Title

Why is a rational blowdown surgery interesting in 4-manifolds?

Date

2024.2.14 (Wed)　16:45-17:45 (16:15- tea)

Place

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

Speaker

Jongil Park (Seoul National University)

Abstract

　A rational blowdown surgery initially introduced by R. Fintushel and R. Stern and later generalized by J. Park is one of the simple but powerful techniques in study of 4-manifolds topology. Note that a rational blowdown surgery replaces a certain linear chain of embedded 2-spheres by a rational homology 4-ball. In particular, a rational homology ball is a key ingredient in the construction of exotic smooth, symplectic 4-manifolds with small Euler characteristic and complex surfaces of general type with $p_g = 0$. It also plays an important role in $\mathbb{Q}$-Gorenstein smoothings and symplectic fillings of the link of normal surface singularities.
　In this talk, I review what we have obtained in study of 4-manifolds using a rational blowdown surgery in various levels. And then, I'd like to discuss some open problems in related topics.

Title

On the number of equivalence classes of irreducible integral binary quartic forms with almost prime discriminants

Date

2024.1.17 (Wed)　16:45-17:45 (16:15- tea)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Takashi Taniguchi (Kobe University)

Title

On Floer theory of divisor complement

Date

2024.1.10 (Wed)　16:45-17:45 (16:15- tea)

Place

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

Speaker

Kenji Fukaya (Stony Brook University)

Title

Variational methods to construct special orbits for dynamical systems

Date

2023.12.20 (Wed)　16:45-17:45 (16:15- tea)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Yuika Kajihara (Kyoto University)

Title

On the Stallings theorem

Date

2023.12.13 (Wed)　16:45-17:45 (16:15- tea)

Place

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

Speaker

Yoshikata Kida (The University of Tokyo)

Title

On frequently-visited sites by simple random walk on a regular tree

Date

2023.12.6 (Wed)　16:45-17:45 (16:15- tea)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Yoshihiro Abe (Tohoku University)

Title

Dynamics on complex networks

Date

2023.11.29 (Wed)　16:45-17:45 (16:15- tea)

Place

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

Speaker

Gouhei Tanaka (Nagoya Institute of Technology)

Title

Metric measure spaces and synthetic Ricci bounds: Fundamental concepts and recent developments

Date

2023.11.15 (Wed)　15:15-16:15 　　

Place

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

Speaker

Karl-Theodor Sturm (Bonn Univ.)

Abstract

　Metric measure spaces with synthetic Ricci bounds have attracted great interest in recent years, accompanied by spectacular breakthroughs and deep new insights. In this survey, I will provide a brief introduction to the concept of lower Ricci bounds as introduced by Lott-Villani and myself, and illustrate some of its geometric, analytic, and probabilistic consequences, among them Li-Yau estimates, coupling properties for Brownian motions, sharp functional and isoperimetric inequalities, rigidity results, and structural properties like rectifiability and rectifiability of the boundary. In particular, I will explain its crucial interplay with the heat flow and its link to the curvature-dimension condition formulated in functional-analytic terms by Bakry-\'Emery. This equivalence between the Lagrangian and the Eulerian approach then will be further explored in various recent research directions: (i) time-dependent Ricci bounds which provide a link to (super-) Ricci flows for singular spaces, (ii) second-order calculus, upper Ricci bounds, and transformation formulas, (iii) distribution-valued Ricci bounds which, e.g., allow singular effects of non-convex boundaries to be taken into account.

Title

Frobenius manifolds and vertex operators

Date

2023.11.15 (Wed)　16:55-17:55 　　

Place

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

Speaker

Todor Milanov (Kavli IPMU)

Abstract

　The problem that I would like to talk about started about 20 years ago when Givental discovered that the Hirota bilinear equations of the KdV hierarchy can be described in terms of the periods of A_1 singularity. Shortly afterwards, myself and Givental were able to prove that the construction can be extended to all simple singularities which gave a description in terms of period integrals of the so-called principal Kac-Wakimoto hierarchies of ADE type. The problem is how far can we go beyond simple singularities or equivalently beyond simple Lie algebras? Can we apply the same ideas to the period integrals appearing in mirror symmetry and construct integrable hierarchies that have applications to enumerative geometry? This question is still not easy to answer but nevertheless there were several interesting developments during the years. I would like to talk about them.

Title

Interplay between ``numerical analysis of differential equations'' and ``data science''

Date

2023.11.8 (Wed)　16:45-17:45 (16:15- tea)

Place

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

Speaker

Yuto Miyatake (Osaka University)

Title

p-adic differential equations and geometricity

Date

2023.11.1 (Wed)　16:45-17:45 (16:15- tea)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Tomoyuki Abe (Kavli IPMU)

Title

Gauge theory on non-compact 4-manifolds and related topics

Date

2023.10.25 (Wed)　16:45-17:45 (16:15- tea)

Place

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

Speaker

Masaki Taniguchi (Kyoto University)

Title

The automorphism groups of C*-algebras from the viewpoint of K-theory

Date

2023.10.18 (Wed)　16:45-17:45 (16:15- tea)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Taro Sogabe (Kyoto University)

Title

Introduction to mean dimension

Date

2023.10.11 (Wed)　16:45-17:45 (16:15- tea)

Place

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

Speaker

Masaki Tsukamoto (Kyoto University)

Title

Constrained optimal stopping under a regime-switching model

Date

2023.7.19 (Wed)　16:45-17:45

Place

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

Speaker

Takuji Arai (Keio University)

Title

Development of the modular representation theory from the symmetric group to cyclotomic quiver Hecke algebras

Date

2023.7.12 (Wed)　16:45-17:45

Place

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

Speaker

Susumu Ariki (Osaka University)

Title

The index theorem of lattice Wilson-Dirac operators via higher index theory

Date

2023.7.5 (Wed)　16:45-17:45

Place

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

Speaker

Yosuke Kubota (Kyoto University)

Title

Trace theorems and related topics on PDE

Date

2023.6.28 (Wed)　16:45-17:45

Place

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

Speaker

Mitsuru Sugimoto (Nagoya University)

Title

Riemann hypothesis for plane curve singularities

Date

2023.6.21 (Wed)　16:45-17:45

Place

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

Speaker

Ivan Cherednik (RIMS, Kyoto University & University of North Carolina at Chapel Hill)

Abstract

　We will extend the Hasse-Weil zeta functions over finite fields F_q to plane curve singularities. There is a direct connection with the compactified Jacobians (from Fundamental Lemma), which will be explained. The functional equation holds for the corresponding L-functions (due to Galkin. 1976), but the Riemann hypothesis requires new approaches. The key is that the motivic superpolynomials (they will be defined) and L-functions depend on q polynomially, which is very different from the smooth case. They are conjectured to be topological invariants of the plane curve singularities. Presumably, the surface singularities related to Seifert 3-folds can result in q-deformations of the Riemann's zeta and the Dirichlet L-functions (if time permits).

Title

Affine quantum groups and quantum Grothendieck rings

Date

2023.6.14 (Wed)　16:45-17:45

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Ryo Fujita (RIMS, Kyoto University)

Title

Locally conjugate Galois sections

Date

2023.6.7 (Wed)　16:45-17:45

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Wojciech Porowski (RIMS, Kyoto University)

Abstract

　Let X be a hyperbolic curve over a number field K and consider the short exact etale homotopy sequence associated to X. When v is a nonarchimedean valuation of K, we say that two splittings of this sequence are locally conjugate at v if their restrictions to a decomposition group of v are conjugate. We introduce the following problem: suppose that two splittings are locally conjugate for a ''large'' set of valuations, can we then deduce that they are locally conjugate for all valuations? In this talk we will discuss a few positive results in this direction.

Title

Tverberg's theorem for cell complexes

Date

2023.5.31 (Wed)　16:45-17:45

Place

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

Speaker

Daisuke Kishimoto (Kyushu University)

Title

Archimedean analog of the Prasad-Takloo-Bighash conjecture

Date

2023.5.24 (Wed)　16:45-17:45

Place

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

Speaker

Miyu Suzuki (Kyoto University)

Title

Noise sensitivity problem for random walks on discrete groups

Date

2023.5.10 (Wed)　16:45-17:45

Place

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

Speaker

Ryokichi Tanaka (Kyoto University)

Title

Motility of microswimmers with perturbation

Date

2023.4.26 (Wed)　16:45-17:45

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Yoshiki Hiruta (RIMS, Kyoto University)

Title

Fukaya category from sheaf theory

Date

2023.4.19 (Wed)　16:45-17:45

Place

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

Speaker

Tatsuki Kuwagaki (Kyoto University)

Title

Sheaves for spacetime

Date

2023.4.12 (Wed)　16:45-17:45

Place

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

Speaker

Pierre Schapira (IMJ-PRG)

Abstract

　We introduce the notion of G-causal manifolds which generalises that of globally hyperbolic manifolds. We prove that on such manifolds the Cauchy problem is globally well-posed for sheaves under suitable microlocal hypotheses. We then apply these results to hyperbolic D-modules and Sato's hyperfunctions.