passage percolation (FPP) is a classical probabilistic model in which random weights are assigned to the edges of a lattice and one studies the minimal passage time between two points. It provides a mathematical description of phenomena such as fluid flow through a random medium and the spread of an infection. Through the geometry of passage times and the associated geodesics, it also serves as a fundamental model in random geometry.
　In recent years, the behavior of fluctuations of passage times and the corresponding tail probabilities has attracted considerable attention because of its connection with the scaling behavior observed in the Kardar–Parisi–Zhang (KPZ) universality class. In this talk, I will review known results on fluctuations of passage times and on the geometry of geodesics in FPP, and then present some recent progress on tail estimates. I will also discuss open problems concerning the relationship with the KPZ equation.

Title

On classifying cellular automaton orbits using one-variable functions

Date

2025.12.3 (Wed)　16:45-17:45 (16:15- tea in Rm105)

Place

Rm110, Bldg no. 3, Graduate School of Science, Kyoto University

Speaker

Akane Kawaharada (National Defense Academy of Japan)

Title

Homotopy theory of dg categories and formal category theoretic methods

Date

2025.11.26 (Wed)　16:45-17:45 (16:15- tea in 2nd floor common room)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Yuki Imamura (RIMS, Kyoto University)

Abstract

　A dg category is a category whose Hom-sets carry the structure of complexes of modules. It is widely used in algebraic geometry and representation theory as an enhancement of triangulated categories, providing a richer underlying structure. Originating from the homotopy theory of complexes up to quasi-isomorphism, dg categories themselves admit a natural homotopical structure, whose theoretical foundations have been extensively developed since the 2000s. In this talk, I will present an approach to the homotopy theory of dg categories from the viewpoint of formal category theory --- a 2-categorical framework that seeks to formalise and axiomatise "category theory" itself by abstracting the structures and phenomena observed in the 2-category of categories. I will first outline the basic ideas of formal category theory, and then explain how these ideas can be applied to the homotopy theory of dg categories.

Title

From Risk-Sensitive Portfolio Optimization to Large Deviations Control

Date

2025.11.19 (Wed)　16:45-17:45 (16:15- tea in Rm105)

Place

Rm110, Bldg no. 3, Graduate School of Science, Kyoto University

Speaker

Hiroaki Hata (Hitotsubashi University)

Abstract

　In this talk, we begin with a risk-sensitive portfolio optimization problem formulated under a stochastic factor model, and introduce its mathematical structure and analytical approach based on dynamic programming, particularly the Hamilton-Jacobi-Bellman (HJB) equation. We then explore the duality between risk-sensitive evaluation and large deviations control, and discuss problem formulations from the perspective of long-term asset management—namely, maximizing growth opportunities and minimizing downside risks. In the latter part, we address limitations of conventional affine-type models and introduce the α-Hypergeometric stochastic volatility model, which allows for more flexible and realistic volatility dynamics. We report on the analysis of the risk-sensitive portfolio optimization problem under this model, including the derivation of nonlinear partial differential equations, their probabilistic representations, the construction of optimal strategies, and the verification theorem. Through these developments, we demonstrate a concrete application of stochastic control theory within the framework of mathematical finance.

Title

Manin's conjecture over function fields via homological sieve

Date

2025.11.12 (Wed)　16:45-17:45 (16:15- tea in 2nd floor common room)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Sho Tanimoto (Nagoya University)

Abstract

　The Manin conjecture was proposed in the late 1980s by Yuri Manin and his collaborators. It predicts an asymptotic formula for the counting function of rational points on a class of varieties called Fano varieties. Over the past forty years, this conjecture has been the subject of intensive study and has become one of the more interdisciplinary areas in mathematics, involving arithmetic geometry, Arakelov geometry, analytic number theory, automorphic forms, ergodic theory, and birational geometry. One can also formulate the Manin conjecture over global function fields, such as the function field of a curve over a finite field. In this setting, the conjecture can be reformulated as a problem of counting $\mathbb{F}_q$-points on moduli spaces of curves on Fano varieties. Batyrev and later Ellenberg–Venkatesh proposed to study this counting problem using the homological stability of the relevant moduli spaces. In this talk, I will present our proof of the Manin conjecture for quartic del Pezzo surfaces, which relies on a homological sieve method—an abstraction of the inclusion–exclusion principle that we have developed. This is joint work with Das, Lehmann, and Tosteson, with additional contributions from Sawin and Shusterman.

Title

Weingarten Calculus: an introduction and recent developments

Date

2025.11.5 (Wed)　15:10-16:10

Place

Rm110, Bldg no. 3, Graduate School of Science, Kyoto University

Speaker

Benoit Collins (Kyoto University)

Abstract

　Weingarten Calculus is a tool to compute integrals of polynomial functions over compact groups with respect to their probability Haar measure (or equivalently, the expectation of polynomial variables). While the existence of Haar measure has been known for almost 100 years in a non-constructive way, an effective method to compute integrals or expectations started being investigated systematically only about 50 years ago (by the Nobel Prize winner ’t Hooft, Weingarten, and other theoretical physicists). The mathematical aspects of this theory are much more recent, and we will review them as well as some of our contributions to the field. In particular, we will describe new methods to compute integrals over unitary groups using the notion of virtual isometries. This latter part is joint work with Sho Matsumoto (Kagoshima University).

Title

Symplectic singularities and Kaledin's conjecture

Date

2025.11.5 (Wed)　16:45-17:45

Place

Rm110, Bldg no. 3, Graduate School of Science, Kyoto University

Speaker

Yoshinori Namikawa (RIMS, Kyoto University)

Abstract

　Symplectic singularities play an important role in algebraic geometry and geometric representation theory. All known examples show up with natural C^*-actions. About 20 years ago, Kaledin conjectured that a symplectic singularity is always conical; more precisely, it admits a conical C^*-action where the symplectic form is homogeneous. Recently we proved Kaledin's conjecture conditionally, but in a substantially stronger form. The idea is to use Donaldson-Sun theory in complex differential geometry to connect with the theory of Poisson deformations of symplectic varieties. This is a joint work with Y. Odaka.

Postponed (new date:TBA)

Title

Yangians and related algebras

Date

2025.10.29 (Wed)　16:45-17:45 (16:15- tea in 2nd floor common room)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Ryosuke Kodera (Chiba University)

Abstract

　Quantum groups and their representation theory have grown up from the Yang-Baxter equations and the R-matrices in lattice models. Yangians, a kind of quantum groups, are related with various algebras such as Hecke algebras, p-adic groups, W-algebras, and quantized Coulomb branches. In this talk, I will give an introduction to Yangians and relationships with other algebras.

Title

Symplectic geometry of cotangent bundles and microlocal sheaf theory

Date

2025.10.22 (Wed)　16:45-17:45 (16:15- tea in Rm105)

Place

Rm110, Bldg no. 3, Graduate School of Science, Kyoto University

Speaker

Tomohiro Asano (Dep.of Math., Kyoto University)

Title

On C*-algebras generated by semigroups of isometries

Date

2025.10.15 (Wed)　16:45-17:45 (16:15- tea in 2nd floor common room)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Camila Sehnem (RIMS, Kyoto University)

Abstract

　By a celebrated theorem of Coburn, the C*-algebra generated by a proper isometry on Hilbert space is unique, in the sense that it is isomorphic to the C*-algebra generated by any other proper isometry, for example, the unilateral shift on $\ell^2(\mathbb{N})$. In this talk I will consider uniqueness for C*-algebras generated by semigroups of isometries, and discuss how this property is related to the ideal structure of C*-algebras built from actions and partial actions of groups on compact spaces. I will discuss examples arising from number theory and group theory.

Title

Remarks on classical and homological Mirror symmetries

Date

2025.10.8 (Wed)　16:45-17:45 (16:15- tea in Rm105)

Place

Rm110, Bldg no. 3, Graduate School of Science, Kyoto University

Speaker

Kenji Fukaya (Yau Mathematical Sciences Center, Tsinghua University)

Title

How to solve polynomial equations? The art of anabelian geometry

Date

2025.7.23 (Wed)　16:45-17:45 (16:15- tea in 2nd floor common room)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Mohamed Saidi (RIMS, Kyoto University & University of Exeter)

Abstract

　How to solve polynomial equations? A famous ancient problem in mathematics is the solubility of polynomials by radicals, which was a major theme in mathematics for a couple of millennia. Two centuries ago, this problem was solved (negatively in general) by Abel-Ruffini and Evariste Galois. The work of Galois, then a teenager, revolutionised algebra, and indeed mathematics. The basic idea of Galois is to think about the symmetries of roots of polynomials. This led him to define what nowadays are called Galois groups, and initiate group theory, the latter became a central topic in mathematics and beyond. The major discovery of Galois was that the group of symmetries of the roots of a polynomial equation encodes the information on the solubility of the polynomial by radicals, which is a property of arithmetic and geometric nature one would argue.
　During the second half of last century, Grothendieck further pushed and refined the ideas of Galois, by introducing the theory of fundamental groups in arithmetic and algebraic geometry. The idea/fact, already observed by Galois, that some geometric and arithmetic aspects of (systems of) polynomial equations, are (should be) encoded in (combinatorial) group theory, was central to Grothendieck's mathematical thinking. He put forward, few decades ago, a vast and far reaching research programme: the so-called anabelian programme. The ultimate goal of this programme is to establish a purely combinatorial group-theoretic framework in which both arithemtic and geometry are encoded, very much in the spirit of the work of Galois.
　In my talk I will review the historical context which led to the birth of anabelian geometry and discuss some developments and results in recent decades, mostly established at RIMS Kyoto! and which are heading towards achieving Grothendieck's aims and beyond. These developments are concerned with the description of the absolute Galois group of the field of rational numbers; a major object of study in number theory, and the (arithmetic version of) mapping class group.

Title

Topology of Busemann nonpositively curved space

Date

2025.7.16 (Wed)　16:45-17:45 (16:15- tea in Rm105)

Place

Rm110, Bldg no. 3, Graduate School of Science, Kyoto University

Speaker

Tadashi Fujioka (Dep. of Math., Kyoto University)

Title

Combinatorial construction of symplectic 6-manifolds via bifibration structures

Date

2025.7.2 (Wed)　16:45-17:45 (16:15- tea in Rm105)

Place

Rm110, Bldg no. 3, Graduate School of Science, Kyoto University

Speaker

Kenta Hayano (Keio University)

Title

Construction of $p$-energy forms and $p$-energy measures on the Sierpinski carpet

Date

2025.6.25 (Wed)　16:45-17:45 (16:15- tea in 2nd floor common room)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Ryosuke Shimizu (Graduate School of Informatics, Kyoto University)

Title

On the Z-module generated by multiple zeta values

Date

2025.6.11 (Wed)　16:45-17:45 (16:15- tea in Rm105)

Place

Rm110, Bldg no. 3, Graduate School of Science, Kyoto University

Speaker

Minoru Hirose (Kagoshima University)

Title

Mathematical problems from supersymmetric field theories

Date

2025.6.4 (Wed)　16:45-17:45 (16:15- tea in 2nd floor common room)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Wenbin Yan (Tsinghua University)

Abstract

　Supersymmetric field theories are closely connected to various fields of mathematics. In this talk, I will review different invariants of supersymmetric theories originated from counting BPS particles and what mathematics is behind. With the help of dualities and other techniques, many interesting mathematical statements and results can be extract from these invariants.

Title

Entropy of degeneration of algebraic variety

Date

2025.5.28 (Wed)　16:45-17:45 (16:15- tea in Rm105)

Place

Rm110, Bldg no. 3, Graduate School of Science, Kyoto University

Speaker

Eiji Inoue (Dep. of Math., Kyoto University)

Title

Kazhdan's Property (T) and Semidefinite Programming

Date

2025.5.21 (Wed)　15:10-16:10 　　

Place

Rm420, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Narutaka Ozawa (RIMS, Kyoto University)

Title

The geometric Brascamp-Lieb inequality

Date

2025.5.21 (Wed)　16:45-17:45 　　

Place

Rm420, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Neal Bez (Nagoya University)

Title

On infinite collisions of simple random walks on graphs

Date

2025.5.14 (Wed)　16:45-17:45 (16:15- tea in 2nd floor common room)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Satomi Watanabe (RIMS, Kyoto University)

Title

Variational problems and PDEs for S^2-valued maps in the ferromagnetic model

Date

2025.5.7 (Wed)　16:45-17:45 (16:15- tea in Rm105)

Place

Rm110, Bldg no. 3, Graduate School of Science, Kyoto University

Speaker

Ikkei Shimizu (Dep. of Math., Kyoto University)

Title

Model checking via fixed points and no-go theorem for product construction

Date

2025.4.30 (Wed)　16:45-17:45 (16:15- tea in 2nd floor common room)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Mayuko Kori (RIMS, Kyoto University)