これまでのセミナー (2020年度)

2020年度 第４回セミナー

題目：On the KPZ fixed point in discrete time TASEPs

講師：新井 裕太 氏（千葉大学）

場所：オンラインセミナー

日時：2020年12月2日（水）17時10分‐18時40分

概要：The totally asymmetric simple exclusion process (TASEP) is one of the simplest interacting stochastic particle system and can be interpreted as a stochastic growth model of an interface, which turns out to belong to the Kardar-Parisi-Zhang (KPZ) universality class. In this talk we consider two versions of TASEPs with geometric and Bernoulli hopping probabilities. In these processes, we obtain a single Fredholm determinant representation for the joint distribution function of particle positions with arbitrary initial data. Using this, we show that in the KPZ 1:2:3 scaling limit, the distribution function converges to the one describing the KPZ fixed point was introduced by Mateski, Quastel and Remenik (2017). This talk is based on the paper DOI:10.1088/1751-8121/aba213.

2020年度 第３回セミナー

題目：Quenched free energy in random matrix model

講師：奥山 和美 氏（信州大学）

場所：オンラインセミナー

日時：2020年11月20日（金）17時10分‐18時40分

概要：We compute the quenched free energy in the Gaussian random matrix model by directly evaluating the matrix integral without using the replica trick.

We find that the quenched free energy is a monotonic function of the temperature and the entropy approaches log N at high temperature and vanishes at zero temperature.

This talk is based on [arxiv:1903.11776] and [arxiv:2009.02840].

2020年度 第２回セミナー

題目：Recent progress on representation theory of i-quantum groups

講師：渡邉英也氏（京大数理研）

場所：オンラインセミナー

日時：2020年10月28日（水）17時10分‐18時40分

概要：i-quantum groups are certain coideal subalgebras of Drinfeld-Jimbo quantum groups appearing in the theory of quantum symmetric pairs. Typical examples of them are generalized q-Onsager algebras. i-quantum groups can be thought of as generalizations of quantum groups. In fact, many facts concerning quantum groups have been generalized to i-quantum groups setting. As a result, i-quantum groups are known or conjectured to play important roles in various branches of mathematics and physics such as harmonic analysis, knot theory, and integrable systems. In this talk, I will review fundamental results about i-quantum groups, and discuss representation theory of them.

2020年度 第１回セミナー

題目：Nonperturbative anomaly inflow for fermions and p-form fields

講師：米倉和也氏（東北大学）

場所：オンラインセミナー

日時：2020年9月30日（水）17時10分‐18時40分

概要：I will talk about a nonperturbative formulation of chiral fermions and chiral (self-dual) p-form fields, in terms of massive theories in one-higher dimensions. The introduction of the higher dimensional bulk is unavoidable due to the existence of anomalies, and I discuss the modern understanding of anomalies which appears very naturally in our formulation of chiral theories.