## 今後の予定

### 2019年10月21日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室

Canonical almost complex structures on ACH Einstein manifolds
[ 講演概要 ]
Einstein ACH (asymptotically complex hyperbolic) manifolds are seen as a device that establishes a correspondence between CR geometry on the boundary and Riemannian geometry in “the bulk.” This talk concerns an idea of enriching the geometric structure of the bulk by adding some almost complex structure compatible with the metric. I will introduce an energy functional of almost complex structures and discuss an existence result of critical points when the given ACH Einstein metric is a small perturbation of the Cheng-Yau complete K?hler-Einstein metric on a bounded strictly pseudoconvex domain. The renormalized Chern-Gauss-Bonnet formula is also planned to be discussed.

### 2019年10月23日(水)

#### Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室
Clemens Weiske 氏 (Aarhus University)
Symmetry breaking and unitary branching laws for finite-multiplicity pairs of rank one (English)
[ 講演概要 ]
Let (G,G’) be a real reductive finite multiplicity pair of rank one, i.e. a rank one real reductive group G with reductive subgroup G’, such that the space of symmetry breaking operators (SBOs) between all (smooth admissible) irreducible representations is finite dimensional.

We give a classification of SBOs between spherical principal series representations of G and G’, essentially generalizing the results on (O(1,n+1),O(1,n)) of Kobayashi—Speh (2015). Moreover we show how to decompose unitary representations occurring in (not necessarily) spherical principal series representations of G in terms of unitary G’ representations, by making use of the knowledge gathered in the classification of the SBOs and the structure of the open P’orbit in G/P as a homogenous G’-space, where P’ is a minimal parabolic in G’ and P is a minimal parabolic in G. This includes the construction of discrete spectra in the restriction of complementary series representations and unitarizable composition factors.

### 2019年10月24日(木)

#### FMSPレクチャーズ

13:00-15:05   数理科学研究科棟(駒場) 002号室

Chung-jun Tsai 氏 (National Taiwan University)
Topic on minimal submanifolds (5/6) (ENGLISH)
[ 講演概要 ]
The main theme of these lectures will be theory about minimal submanifolds, which are higher dimensional generalizations of geodesics. A naive motivation is that one tries to understand the geometry from its special submanifolds (minimal, etc.).

For minimal submanifolds, the equations are no longer ODEs, but elliptic PDEs. This increases the difficulties. The study are very good examples for the application of methods from PDEs and calculus of variations. We will try to explain some important results in this theory, which stimulate many of the researches today.

Here are some specific materials we plan to cover: Simon’s work based on the second variational formula, Sacks - Uhlenback theorem on the existence of minimal 2-spheres, the theory of stable minimal hypersurfaces by Schoen-Simon-Yau.

#### 基礎論セミナー

13:30-15:00   数理科学研究科棟(駒場) 156号室

[ 講演概要 ]

$T + \varphi \vdash \psi$ ならば $T \vdash \psi$ が成立することをいう.
1979 年 Guaspari は複数の理論に対して,

その一般的な状況を解明するという問いを残していた.
この問いに対し, 1986年 Bennet は特に2つの理論に対する分析を行い,

この Bennet の結果は任意有限個の理論に拡張可能であることが判明した.

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 128号室
オム　ジュンヨン 氏 (東京大学)

[ 講演概要 ]

### 2019年10月25日(金)

#### 談話会・数理科学講演会

15:30-16:30   数理科学研究科棟(駒場) 123号室
Yves Benoist 氏 ( CNRS, Paris-Sud)
Arithmeticity of discrete subgroups (英語)
[ 講演概要 ]
By a theorem of Borel and Harish-Chandra,
an arithmetic group in a semisimple Lie group is a lattice.
Conversely, by a celebrated theorem of Margulis,
in a higher rank semisimple Lie group G
any irreducible lattice is an arithmetic group.

The aim of this lecture is to survey an
arithmeticity criterium for discrete subgroups
which are not assumed to be lattices.
This criterium, obtained with Miquel,
generalizes works of Selberg and Hee Oh
and solves a conjecture of Margulis. It says:
a discrete irreducible Zariski-dense subgroup
of G that intersects cocompactly at least one
horospherical subgroup of G is an arithmetic group.

### 2019年10月28日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室

On Kiyoshi Oka's unpublished papers 1943 (Japanese)
[ 講演概要 ]
いわゆる岡の解決した不分岐リーマン領域に対する3大問題(Oka IX, 1953)は、実はこの未発表論文(VII～XI)で終わっている。　Oka　VII、VIIIで示された連接性、不定域イデアルの理論はこれ等を、分岐リーマン領域へ確立しようとする試みより生まれたことが、この未発表論文から明らかになる。この講演では、この未発表論文で擬凸問題がどのように解決されたかを紹介する。 分岐リーマン領域の場合の擬凸問題は、Fornaessによる反例が与えられたとはいえ、情況は不明で未解決問題として今も残っている（岡の夢）ことにも言及したい。

### 2019年10月29日(火)

#### トポロジー火曜セミナー

17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
Chung-Jun Tsai 氏 (National Taiwan University)
Strong stability of minimal submanifolds (ENGLISH)
[ 講演概要 ]
It is well known that the distance function to a totally geodesic submanifold of a negatively curved ambient manifold is a convex function. One can identify a strong stability condition on minimal submanifolds that generalizes the above scenario. Besides a strong local uniqueness property, a strongly stable minimal submanifold is also Lipschitz stable under the mean curvature flow. We will also discuss some famous local (complete, non-compact) models. This is based on a joint work with Mu-Tao Wang.

### 2019年10月31日(木)

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 128 (TBD)号室
Marius Ghergu 氏 (University College Dublin)
Behaviour around the isolated singularity for solutions of some nonlinear elliptic inequalities and systems (English)
[ 講演概要 ]
We present some results on the behaviour around the isolated singularity for solutions of nonlinear elliptic inequalities driven by the Laplace operator. We derive optimal conditions that imply either a blow-up or the existence of pointwise bounds for solutions. We obtain that whenever a pointwise bound exists, then an optimal bound is given by the fundamental solution of the Laplace operator. This situation changes in case of systems of inequalities where other types of optimal bounds may occur. The approach relies on integral representation of solutions combined with various nonlinear potential estimates. Further extensions to the parabolic case will be presented. This talk is based on joint works with S. Taliaferro (Texas A&M University) and I. Verbitsky (Missouri University).

#### FMSPレクチャーズ

13:00-15:05   数理科学研究科棟(駒場) 002号室

Chung-jun Tsai 氏 (National Taiwan University)
Topic on minimal submanifolds (6/6) (ENGLISH)
[ 講演概要 ]
The main theme of these lectures will be theory about minimal submanifolds, which are higher dimensional generalizations of geodesics. A naive motivation is that one tries to understand the geometry from its special submanifolds (minimal, etc.).

For minimal submanifolds, the equations are no longer ODEs, but elliptic PDEs. This increases the difficulties. The study are very good examples for the application of methods from PDEs and calculus of variations. We will try to explain some important results in this theory, which stimulate many of the researches today.

Here are some specific materials we plan to cover: Simon’s work based on the second variational formula, Sacks - Uhlenback theorem on the existence of minimal 2-spheres, the theory of stable minimal hypersurfaces by Schoen-Simon-Yau.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Tsai.pdf

#### 情報数学セミナー

16:50-18:35   数理科学研究科棟(駒場) 122号室

[ 講演概要 ]

4回構成の本講義ではまず1回目に量子計算の基礎的な枠組みを学んだ後、2,3回目でNISQアルゴリズムとして有望視される量子化学計算と機械学習への量子計算機の応用についてそれぞれ解説し、4回目に量子誤り訂正について解説を行う。

### 2019年11月05日(火)

#### トポロジー火曜セミナー

17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00

Magnitude homology of geodesic space (JAPANESE)
[ 講演概要 ]
Magnitude is an invariant which counts `effective number of points' on a metric space. Its categorification is magnitude homology. This notion is first formulated for metric spaces associated to simple graphs by Hepworth and Willerton, and then for any metric spaces by Leinster and Shulman. The definition of the magnitude homology is easy, but its calculation is rather difficult. For example, the magnitude homology of the circle with geodesic metric was known partially. In my talk, I will explain my result that fully determines the magnitude homology of any geodesic metric space subject to a certain non-branching assumption. In this result, the magnitude homology is described in terms of geodesics. Complete and connected Riemannian manifolds are examples of the geodesic metric spaces satisfying the assumption.

### 2019年11月08日(金)

#### 談話会・数理科学講演会

15:30-16:30   数理科学研究科棟(駒場) 056号室

モチーフ理論と分岐理論への応用 (日本語)
[ 講演概要 ]
モチーフ理論とは，代数多様体の普遍的コホモロジー理論の構成を目的とする理論である．
すでに1970年代にGrothendieckがさまざまなコホモロジー理論の背後に潜むものとしてその存在を予見し，1980年にBeilinsonがそれを正確に定式化し予想として提出した．
それ以来、モチーフ理論は哲学的指導原理として多くの優れた研究を導びきつつ発展してきた．

しかし一般の場合のモチーフ理論の構成(Beilinson予想)は未解決である．

### 2019年11月18日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室

### 2019年11月19日(火)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
Peter Topping 氏 (University of Warwick)
Starting Ricci flow with rough initial data (English)
[ 講演概要 ]
Ricci flow is a nonlinear PDE that is traditionally used to deform a manifold we would like to understand into a manifold we already understand. For example, Hamilton showed that a simply connected closed 3-manifold with positive Ricci curvature is deformed into a manifold of constant sectional curvature, thus allowing us to identify it as topologically a sphere.
In this talk we take a look at a different use of Ricci flow. We would like to exploit the regularising effect of parabolic PDE to turn a rough space into a smooth space by running the Ricci flow. In practice, this revolves around proving good a priori estimates on solutions, and taking unorthodox approaches to solving parabolic PDE. We will see some theory, first in 2D, then in higher dimension, and some applications.

### 2019年11月20日(水)

#### 代数学コロキウム

18:00-19:00   数理科学研究科棟(駒場) 056号室
Vasudevan Srinivas 氏 (Tata Institute of Fundamental Research)
Algebraic versus topological entropy for surfaces over finite fields (ENGLISH)
[ 講演概要 ]
For an automorphism of an algebraic variety, we consider some properties of eigenvalues of the induced linear transformation on l-adic cohomology, motivated by some results from complex dynamics, related to the notion of entropy. This is a report on joint work with Hélène Esnault, and some subsequent work of K. Shuddhodan.

（本講演は「東京北京パリ数論幾何セミナー」として，インターネットによる東大数理，Morningside Center of Mathematics と IHES の双方向同時中継で行います．今回は東京からの中継です．）

### 2019年11月27日(水)

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 126号室

The homotopy groups of the automorphism groups of Cuntz-Toeplitz algebras

### 2019年12月02日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室