## 今後の予定

### 2017年10月24日(火)

#### 諸分野のための数学研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
Christian Klingenberg 氏 (Würzburg University)
The initial value problem for the multidimensional system of gas dynamics may have infinitely many weak solutions (English)
[ 講演概要 ]
We consider the isentropic compressible Euler equations in two space dimensions together with particular initial data. This data consists of two constant states only, where one state lies on the lower and the other state on the upper half plane. The aim is to investigate if there exists a unique entropy solution or if the convex integration method produces infinitely many entropy solutions. In this lecture we will show that the solution of this Riemann problem for the 2-d isentropic Euler equations is non-unique (except if the solution is smooth). Next we are able to show that there exist Lipschitz data that may lead to infinitely many solutions even for the full system of Euler equations. This is joint work with Simon Markfelder.

#### トポロジー火曜セミナー

17:30-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 17:00-17:30, Lie群論・表現論セミナーと合同

ラグランジュ交叉のフレアホモロジーに対する部分多様体論からのアプローチ (JAPANESE)
[ 講演概要 ]

#### Lie群論・表現論セミナー

17:30-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 17:00-17:30, トポロジー火曜セミナーと合同

ラグランジュ交叉のフレアホモロジーに対する部分多様体論からのアプローチ (JAPANESE)
[ 講演概要 ]

### 2017年10月25日(水)

#### 講演会

11:00-12:00   数理科学研究科棟(駒場) 128号室
Ahmed Abbes 氏 (CNRS/IHES)
On Faltings' main comparison theorem in p-adic Hodge theory : the relative case (ENGLISH)
[ 講演概要 ]
In the appendix of his 2002 Asterisque article, Faltings roughly sketched a proof of a relative version of his main comparison theorem in p-adic Hodge theory. I will briefly review the absolute case and then explain some of the key new inputs for the proof of the relative case (joint work with Michel Gros).

### 2017年10月30日(月)

#### 東京確率論セミナー

16:00-17:30   数理科学研究科棟(駒場) 128号室

Integration of controlled rough paths via fractional calculus (JAPANESE)
[ 講演概要 ]

#### 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 bicategory of $W^*$-bimodules

#### 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

Odd dimensional complex analytic Kleinian groups
[ 講演概要 ]
In this talk, I would explain an idea to construct a higher dimensional analogue of the classical Kleinian group theory. For a group $G$ of a certain class of discrete subgroups of $\mathrm{PGL}(2n+2,\mathbf{C})$ which act on $\mathbf{P}^{2n+1}$, there is a canonical way to define the region of discontinuity, on which $G$ acts properly discontinuously. General principle in the discussion is to regard $\mathbf{P}^{n}$ in $\mathbf{P}^{2n+1}$ as a single point. We can consider the quotient space of the discontinuity region by the action of $G$. Though the Ahlfors finiteness theorem is hopeless because of a counter example, the Klein combination theorem and the handle attachment can be defined similarly. Any compact quotients which appear here are non-Kaehler. In the case $n=1$, we explain a new example of compact quotients which is related to a classical Kleinian group.

#### 代数幾何学セミナー

10:30-12:00   数理科学研究科棟(駒場) 123号室
Roberto Svaldi 氏 (Cambridge)
Towards birational boundedness of elliptic Calabi-Yau varieties (English)
[ 講演概要 ]
I will discuss new results towards the birational boundedness of
low-dimensional elliptic Calabi-Yau varieties, joint work with Gabriele
Di Certo.
Recent work in the minimal model program suggests that pairs with trivial log canonical
class should satisfy some boundedness properties.
I will show that 4-dimensional Calabi-Yau pairs which are not birational to a product are
indeed log birationally bounded. This implies birational boundedness of elliptically fibered
Calabi-Yau manifolds with a section, in dimension up to 5.
If time allows, I will also try to discuss a first approach towards boundedness of rationally
connected CY varieties in low dimension.

### 2017年10月31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
Yash Lodha 氏 (École Polytechnique Fédérale de Lausanne)
Nonamenable groups of piecewise projective homeomorphisms (ENGLISH)
[ 講演概要 ]
Groups of piecewise projective homeomorphisms provide elegant examples of groups that are non amenable, yet do not contain non abelian free subgroups. In this talk I will present a survey of these groups and discuss their striking properties. I will discuss properties such as (non)amenability, finiteness properties, normal subgroup structure, actions by various degrees of regularity and Tarski numbers.

#### 代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 122号室
Zhan Li 氏 (Beijing)
ACC for log canonical threshold polytopes (English)
[ 講演概要 ]
We show that the log canonical threshold polytopes of varieties with log canonical singularities satisfy the ascending chain condition. This is a joint work with Jingjun Han and Lu Qi.

#### 離散数理モデリングセミナー

17:00-18:00   数理科学研究科棟(駒場) 126号室
Basile Grammaticos 氏 (Université de Paris VII・XI)
The end of the World (ENGLISH)
[ 講演概要 ]
This is not a seminar on astrophysics or cosmology. I am not going to talk about something that will happen in billions of years. I will rather explain the menace to our civilisation and to the human species. Inspired from the works of several authors I will explain the existing risks. I will also present mathematical models which show that a general collapse is possible in the decades that follow.

#### 離散数理モデリングセミナー

16:00-17:00   数理科学研究科棟(駒場) 126号室
Fon-Che Liu 氏 (National Taiwan University)
TBA
[ 講演概要 ]
A tutorial talk on real analysis is presented. Details will be announced soon.

### 2017年11月01日(水)

#### 離散数理モデリングセミナー

17:00-18:00   数理科学研究科棟(駒場) 056号室
Basile Grammaticos 氏 (Université de Paris VII・XI)
Discrete Painlevé equations associated with the E8 group (ENGLISH)
[ 講演概要 ]
I'll present a summary of the results of the Paris-Tokyo-Pondicherry group on equations associated with the affine Weyl group E8. I shall review the various parametrisations of the E8-related equations, introducing the trihomographic representation and the ancillary variable. Several examples of E8-associated equations will be given including what we believe is the simplest form for the generic elliptic discrete Painlevé equation.

### 2017年11月02日(木)

#### 統計数学セミナー

14:00-15:10   数理科学研究科棟(駒場) 052号室
Tudor Ciprian 氏 (Université Lille 1)
Hermite processes and sheets
[ 講演概要 ]
The Hermite process of order $\geq 1$ is a self-similar stochastic process with stationary increments living in the $q$th Wiener chaos. The class of Hermite processes includes the fractional Brownian motion (for $q=1$) and the Rosenblatt process (for $q=2$). We present the basic properties of these processes and we introduce their multiparameter version. We also discuss the behavior with respect to the self-similarity index and the possibility so solve stochastic equations with Hermite noise.

### 2017年11月07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

On an explicit example of topologically protected corner states (JAPANESE)
[ 講演概要 ]
In condensed matter physics, topologically protected (codimension-one) edge states are known to appear on the surface of some insulators reflecting some topology of its bulk. Such phenomena can be understood from the point of view of an index theory associated to the Toeplitz extension and are called the bulk-edge correspondence. In this talk, we consider instead the quarter-plane Toeplitz extension and index theory associated with it. As a result, we show that topologically protected (codimension-two) corner states appear reflecting some topology of the gapped bulk and two edges. Such new topological phases can be obtained by taking a product’’ of two classically known topological phases (2d type A and 1d type AIII topological phases). By using this construction, we obtain an example of a continuous family of bounded self-adjoint Fredholm quarter-plane Toeplitz operators whose spectral flow is nontrivial, which gives an explicit example of topologically protected corner states.

#### 代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 122号室

TBA (JAPANESE or ENGLISH)
[ 講演概要 ]
TBA

### 2017年11月08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
Xin Wan 氏 (Morningside Center for Mathematics)
Iwasawa theory and Bloch-Kato conjecture for modular forms (ENGLISH)
[ 講演概要 ]
Bloch and Kato formulated conjectures relating sizes of p-adic Selmer groups with special values of L-functions. Iwasawa theory is a useful tool for studying these conjectures and BSD conjecture for elliptic curves. For example the Iwasawa main conjecture for modular forms formulated by Kato implies the Tamagawa number formula for modular forms of analytic rank 0.
In this talk I'll first briefly review the above theory. Then we will focus on a different Iwasawa theory approach for this problem. The starting point is a recent joint work with Jetchev and Skinner proving the BSD formula for elliptic curves of analytic rank 1. We will discuss how such results are generalized to modular forms. If time allowed we may also explain the possibility to use it to deduce Bloch-Kato conjectures in both analytic rank 0 and 1 cases. In certain aspects such approach should be more powerful than classical Iwasawa theory, and has some potential to attack cases with bad ramification at p.

（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．今回は北京からの中継です．）

### 2017年11月09日(木)

#### Kavli IPMU Komaba Seminar

13:30-14:30   数理科学研究科棟(駒場) 056号室
Edouard Brezin 氏 (lpt ens, Paris)
Various applications of supersymmetry in statistical physics (English)
[ 講演概要 ]
Supersymmetry is a fundamental concept in particle physics (although it has not been seen experimentally so far). But it is although a powerful tool in a number of problems arising in quantum mechanics and statistical physics. It has been widely used in the theory of disordered systems (Efetov et al.), it led to dimensional reduction for branched polymers (Parisi-Sourlas), for the susy classical gas (Brydges and Imbrie), for Landau levels with impurities. If has also many powerful applications in the theory of random matrices. I will briefly review some of these topics.

### 2017年11月13日(月)

#### 東京確率論セミナー

16:00-17:30   数理科学研究科棟(駒場) 128号室

TBA (JAPANESE)

#### 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
Georg Schumacher  氏 (Philipps-Universität Marburg)
Relative Canonical Bundles for Families of Calabi-Yau Manifolds
[ 講演概要 ]
We consider holomorphic families of Calabi-Yau manifolds (here being defined by the vanishing of the first real Chern class). We study induced hermitian metrics on the relative canonical bundle, which are related to the Weil-Petersson form on the base. Under a certain condition the total space possesses a Kähler form, whose restriction to fibers are equal to the Ricci flat metrics. Furthermore we prove an extension theorem for the Weil-Petersson form and give applications.

#### 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
Juan Orendain 氏 (UNAM)
Higher dimensional categorical structures associated with positive topological quantum field theory (English)

### 2017年11月14日(火)

#### 代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 122号室
Meng Chen 氏 (Fudan )
A characterization of the birationality of 4-canonical maps of minimal 3-folds (English)
[ 講演概要 ]
We explain the following theorem: For any minimal 3-fold X of general type with p_g>4, the 4-canonical map is non-birational if and only if X is birationally fibred by a pencil of (1,2) surfaces. The statement fails in the case of p_g=4.

### 2017年11月20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

TBA
[ 講演概要 ]
TBA

### 2017年11月21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

The space of short ropes and the classifying space of the space of long knots (JAPANESE)
[ 講演概要 ]
We prove affirmatively the conjecture raised by J. Mostovoy; the space of short ropes is weakly homotopy equivalent to the classifying space of the topological monoid (or category) of long knots in R^3. We make use of techniques developed by S. Galatius and O. Randal-Williams to construct a manifold space model of the classifying space of the space of long knots, and we give an explicit map from the space of short ropes to the model in a geometric way. This is joint work with Syunji Moriya (Osaka Prefecture University).

### 2017年11月24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) 002号室

[ 講演概要 ]