Titles and Abstracts

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March 15 (Sun)

Yoshitsugu Takei (Doshisha University) 14:00-15:00 pm

Title: Toward the exact WKB analysis for difference equations

Abstract: The exact WKB analysis, that is, the analysis using Borel resummed WKB solutions, is very successful for differential equations with a large parameter. For example, global behavior of solutions (such as the monodromy group) of second-order Fuchsian equations can be computed through the exact WKB analysis. In this talk we discuss its extension to difference equations with a small shift operator. After discussing several typical examples of difference equations from the viewpoint of the exact WKB analysis, we try to construct a general framework of the exact WKB analysis for difference equations. To this end, a new kinf of turning points called logarithmic turning points will play an important role.

Masahiko Yoshinaga (The University of Osaka)  15:30 -16:30 pm

Title: Magnitude of finite metric spaces

Abstract: Magnitude is an invariant of metric spaces introduced by Leinster around 2013 which is considered to be the ”effective number of points in the spaec”. We discuss basic properties and behaviour of magnitudes for Gromov-Hausdorff limits (based on joint works with E. Roff and H. Katsumasa).

March 16 (Mon)

Ryo Namba (RIKEN)  10:00-11:00 am

Title: Application of exact WKB analysis in the context of cosmology

Abstract:  The exact WKB analysis, based on the Borel sum of the WKB infinite series, has been found useful to handle several classes of problems in physics. In this talk, I focus on its application to perturbations around curved spacetime backgrounds - in particular, black hole perturbations, i.e. boundary value problems in spherically symmetric

spacetime, and cosmological particle production, i.e. initial condition problems in time-dependent background.

Hideyuki Ishi (Osaka Metropolitan University)  11:15 -12:15  am

Title: Generalized highest weight unitary representations of solvable Lie groups

Abstract:  In 1985, Kac and Jakobsen introduced a notion of unitarizable highest weight representations for a general Lie algebra which is not necessarily reductive. In my talk, we shall consider unitary representations of finite dimensional real Lie groups whose differential representations are highest weight representations in this generalized sense. Especially, we consider the case that the Lie group is split solvable. We show that such unitary representations are realized on reproducing kernel Hilbert spaces of holomorphic functions over a complex submanifold of the Siegel-Jacobi domain.

Hirotaka Hayashi (Tokai University)  14:00 -15:00 pm

Title: More on Higgsing of D-type conformal matter from web diagrams

Abstract:  We revisit Higgsing of D-type conformal matter theories compactified on a circle from web diagrams with trivalent gluing. We argue that the Higgsing yields a web diagram for the 5d theory which arises from a circle compactification of the 6d SO(12) gauge theory with half-hypermultiplets in two different spinor representations and also web diagrams for the 5d theories arising from a twisted compactification of the 6d SO(12)/SO(11) gauge theories with spinor matter. The web diagrams also characterize the dual geometries associated with the 5d theories and capture information of the dual geometries as well as the 5d theories.

Yoshimichi Ueda (Nagoya University)   15:30 -16:30  pm

Title:Free product von Neumann algebras

Abstract: The concept of free product for von Neumann algebras was introduced in the 70s, but its detailed study was started after the introduction of random matrix technique into the so-called free probability theory initiated by Dan Voiculescu. Recently, free product von Neumann algebras emerge even in some studies on black holes, a bit surprise to us. We will summarize all the known general results on free product von Neumann algebras. A large part of those results are due to my works during 2010-2015. A very brief overview of free probability theory will be included in the talk too. This overview part may contain my on-going work.

March 17 (Tue)

Akihito Hora (Hokkaido University) 10:00-11:00 am

Title: Dynamical limit shape of random multi-diagrams, representations of wreath products and free probability

Abstract:  As a topic in asymptotic representation theory, I will talk about an evolutional model for limit shapes of random multi-diagrams. In our model, multi-diagrams interchange their boxes at random while they grow as a whole. The randomness originates from the branching rule for a tower of wreath product groups. Considering appropriate space-time scaling limit for the resulting stochastic process on the set of multi-diagrams, we intend to describe the most likely deterministic shape at each macroscopic time and observe its time evolution. In order to characterize the limiting pictures, we use tools in free probability theory.

Toshifumi Noumi (The University of Tokyo)  11:15- 12:15am

Title: Cosmology Meets Hypergeometric Functions at the Cosmological Collider

Abstract: 　Cosmic inflation, an epoch of accelerated expansion in the early universe, offers a unique opportunity to probe ultra-high energy physics beyond the reach of ground-based experiments. In the so-called cosmological collider program, we physicists study signatures of such high energy physics in cosmological correlators (correlation functions of quantum fluctuations generated during inflation), which typically take the form of multivariable hypergeometric functions. In this talk, I will review recent developments in the cosmological collider program and discuss future directions, with mathematicians in mind.