[geometry-ml:05377] 何学セミナー：Brian Harvie 氏, 宇田川 衷 氏

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幾何学分科会メーリングリストの皆様

下記のようにセミナーを開催いたしますのでご案内申し上げます。

場所：早稲田大学 西早稲田キャンパス 51-17-06
日程：２０２３年１０月１８日  (水)（15:30 -16:30)

講演者：Brian Harvie (NCTS, Taiwan)
 題目："A rigidity theorem for asymptotically flat static manifolds and its
applications"
ABSTRACT: In general relativity, many physically and mathematically
important questions concern the uniqueness of the Schwarzschild space. For
example, the black hole uniqueness theorem states that the Schwarzschild
space is the only asymptotically flat static manifold with stable minimal
surface boundary, and similar uniqueness questions for photon surfaces and
for static metric extensions have generated great interest recently. In
this talk, I will present a new approach to these questions that is based
on a recently-discovered Minkowski-type inequality for asymptotically flat
static manifolds. In recent joint work with Prof. Ye-Kai Wang of NYCU, we
prove that the only manifolds which achieve equality within the static
Minkowski inequality are pieces of Schwarzschild space. Using this, we
establish several new uniqueness theorems for Schwarzschild. Notably, we
confirm the uniqueness of static metric extensions for Schwarzschild
coordinate spheres in all dimensions, a question which was motivated by R.
Bartnik's proposed definition for the mass of compact Riemannian manifolds.
I will assume some knowledge of Riemannian geometry for this talk, but
prior knowledge of general relativity is not required.

場所：早稲田大学 西早稲田キャンパス 51-17-06
日程：２０２３年１０月２５日  （水）（15:30 -16:30)

講演者：Tadashi Udagawa (Waseda University)
 題目："Solutions of the tt*-equations constructed from the (SU_2)_k-fusion
ring, and Smyth potentials"
ABSTRACT: Cecotti and Vafa introduced the tt*
equations(topological-antitopological fusion equations), whose solutions
describe massive deformations of supersymmetric conformal field theories.
>From a mathematical point of view, the tt* equations give examples of
pluriharmonic maps into the symmetric space GL_n(R)/O_n. As a special case,
the tt*-equations include the sinh-Gordon equation, and more generally the
tt*-Toda equations which were studied by Guest, Its, and Lin. In this talk,
we consider another series of examples. Solutions are constructed directly
from a finite number of solutions to the radial sinh-Gordon equation, but
the construction itself is quite different from the case of the tt*-Toda
equations. It involves the (SU_2)_k-fusion algebra, an object which has a
prominent role in conformal field theory. The idea of the construction is
due to Cecotti and Vafa, but we give a precise mathematical formulation and
a description of the “holomorphic data” corresponding to the solutions by
using the DPW method. Furthermore, we show that a natural equivalence
relation on the representations of SU_2 corresponds to an equally natural
notion of gauge equivalence on harmonic maps.

皆様のご参加をお待ち申し上げます。

世話人
Martin Guest

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