2013 academic year

No. 5

(This seminar starts at irregular time)

Date: November 29 (Fri) 15:00 - 16:00

Place: B707, Fac. Sci., Hiroshima University

Speaker: Shinsuke IWAO (Aoyama Gakuin University)

Title: Semi-infinite ultradiscrete KdV equation and singular tropical curves

Abstract:

The ultradiscrete integrable system is a dynamical system which is obtained from a discrete integrable system (such as discrete KdV equation) through some limiting procedure called ultrradiscretization. The ultradiscrete system inherits geometric information from the original discrete system. In this talk, I introduce the periodic Box-Ball system, which is the most fundamental ultradiscrete system and its relation to the tropical geometry. I also explain the "singular case" which appears when one changes the periodic boundary condition to the semi-infinite one.

No. 4

Date: November 1 (Fri) 16:30 - 17:30

Place: B707, Fac. Sci., Hiroshima University

Speaker: Yoshihiro SAWANO (Tokyo Metropolitan University)

Title: An introduction to function spaces on Rⁿ

Abstract:

This is a small discussion of function spaces on Rⁿ. The speaker will present a recent result after giving an introduction to function spaces on Rⁿ. The main topic will be decompositon methods of functions.

No. 3

Date: August 2 (Fri) 16:30 - 17:30

Place: B707, Fac. Sci., Hiroshima University

Speaker: Kiyoki TANAKA (Osaka City University)

Title: Toeplitz operators on harmonic Bergman spaces

Abstract:

We denote the harmonic Bergman space by the space of all square-integrable harmonic functions. It is known that the harmonic Bergman space is a reproducing kernel Hilbert space. In this talk, we discuss a representation for harmonic Bergman functions. As an application, we give a condition that the Toeplitz operator on the harmonic Bergman space belongs to the Schatten class.

No. 2

(The room is changed)

Date: July 19 (Fri) 16:00 - 17:30

Place: B701, Fac. Sci., Hiroshima University

Speaker: Hiroaki AIKAWA (Hokkaido University)

Title: Intrinsic ultracontractivity and the boundary Harnack principle --- A unified approach with capacitary width

Abstract:

We study intrinsic ultracontractivity for the semigroup associated with Dirichlet heat kernel. We give a sharp sufficient condition for intrinsic ultracontractivity, valid for arbitrary domains, in terms of capacitary width of sublevel sets of the Green function and the ground state. This condition, together with the Harnack inequality, yields sufficient conditions for intrinsic ultracontractivity of nonsmooth domains. Our approach employs a parabolic box argument, a counterpart of the box argument for the boundary Harnack principle. It enables us to treat intrinsic ultracontractivity and the boundary Harnack principle in parallel.

No. 1

(This seminar starts at irregular time)

Date: June 7 (Fri) 15:00 - 16:00

Place: B707, Fac. Sci., Hiroshima University

Speaker: Takao OHNO (Oita University)

Title: Sobolev's inequality on variable exponent Sobolev spaces

Abstract:

Sobolev's inequality plays a central role in the study of partial differential equations. In the mean time, variable exponent Sobolev spaces have attracted more and more attention, in connection with the study of elasticity. Our aim in this talk is to establish Sobolev's inequality on variable exponent Sobolev spaces. Also, we give recent results on Sobolev's inequality.

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