2014-1 Blog Entry List


日  時: 2月18日(火)15時30分~17時00分

講 演 者: Elmar Schrohe 氏 (Leibniz Universit\"at Hannover)

題  目: Solvability of a Degenerate Boundary Value Problem

要  旨: Following work of K.\ Taira we consider the boundary value problem
$$Au=f\text{ in } X,\qquad Lu=g \text{ on }\partial X,$$
where $X$ is a compact manifold with boundary,
$A$ is a strongly elliptic second order operator which in local coordinates is of the form
$$A=\sum_{jk}a^{jk}\partial_{x_j}\partial_{x_k}+\sum b^j\partial_{x_j} + c$$
with real coefficients $a^{jk}=a^{jk}, b^j,c$ in the Htlder class $C^\tau$, $\tau>2$.
We require that
$\sum a^{jk}\xi_j\xi_k\ge \alpha |\xi|^2$ for some $\alpha>0$ and  $0\not\equiv c\le0$.

The  boundary condition $L$ is assumed to be of the form
$$Lu = \mu_0\gamma_0u + \mu_1\gamma_1u,$$
where $\gamma_0$ is the evaluation map at the boundary
and $\gamma_1$ is the evaluation of the exterior normal derivative at the boundary.
The $C^\tau$-functions $\mu_0$ and $\mu_1$ on $\partial X$
are supposed to be nonnegative with $\mu_0+\mu_1$ strictly positive everywhere.

Using the calculus of pseudodifferential operators with symbols of limited regularity
we then show the solvability of the boundary value problem
in various classes of Sobolev and Zygmund spaces with regularity
depending on the smoothness $\tau$ of the coefficients.
We also study the resolvent in suitable sectors of the complex plane.

\hfill (joint work with M. Hassan Zadeh)

【 場所 】 自然学系D棟 509教室

Tsukuba Mini-Workshop on Hopf Algebras (2月17日)

日時: 2月17日(月) 10:30-18:00
場所: 自然系学系棟 D509 セミナー室

10:30-12:00  津野 祐司 (千葉工大)
                   Galois objects and cleft objects for free Hopf algebras
13:30-15:00  増岡 彰 (筑波大)
                   Cleftness results on universal quantum groups
15:15-18:00  ディスカッション

世話人  増岡 彰


科目名:代数学特論Ⅱ (1単位)
講師:鈴木武史 氏 (岡山大学大学院自然科学研究科・准教授)

日程:2月17日(月) 10:00~
     2月18日(火) 未定 当日決定
     2月19日(水) 未定 当日決定
     2月20日(木) 未定 当日決定



Tsukuba Workshop for Young Mathematicians (Feb 13-14)

Tsukuba Workshop for Young Mathematicians started in 2008 and has been held annually in Tsukuba. This workshop is organized with the aim of promoting communication and networking among young mathematicians, especially the graduate students studying at Asian universities.

Date: February 13 (Thu) - 14 (Fri), 2014
Place: The Tsukuba Center for Institutes
Address: 2-20-5 Takezono, Tsukuba, Ibaraki 305-0032, JAPAN


Satellite Seminar to Tsukuba Workshop for Young Mathematicians
講演者:Prof.Wang Qing(Xiamen University)

日時:2月12日(水) 16:00~17:00
場所:自然系学系棟 D814 セミナー室

タイトル:Module categories for toroidal Lie algebra

Abstract  In this talk,I will present some recent work on toroidal Lie algebra. We use basic formal variable techniques to study certain categories of modules for the toroidal Lie algebra τ. More specifically,we define and study two categories ετ and cτ of τ-modules using generating functions,where ετ is proved to contain the evaluation modules while cτ contains certain restricted τ-modules,the evaluation modules,and their tensor product modules. Furthermore,we classify the irreducible integrable modules in categories ετ and cτ. This is a joint work with Hongyan Guo and Shaobin Tan.