To Japanese version
Record of 2021 April - 2022 March
Date ： 29 May
Place ： Online by Zoom
15:00-16:00
Speaker ： Toru Kajigaya （Tokyo University of Science）
Title : Equivariant realizations of Hermitian symmetric space of noncompact type
Abstract ：
Let M=G/K be a Hermitian symmetric space of noncompact type. We provide
a way of constructing K-equivariant embeddings from M to its tangent space
at the origin by using the polarity of the K-action. As an application,
we reconstruct the
16:15-17:15
Speaker ： Shunsuke Saito （Tokyo University of Science）
Title : On polytopeal sufficient conditions for uniform relative K-polystability
and relative K-instability of polarized toric varieties
Abstract ：
It is well known that there is a one-to-one
correspondence between polarized toric varieties and integral convex polytopes.
Under this correspondence, uniform relative K-polystability/relative
K-instability of varieties can be completely described by polytopes and convex
functions. In this talk, I will introduce a condition of
polytopes that lead to uniform relative K-polystability. I will also explain a
result which is related to the polytopal sufficient condition for relative
K-instability on toric Fano varieties proved by Yotsutani-Zhou.
The contents of the talk are based on a joint
work with Yasufumi Nitta (Tokyo University of Science).
Date ： 24 July
Place ： Online by Zoom
15:00-16:00
Speaker ： Shota Hamanaka （Chuo University）
Title : Closed Ricci flow with integral or pointwise bound of the scalar
curvature
Abstract ：
In this talk,
a closed manifold has a unique short time solution for any initial metric. The
next immediate question is the so-called ``maximal existence time'' for
the Ricci flow with respect to initial metric. Hamilton proved that T <
+∞ is the maximal existence time of a closed Ricci flow
(M, g(t)) (t ∊ [0,T), dim M ≧ 2) if and only if its norm of the Riemannian
curvature tensor is unbounded as $t \rightarrow T$. Therefore a uniform
bound for the norm of the Riemannian curvature tensor on M × [0,T) is enough
to extend the Ricci flow smoothly over T. Moreover, another known such
sufficient conditions to extend the flow smoothly are, for example,
uniformly bound of the norm of the Ricci curvature tensor on M × [0,T)
(by Sesum) or
certain
integral bounds of geometric quantities rather than point-wise one (by Wang).
Di-Matteo
generalized Wang's results using mixed integral norms (i.e., space and time)
which is parametrized by (α, β) ∊ (1, ∞).
In the talk, we will give new extendable result on the closed four dimensional
Ricci flow
under the conditions corresponding to (α, β) = (p, +∞) (p > 2) and (+∞, 1). If there is
time, we also discuss the condition sup_{|R| | x ∊ M × [0,T)} < +∞ (the uniformly bound of
the scalar curvature).
16:15-17:15
Speaker ： Youhei Sakurai （Saitama University）
Title : Liouville theorems for harmonic map heat flow
along ancient super Ricci flow via reduced geometry
Abstract ：
This talk is based on the joint work with Keita Kunikawa (Utsunomiya university).
We have obtained a Liouville theorem for heat equation along ancient super
Ricci flow via Perelman’s reduced geometry. Recently, we generalize the
target spaces, and formulate several Liouville theorems for harmonic map
heat flow. In this talk, I will introduce such Liouville theorems. In our
Liouville theorems, we impose a growth condition concerning Perelman’s
reduced distance. For non-positively curved target spaces, our growth condition
is sharp. On the other hand, for positively curved target spaces, it is
not clear that our growth condition is sharp. However, in the static case,
the growth condition can be improved, which is almost sharp in view of
the example constructed by Schoen-Uhlenbeck. I will discuss the sharpness
in more detail in the talk.
Date ： 28 August
Place ： Online by Zoom
15:00-16:00
Speaker ： Tomoki Fujii （Tokyo Uiniversity of Science）
Title : Graphical translating solitons for the mean curvature flow and isoparametric functions
Abstract ：
In this talk, I will discuss the condition that the graph of a function over a Riemannian
manifold M whose level sets give isoparametric foliation is a translating soliton for the
mean curvature flow.This translating soliton is given as the graph of a function which
is given as a composition of
ordinary differential equation.
explain the classification of the shape of such translating solitons in case where the
Riemannian manifold M is the n-dimensional sphere (n≧2).
16:15-17:15
Speaker ： Takuma Tomihisa （Waseda University）
Title :The Rarita-Schwinger operator and some related topics
Abstract:
The Rarita-Schwinger fields play an important role in physics by describing
the gravitino.
The Rarita-Schwinger
operator is also important to define the Rarita-Schwinger fields.
Recently, in mathematics, there are many researches about the Rarita-Schwinger
operator,
the "spin-3/2 version" of the Dirac operator.
(1) spectra of the Rarita-Schwinger operators on some symmetric spaces
(joint work with
Yasushi Homma),
(2) the Rarita-Schwinger fields on nearly Kähler manifolds (joint work with Soma Ohno).
Date ： 30 October
Place ： Online by Zoom
15:00-16:00
Speaker ： Yuya Takahashi （Nagoya University）
Title : The moduli space of spatial polygons and geometric quantization
Abstract:
The moduli space of spatial polygons is known as a symplectic manifold equipped with both Kahler and real polarizations. In this talk, we will construct morphisms of operads $\mathsf{f}_{Kah}$ and $\mathsf{f}_{re}$ by using the quantum Hilbert spaces $\mathcal{H}_{Kah}$ and $\mathcal{H}_{re}$ associated to the Kahler and real polarizations respectively. Moreover, we will relate the two morphisms $\mathsf{f}_{Kah}$ and $\mathsf{f}_{re}$, and prove the equality
$\dim \mathcal{H}_{Kah} = \dim \mathcal{H}_{re}$ in general setting.
This operadic framework is regarded as a development of the recurrence relation
method by Kamiyama (2000) for proving $\dim\mathcal{H}_{Kah} =
\dim \mathcal{H}_{re}$ in a special case.
16:15-17:15
Speaker ： Kurando Baba （Tokyo University of Science）
Title : Calabi-Yau structure and Bargmann type transformation
on the Cayley projective plane
Abstract:
In this talk, I would like to show the existence of Calabi-Yau structure on the punctured cotangent bundle of the Cayley projective plane, and to construct a Bargmann type transformation between a space of holomorphic functions on the bundle and the L2-space on the Cayley projective space. The transformation gives a quantization of the geodesic flow in terms of one parameter group of elliptic Fourier integral operators. This talk is based on a joint work with Kenro Furutani (Osaka City University Advanced Mathematical Institute) arXiv:2101.07505.
Organizers : Naoyuki Koike, Makiko Tanaka, Akifumi Sako,
Yasufumi Nitta, Kurando Baba, Toru Kajigaya,
Shunsuke Saito，Tsukasa Takeuchi
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