Title

Duflo--Kontsevich Type Theorem for DG Manifolds

Date

2026.6.17 (Wed)　15:10-16:10 　　

Place

Rm420, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Ping Xu (Pennsylvania State University)

Abstract

　It is a classical result that for any dg algebra A, the pair of its Hochschild (co)homologies \( (HH^\bullet (A), HH_\bullet (A)) \) carries rich algebraic structures resembling the usual Cartan calculus, often referred to as the Tamarkin--Tsygan calculus. DG manifolds provide a useful geometric framework for describing spaces with singularities. In this talk, I will discuss the Tamarkin--Tsygan calculus associated with the dg algebra of a dg manifold and present a Duflo--Kontsevich type theorem in this setting. As applications to several important examples, we recover the Duflo theorem on the center of the universal enveloping algebra of a Lie algebra and Kontsevich's theorem on the Hochschild cohomology of complex manifolds, placing them under a unified framework. This is joint work with Hsuan-Yi Liao and Mathieu Stiénon.

Title

Applications of gauge theory on 4-dimensional orbifold cobordisms

Date

2026.6.17 (Wed)　16:45-17:45 　　

Place

Rm420, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Yoshihiro Fukumoto (Ritsumeikan University)

Title

Free probability and Random Matrix

Date

2026.6.10 (Wed) 16:45-17:45 (16:15- tea in Rm105)

Place

Room 110, Faculty of Science Bldg. No. 3, Kyoto University

Speaker

Akihiro Miyagawa (Kyoto University)

Abstract

　Free probability theory is a framework obtained by replacing the notion of independence in classical probability theory with a concept called free independence. The random variables considered in free probability appear as operators on a Hilbert space and possess a noncommutative structure. On the other hand, a random matrix is a matrix whose entries are random vari ables, and random matrix theory has found applications not only in mathematics but also in various fields such as quantum physics and machine learning. The relationship between free probability and random matrix theory has been actively studied since the 1990s, following Voiculescu’s discovery of asymptotic freeness. In this talk, I will introduce several results concerning the relationship between free probability and random matrix theory, accompanied by figures obtained through numerical computations. Finally, I will discuss some of my recent work on the spectra of polynomials in freely independent semicircular and circular distributions.

Title

Length penalised ideal curve flow for closed planar curves

Date

2026.6.3 (Wed) 16:45-17:45 (16:15- tea in 2nd floor common room)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Shinya Okabe (Tohoku University)

Title

Branching problems for covering groups

Date

2026.5.27 (Wed) 16:45-17:45 (16:15- tea in Rm105)

Place

Room 110, Faculty of Science Bldg. No. 3, Kyoto University

Speaker

Yuanqing Cai (Faculty of Science, Hokkaido University)

Abstract

　How does an irreducible representation of a group decompose when restricted to a subgroup? This question lies at the heart of branching problems, a fundamental topic in representation theory with deep connections to other areas of mathematics. For reductive groups, the relative Langlands program predicts hidden spectral structures underlying such problems. However, much less is known for non-linear covers of reductive groups.
　In this talk, we discuss several examples of branching problems for covering groups, with particular emphasis on multiplicity-free restrictions.

Title

Tame geometry and applications

Date

2026.5.20 (Wed) 16:45-17:45 (16:15- tea in 2nd floor common room)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Bruno Klingler (Humboldt Universität zu Berlin)

Abstract

　In his Esquisse d’un programme, Grothendieck called for the development of a “tame” topology, free from the pathologies of general topology. Such a framework was developed in the 1980s and 1990s by logicians under the name o-minimal geometry, based on the simple principle that, in dimension one, the only sets considered are finite unions of intervals. Remarkably, this setting has recently led to striking applications in complex algebraic geometry-particularly in Hodge theory- as well as in number theory, notably in Diophantine geometry. This talk will offer an elementary introduction to these ideas.

Title

On the K-moduli of Calabi–Yau fiber spaces over curves

Date

2026.5.13 (Wed) 16:45-17:45 (16:15- tea in Rm105)

Place

Room 110, Faculty of Science Bldg. No. 3, Kyoto University

Speaker

Masafumi Hattori (Kyoto University)

Abstract

　Deformations of algebraic varieties are an important concept, and moduli are geometric objects that realize the totality of such deformations as a single unified space. Once a moduli space is constructed, elusive phenomena—such as how varieties degenerate and how invariants behave in families—can be visualized as concrete geometric information. However, the construction of moduli spaces for higher-dimensional varieties has long been a difficult problem.
　On the other hand, K-stability is an algebro-geometric notion introduced in Kähler geometry, and it is expected to characterize varieties that admit “good” metrics. Yusuke Odaka proposed the so-called K-moduli conjecture, which predicts that moduli spaces of algebraic varieties can be constructed using the notion of K-stability. The philosophy is that, by allowing only K-stable degenerations (that is, degenerations admitting good metrics), one should be able to construct moduli spaces for higher-dimensional varieties.
　The K-moduli conjecture has been solved in the cases of negative curvature, Fano varieties (positive curvature), and Calabi-Yau varieties (zero curvature). However, for higher-dimensional varieties in which these curvature properties are mixed, the situation is still not well understood. 　In this talk, we focus on Calabi-Yau fiber spaces, namely varieties whose fibers have zero curvature while the base direction has positive curvature, and discuss how the K-moduli conjecture should be formulated in such “mixed” situations. We will also explain, time permitting, the geometric intuition underlying this problem and the difficulties that are currently encountered.

Title

Linear Variance of First-Passage Percolation on the Book Graph

Date

2026.4.22 (Wed)　16:45-17:45 (16:15- tea in 2nd floor common room)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Noe Kawamoto (Kyoto University)

Abstract

　We consider first-passage percolation (FPP) on the book graph with multiple pages, where upper-half planes are glued along the common axis. FPP was introduced by Hammersley and Welsh in 1965 as a model of fluid flow through a random medium. In the model, a non-negative random variable \( t_e \) is assigned on each edge of the graph, independently of the others. The passage time of a path is defined as the sum of the \( t_e \)'s over edges traversed by the path. Our interest is in the infimum of the passage times over all finite paths from \( o \) to \( ne_1 \), which is defined by \( T(0,ne_1) \). In this talk, we prove that when the number of pages of the book graph is sufficiently large, the variance of \( T(0,ne_1) \) is of order \( n \), which is markedly different from the conjectured behavior on two-dimentional integer lattice, where the variance is of order \( n^{2/3} \). This talk is based on joint work with Tzu-Han Chou (NUS) and Wai-Kit Lam (NTU).