Tomohiro Sasamoto（Tokyo Institute of Technology） 

Determinantal formulas for KardarParisiZhang models 
17：0018：30, January 31 (Thu), 2019 
Room B314, Faculty of Science 

Abstract: 



The KardarParisiZhang (KPZ) equation, is a stochastic partial
differential equation, introduced in 1986 to explain behaviors
of surface growth. Large scale behaviors of its solution are
universal and shared by various systems, constituting the KPZ
universality class.
A class of models in the KPZ class have turned out to be integrable
and admit determinantal formulas, from which one can establish the
limiting universal laws of fluctuations, typically given by
the TracyWidom distributions.
In this presentation, after a brief review on the basics about the
KPZ equation, we introduce several models in the KPZ class and explain
how the determinantal formulas are obtained for these models. In particular
we will see that our approach of using Ramanujan’s bilateral sum and
Frobenius determinant proposed in [1,2] can be applied to many models
in a unified fashion.
The talk is based on joint works with M. Mucciconi and T. Imamura.
The talk will be in Japanese (slides will be prepared in English).
References:
[1]T. Imamura and T. Sasamoto, Fluctuations for stationary qTASEP,
arXiv:1701.05991, to appear in Prob. Th. Rel. Fields.
[2]M. Mucciconi, T. Imamura and T. Sasamoto, Stationary Stochastic Higher
Spin Six Vertex Model and qWhittaker measure, in preparation.


Anton Zabrodin (National Research University Higher School of Economics
) 

Elliptic solutions to BKP equation and manybody systems 
17：0018：30, February 5 (Tue), 2019 
Room B314, Faculty of Science 

Abstract: 



We derive equations of motion for poles of doubleperiodic (elliptic)
solutions to the BKP equation. The basic tool is the auxiliary linear
problem for the wave function.
The result is a new manybody dynamical system with threebody interaction
expressed through the Weierstrass elliptic function. This system does not
admit Lax representation but, instead, it is equivalent to a sort of
Manakov's triple equation with a spectral parameter.
We also discuss integrals of motion which follow from the equation of
the spectral curve and analyze analytic properties of the wave function on
the spectral curve. 

Akane Nakamura（Josai University） 

Recovering linear from nonlinear 
17：0018：30, February 14 (Thu), 2019 
Room B301, Faculty of Science 

Abstract: 



One of the important aspects of the integrable systems is that these
nonlinear systems possess linear problems. However, it is not easy to find
a linear problem (Lax equation) just by looking at the nonlinear equations.
In this talk, we will explain a way to recover a linear problem from the
nonlinear autonomous 4dimensional Painlevétype systems (the Hitchin
systems).
Our way is to compare generic degenerations of the families of curves arising
from the nonlinear problem (i.e., the boundary divisors adjoined in the
compactification of the Liouville tori) and curves appearing in the linear
side (the spectral curves). We have proved that the Jacobian of generic curve
of these systems has unique principal polarization, so that we can recover
curves.
This talk is based on joint work with Eric Rains.
