Title

From frieze patterns to Nichols algebras

Date

2024.8.7 (Wed)　16:45-17:45 (16:15- tea)

Place

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

Speaker

István Heckenberger (University of Marburg)

Abstract

　Frieze patterns are infinite strips of integers with funny periodic patterns, introduced by Coxeter. The aim of the talk is to introduce different aspects of the mathematics of friezes, with special emphasis of their role in the structure theory of Hopf algebras.

Title

Level crossings of Gaussian stationary processes

Date

2024.7.24 (Wed)　16:45-17:45 (16:15- tea)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Ohad Noy Feldheim (Hebrew University of Jerusalem)

Abstract

　Centered Stationary Gaussian Processes (SGPs) are real valued continuous stochastic processes on R^d or Z^d whose marginals are centered normal random variables. Gaussianity occurs when a process is obtained as a sum of many infinitesimal independent contributions, and Stationarity occurs when the phenomenon in question is invariant under translations in time or in space. This makes stationary Gaussian processes an excellent model for stationary noise and random signals, placing them amongst the most well studied stochastic processes.
　Level crossings of SGPs have been extensively studied for several reasons: firstly, as a point process related to particle systems in various media. Secondly, as an instrument for understanding the behaviour of the Gaussian process itself, and finally, due to the fact that many physical processes are closely approximated by a stationary Gaussian processes conditioned not to cross a certain level.
　In this talk we will define SGPs and survey classical and recent results concerning their level crossings, starting from early works in the 1940s by Kac, Rice and Slepian, through works of Dembo and Bryc in early 2000's and ending up with recent state of the art developments obtained with several co-authors. Our journey shall take us through the forming relations between the theory of SGPs and convex geometry, Hilbert spaces and finally -- harmonic analysis. Our focus will be the direction of progress, its interaction with various subfields of analysis and the ultimate goals it pursues.
　No prior knowledge of the subject will be assumed.

Title

On time-fractional partial differential equations and their inverse problems

Date

2024.7.17 (Wed)　16:45-17:45 (16:15- tea)

Place

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

Speaker

Yikan Liu (Kyoto University)

Title

Geometric inequalities and phenomena

Date

2024.7.10 (Wed)　16:45-17:45 (16:15- tea)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Tatsuya Miura (Kyoto University)

Title

Inspirations for Moduli Spaces from Counting Problems

Date

2024.7.3 (Wed)　15:10-16:10 　　

Place

Rm420, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Motohico Mulase (University of California, Davis/RIMS, Kyoto University)

Abstract

　In this talk I will weave a story of a simple counting problem about cell-decompositions of a closed topological surface. Despite the elementary formulation of the problem, the results as concrete formulas exhibit unexpected connections to, and new interpretations of, the topological properties of the moduli stacks of stable algebraic curves. The key idea of proving all these formulas lies in "topological recursion," the Laplace transform of an elementary combinatorial relation. The story spotlights the hidden "spectral curve" and its quantization known as an "oper." Finally we switch to a new, still developing story of the geometry translating Apéry's irrationality proof of $\zeta(3)$. In this new situation, we have an oper and well-understood moduli problem. Yet we do not know what the spectral curve is, which is expected to be the (semi) classical limit of the oper.
　The first part of the talk is based on my joint papers with Olivia Dumitrescu, Bertrand Eynard, Paul Norbury, Sergey Shadrin, Piotr Sułkowski, and others.

Title

The Powell Conjecture for the genus-3 and 4 Heegaard splittings of the 3-sphere

Date

2024.7.3 (Wed)　16:45-17:45 　　

Place

Rm420, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Yuya Koda (Keio University)

Title

Tropical rational function semifields and congruences

Date

2024.6.26 (Wed)　16:45-17:45 (16:15- tea)

Place

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

Speaker

Song, JuAe (Kyoto University)

Abstract

　Since tropical geometry, the main topics of this talk belong to, is an algebraic geometry over a semifield called tropical semifield, we first explain classical algebraic geometry, in particular, the duality of geometry and algebra. Next, we give a brief introduction to tropical geometry. This includes its history, sources, easy examples and important theorems. Then focusing on the tropical version of duality of geometry and algebra, we explain how tropical rational function semifields are well-behaved, i.e., my results on them.

Title

On a discretization of the iterated integral expression of the multiple polylogarithm

Date

2024.6.12 (Wed)　16:45-17:45 (16:15- tea)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Shin-ichiro Seki (Aoyama Gakuin University)

Title

Limit shapes of random Young diagrams and spin representations of symmetric groups

Date

2024.6.5 (Wed)　16:45-17:45 (16:15- tea)

Place

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

Speaker

Sho Matsumoto (Kagoshima University)

Abstract

　The Plancherel measure of the symmetric group gives the most basic random Young diagram. The limit shape of Plancherel Young diagrams is well known as the Logan--Shepp--Vershik--Kerov curve. Philippe Biane obtained results on the derivation of limit shapes using free cumulants for a wider class of random Young diagrams. In this colloquium, Biane's result will be the main focus of the presentation. Furthermore, we touch upon the limit shapes of random Young diagrams determined from spin representations of symmetric groups, obtained in collaboration with Piotr \'Sniady and the speaker.

Title

The study of reduction and finiteness

Date

2024.5.29 (Wed)　16:45-17:45 (16:15- tea)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Teppei Takamatsu (Kyoto University)

Title

Doing algebra with paths in place of equalities

Date

2024.5.22 (Wed)　16:45-17:45 (16:15- tea)

Place

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

Speaker

Yuki Maehara (Kyoto University)

Abstract

　The usual definition of associativity simply states that (ab)c = a(bc)holds for any triple a, b, and c. However, when we use associativity in practice, often our products have more than three factors. When one is working in a context where the natural notion of sameness is not that of equality, this discrepancy becomes a serious issue and one is forced to consider "higher" associativity. (For example, the fundamental group of a topological space enjoys a shadow of this sort of associativity.) In this talk, I will explain how category theory may be used to deal with such "higher" algebra.

Title

Higher-rank skein algebras and quantum cluster algebras

Date

2024.5.15 (Wed)　16:45-17:45 (16:15- tea)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Wataru Yuasa (Kyoto University)

Title

Quasi-F-splitting and birational geometry in positive characteristic

Date

2024.5.8 (Wed)　16:45-17:45 (16:15- tea)

Place

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

Speaker

Tatsuro Kawakami (Kyoto University)

Title

Scheduling recurring tasks

Date

2024.4.24 (Wed)　16:45-17:45 (16:15- tea)

Place

Rm110, Research Institute for Mathematical Sciences, Kyoto University

Speaker

Akitoshi Kawamura (Kyoto University)