[geometry-ml:05749] 「One day workshop on complex and algebraic geometry」7/17 at 東大数理について

[shigeharu takayama]

皆様、

東大数理の高山です。先日お知らせしました研究集会の続報をお知らせします。

集会名：One day workshop on complex and algebraic geometry
日時：2024年7月17日(水）
会場：東京大学（駒場キャンパス）数理科学研究科棟117号室
プログラム：
13:30--14:30 Sai Kee Yeung (Purdue Univ.)
14:50--15:50 井上 瑛二（理研）
16:10--17:10 中村 勇哉（名大）

世話人：權業 善範（東大）、小木曽 啓示（東大）、高山 茂晴（東大）

この集会は次の科研費からの補助を受けています。
基盤研究(A) 20H00116 (代表者: 平地 健吾）
基盤研究(B) 23K20792 (代表者: 高山 茂晴）

---------------　題目、アブストラクト　---------------

Sai Kee Yeung (Purdue Univ.)
Title: Some directions in the study of Torelli map and rigidity
Abstract: The classical Abel-Jacobi map induces the Torelli map from a
moduli space of curves of genus $g\geq 2$ into a corresponding Siegel
modular variety. The goal of the talk is to explain some geometric
problems related to the mapping, focusing on a conjecture of Oort on
scarcity of totally geodesic subvarieties in the Torelli image.  We
will also explain its relation to rigidity in complex geometry,
algebraic geometry and representation theory.

井上 瑛二（理研）
Title: Non-archimedean aspect of Perelman entropy
Abstract: In K\"ahler geometry, there is an inequality between
Perelman entropy and a certain quantity called mu-entropy of test
configurations, which is analogous to Donalson's inequality between
Calabi functional and normalized Donaldson-Futaki invariant. Compared
to Donaldson-Futaki invariant, the mu-entropy reflects richer
information (higher equivariant intersection) of test configuration,
which was the central difficulty of the study. To solve this
difficulty, we introduce a new notion called "distortion". Studying a
non-archimedean potential theoretic aspect of this distortion, we find
a new simple formula of the mu-entropy of test configuration and give
answers to various questions on mu-entropy.

中村 勇哉（名大）
Title: A counterexample to the PIA conjecture
Abstract: In this talk, I will give a counterexample to the PIA
(precise inversion of adjunction) conjecture for MLD's (minimal log
discrepancy). The usual inversion of adjunction is a type of claim
"the information of the singularity of a pair (X,D) can be recovered
from the information of the singularity of D". The precise version
(PIA conjecture) states that this is correct at the level of MLD
(minimal log discrepancy), the invariant of the singularity. The PIA
conjecture is known to be true in dimension 3. In this talk, I will
give a counterexample in dimension 5. I also give a counterexample to
the LSC conjecture for families based on the same example. This talk
is based on joint work with Kohsuke Shibata.