[geometry-ml:05647] 村瀬元彦先生による講演

[Takuro Mochizuki]

皆様

5月8日と15日に京都大学数理解析研究所110号室において
UC Davisの村瀬元彦先生による講演が行われます。

タイトルとアブストラクトは下記の通りです。
大学院生や意欲的な学部生の方々による御聴講も歓迎いたします。

変更等がある場合はホームページ上で告知いたします。
https://www.kurims.kyoto-u.ac.jp/en/seminar/seminar-takuro-wed.html

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京都大学数理解析研究所
望月拓郎

================================

講演者: Motohico Mulase (UC Davis)
日時: 5月8日 5月15日 10:00--12:00
場所: 数理研本館 110号室
タイトル: Inspirations from Mathematics
Lecture 1: From Zeta(3) to Mirror Symmetry
Lecture 2: Discontinuous and Biholomorphic?

アブストラクト:
These are the lectures aimed at a wider audience, including graduate
students and undergraduate students with a strong curiosity and background
of modern mathematics, to display frontiers of mathematical research in the
scope of "Development in Algebraic Geometry related to Integrable Systems
and Mathematical Physics."

The goal is to present *inspirations from mathematics*. The lectures will
not be anything like "an introduction to xyz" type talks. Key terminologies
may be used even without definition, if it is easily available in books and
trusted online resources (excluding ChatGPT). I will present an inspiration
from mathematics of the past, and inspire the audience toward the frontiers
in mathematics of today by this inspiration as a guide. A large part of the
topics is based on my own research, both current interest and past
accomplishments, but the most recent materials are not mine.

Each talk will be 75-minute long, and open discussions follow after a short
break.

Lecture 1: "From Zeta(3) to Mirror Symmetry"
Wednesday, May 8. 10:00--12:00

Abstract: The Riemann Zeta function is the most mysterious function in
mathematics. This talk focuses on its special values. In the first part, I
will explain my own unexpected encounter with some special values of Zeta.
Topological recursion and moduli spaces of curves are behind the scene,
which gives a new understanding of the Kontsevich proof of the Witten
conjecture. Then I will present recent discoveries associated with Zeta(3)
in the context of algebraic geometry and differential equations. Apéry's
irrationality proof of Zeta(3) is the source of our inspiration. Apéry
discovered a mysterious integer sequence in his proof. Later it was noticed
that these numbers have direct relevance to mirror symmetry of a particular
Fano 3-fold and its mirror Landau-Ginzburg model. I will report what has
been proven in this direction. In the discussion part, I will formulate
what seems to be true. Still we do not know the whole story.

Lecture 2: "Discontinuous and Biholomorphic?"
Wednesday, May 15. 10:00--12:00

Abstract: How can we define a global higher order differential operator on
a compact Riemann surface? This naïve question leads us to encountering the
half-canonical sheaf and the concept of *opers*. They are connections in
holomorphic vector bundles, but form only a very thin slice of the moduli
space of connections. This slice forms a holomorphic Lagrangian subvariety
of the moduli space, which is a holomorphic symplectic manifold. Are there
other Lagrangians in this symplectic space, and if so, can we realize the
moduli space as the total space of an analytic family of disjoint
Lagrangians? This is the Lagrangian foliation conjecture of Carols Simpson.
Very recently, an amazing proof was discovered for the case of SL(2)
connections by a starting postdoctoral scholar. I will present several
exciting moments of discoveries of the key facts appearing in this new
result.


-- 
MOCHIZUKI Takuro <takuro ＠ kurims.kyoto-u.ac.jp>