## 過去の記録

### 2019年05月22日(水)

#### 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

Bogomolov type vanishing on three-dimensional Mori fiber spaces in positive characteristic

[ 講演概要 ]
In characteristic zero, cotangent bundle of n(>1)-dimensional smooth projective varieties does not contain a big line bundle. This is a part of Bogomolov vanishing and this vanishing plays an important role in the proof of Miyaoka-Yau inequality. In positive characteristic, it is known that Bogomolov vanishing does not hold. There exists a general type surface whose cotangent bundle contains an ample line bundle. So, it is natural to ask when Bogomolov type vanishing holds in positive characteristic. In this talk, I discuss Bogomolov type vanishing on three-dimensional Mori fiber spaces in positive characteristic.

### 2019年05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
Maria de los Angeles Guevara 氏 (大阪市立大学)
On the dealternating number and the alternation number (ENGLISH)
[ 講演概要 ]
Links can be divided into alternating and non-alternating depending on if they possess an alternating diagram or not. After the proof of the Tait flype conjecture on alternating links, it became an important question to ask how a non-alternating link is “close to” alternating links. The dealternating and alternation numbers, which are invariants introduced by C. Adams et al. and A. Kawauchi, respectively, can deal with this question. By definitions, for any link, its alternation number is less than or equal to its dealternating number. It is known that in general the equality does not hold. However, in general, it is not easy to show a gap between these invariants. In this seminar, we will show some results regarding these invariants. In particular, for each pair of positive integers, we will construct infinitely many knots, which have dealternating and alternation numbers determined for these integers. Therefore, an arbitrary gap between the values of these invariants will be obtained.

### 2019年05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

Cohomology and normal reduction numbers of normal surface singularities (Japanese)
[ 講演概要 ]
The normal reduction number of a normal surface singularity relates the maximal degree of the generators of associated graded algebra for certain line bundles on resolution spaces. We show fundamental properties of this invariant and formulas for some special cases. This talk is based on the joint work with Kei-ichi Watanabe and Ken-ichi Yoshida.

### 2019年05月16日(木)

#### 情報数学セミナー

16:50-18:35   数理科学研究科棟(駒場) 128号室

ビットコイン：電子マネー革命 (Japanese)
[ 講演概要 ]
1980年代から暗号分野では電子マネーの研究が行われてきたが，いずれも権威ある(電子マネー)発行機関の存在を前提としていた．ところが，2008年に誕生したビットコインは，特権的な機関は存在せず，非中央集権的な形でマネー（コイン）を発行する仕組みを作り上げた．今回は基本的な暗号機能を利用してどのように非中央集権的にコインを発行するのかなど，ビットコインの仕組みを説明する．

### 2019年05月15日(水)

#### FMSPレクチャーズ

17:30-18:30   数理科学研究科棟(駒場) 122号室
*The date and room have changed.
Gábor Domokos 氏 (Hungarian Academy of Sciences/Budapest University of Technology and Economics)
'Oumuamua, the Gömböc and the Pebbles of Mars (ENGLISH)
[ 講演概要 ]
In this talk I will concentrate on two examples from planetary science, which made the headlines in recent years to highlight the power and significance of nonlinear geometric partial differential equations (PDEs) explaining puzzles presented by Nature. One key link between PDE theory of shape evolution and natural phenomena is the Gömböc, the first mono-monostatic object whose existence was first conjectured by V.I. Arnold in 1995. I will explain the connection and illustrate the process how mathematical models of Nature may be identified.
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Domokos.pdf

#### FMSPレクチャーズ

15:00-17:20   数理科学研究科棟(駒場) 122号室
J. Scott Carter 氏 (University of South Alabama / Osaka City University)
Part 1 : Categorical analogues of surface singularities
Part 2 : Prismatic Homology (ENGLISH)
[ 講演概要 ]
Part 1 :
Isotopy classes of surfaces that are embedded in 3-space can be described as a free 4-category that has one object and one weakly invertible arrow. That description coincides with a fundamental higher homotopy group. The surface singularities that correspond to cusps and optimal points on folds can be used to develop categorical analogues of swallow-tails and horizontal cusps. In this talk, the 4-category will be constructed from the ground up, and the general structure will be described.

Part 2 :
A qualgebra is a set that has two binary operations whose relationships to each other are similar to the relations between group multiplication and conjugation. The axioms themselves are described in terms of isotopies of knotted trivalent graphs and the handle-body knots that are represented. The moves naturally live in prisms. By using a generalization of the tensor product of chain complexes, a homology theory is presented that encapsulates these axioms and the higher order relations between them. We show how to use this homology theory to give a solution a system of tensor equations related to the Yang-Baxter relation.
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Carter.pdf

#### 代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 118号室

On quasi-log canonical pairs
(Japanese)
[ 講演概要 ]
The notion of quasi-log canonical pairs was introduced by Florin Ambro. It is a kind of generalizations of that of log canonical pairs. Now we know that quasi-log canonical pairs are ubiquitous in the theory of minimal models. In this talk, I will explain some basic properties and examples of quasi-log canonical pairs. I will also discuss some new developments around quasi-log canonical pairs. Some parts are joint works with Haidong Liu.

#### 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

Combinatorial aspects of Borel functions

### 2019年05月14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
J. Scott Carter 氏 (University of South Alabama, 大阪市立大学)
Diagrammatic Algebra (ENGLISH)
[ 講演概要 ]
Three main ideas will be explored. First, a higher dimensional category (a category that has arrows, double arrows, triple arrows, and quadruple arrows) that is based upon the axioms of a Frobenius algebra will be outlined. Then these structures will be promoted into one higher dimension so that braiding can be introduced. Second, relationships between braiding and multiplication will be studied from a homological perspective. Third, the next order relations will be used to formulate a system of abstract tensor equations that are analogous to the Yang-Baxter relation. In this way, a broad outline of the notion of diagrammatic algebra will be presented.

### 2019年05月13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

Some Bonnet--Myers Type Theorems for Transverse Ricci Solitons on Complete Sasaki Manifolds (Japanese)
[ 講演概要 ]
The aim of this talk is to discuss the compactness of complete Ricci solitons and its generalizations. Ricci solitons were introduced by R. Hamilton in 1982 and are natural generalizations of Einstein manifolds. They correspond to self-similar solutions to the Ricci flow and often arise as singularity models of the flow. The importance of Ricci solitons was demonstrated by G. Perelman, where they played crucial roles in his affirmative resolution of the Poincare conjecture.
In this talk, after we review basic facts on Ricci solitons, I would like to introduce some Bonnet--Myers type theorems for complete Ricci solitons. Our results generalize the previous Bonnet--Myers type theorems due to W. Ambrose (1957), J. Cheeger, M. Gromov, and M. Taylor (1982), M. Fernandez-Lopez and E. Garcia-Rio (2008), M. Limoncu (2010, 2012), Z. Qian (1997), Y. Soylu (2017), and G. Wei and W. Wylie (2009). Moreover, I would also like to extend such Bonnet--Myers type theorems to the case of transverse Ricci solitons on complete Sasaki manifolds. Our results generalize the previous Bonnet--Myers type theorems for complete Sasaki manifolds due to I. Hasegawa and M. Seino (1981) and Y. Nitta (2009).

#### 数値解析セミナー

16:50-18:20   数理科学研究科棟(駒場) 056号室

[ 講演概要 ]

### 2019年05月09日(木)

#### 情報数学セミナー

16:50-18:35   数理科学研究科棟(駒場) 128号室

[ 講演概要 ]

### 2019年05月08日(水)

#### 代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 118号室

On Minimal model theory for log canonical pairs with big boundary divisors
[ 講演概要 ]
In 2010, Birkar--Cascini--Hacon--McKernan established the minimal model theory for Kawamata log　terminal pairs with big boundary divisors, and a lot of theorems in the birational geometry are
proved by applying this result. It is expected that this result can be generalized to log canonical pairs. Currently, it is known that the minimal model theory for log canonical pairs can be reduced to the case of big boundary divisors. In this talk, we introduce a partial generalization of the result by Birkar--Cascini--Hacon--McKernan. Roughly speaking, we generalized their result to lc pairs with big boundary divisors having only small lc centers. We also explain another generalization, which is originally announced by Hu, and we discuss termination of log minimal model program in a spacial case. This is a joint work with Zhengyu Hu, and the work is in progress.

#### 代数学コロキウム

17:00-18:00   数理科学研究科棟(駒場) 056号室

On the types for supercuspidal representations of inner forms of GL_n (Japanese)
[ 講演概要 ]
Aを非アルキメデス的局所体F上の中心的単純環とし，Gをその乗法群とする．
Gのsmooth表現を考察する際に有用な理論の一つとしてtypeの理論が存在する．
type (J, ¥lambda) とはGのコンパクト部分群Jと J の既約部分表現 ¥lambda の組であって，Gの既約表現をある意味で分類することのできるものである．
S¥'echerre-Stevenにより，Gのtypeの族としてsimple typeという概念が構成されている．

#### 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

Unitary conjugacy for type III subfactors and W*-superrigidity

### 2019年05月02日(木)

#### 情報数学セミナー

16:50-18:35   数理科学研究科棟(駒場) 128号室

[ 講演概要 ]
1970年代に誕生した現代暗号は、1980年代にその理論的な基礎づけが確立された．今回は、その中核となる概念として，安全性証明のための標準モデル，証明手法としてのシミュレーションパラダイムおよび識別不可能性などを紹介するとともに，それらの概念に基づく代表的暗号機能として，ゼロ知識証明を紹介する．

### 2019年04月30日(火)

#### 代数学コロキウム

17:00-18:00   数理科学研究科棟(駒場) 122号室
Jean-Francois Dat 氏 (Sorbonne University)
Moduli space of l-adic Langlands parameters and the stable Bernstein center (English)
[ 講演概要 ]
Motivated by the description of the integral l-adic cohomology of certain Shimura varieties in middle degree, Emerton and Helm have conjectured the existence of a certain local Langlands correspondence for l-adic families of n-dimensional Galois representations. The proof of this conjecture by Helm and Moss relies on a beautiful isomorphism between the ring of functions of the moduli space of l-adic representations and the integral Bernstein center of GL_n(F). We will present a work in progress with Helm, Korinczuk and Moss towards a generalization of this result for arbitrary (tamely ramified) reductive groups.

### 2019年04月26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

Lie-Poisson代数の「変形」とカイラルな場の理論 (日本語)
[ 講演概要 ]

### 2019年04月25日(木)

#### 応用解析セミナー

16:00-18:00   数理科学研究科棟(駒場) 118号室
この日は２つ講演があります．教室と時間にご注意下さい．
Matteo Muratori 氏 (Polytechnic University of Milan) 16:00-17:00
The porous medium equation on noncompact Riemannian manifolds with initial datum a measure
(English)
[ 講演概要 ]
We investigate existence and uniqueness of weak solutions of the Cauchy problem for the porous medium equation on Cartan-Hadamard manifolds. We show existence of solutions that take a finite Radon measure as initial datum, possibly sign-changing. We then prove uniqueness in the class of nonnegative solutions, upon assuming a quadratic lower bound on the Ricci curvature. Our result is "optimal" in the sense that any weak solution necessarily solves a Cauchy problem with initial datum a finite Radon measure. Moreover, as byproducts of the techniques we employ, we obtain some new results in potential analysis on manifolds, concerning the validity of a modified version of the mean-value inequality for superharmonic functions and related properties of potentials of positive Radon measures. Finally, we briefly discuss some work in progress regarding stability of the porous medium equation with respect to the Wasserstein distance, on Riemannian manifolds with Ricci curvature bounded below.
Maurizia Rossi 氏 (University of Pisa) 17:00-18:00
On sharp large deviations for the bridge of a general diffusion
(English)
[ 講演概要 ]
In this talk we provide sharp Large Deviation estimates for the probability of exit from a domain for the bridge of a d-dimensional general diffusion process X, as the conditioning time tends to 0. This kind of results is motivated by applications to numerical simulation. In particular we investigate the influence of the drift b of X. It turns out that the sharp asymptotics for the exit time probability are independent of the drift, provided b enjoyes a simple condition that is always satisfied in dimension 1. On the other hand, we show that the drift can be influential if this assumption is not satisfied. This talk is based on a joint work with P. Baldi and L. Caramellino.

#### 情報数学セミナー

16:50-18:35   数理科学研究科棟(駒場) 128号室

[ 講演概要 ]

まず、第１回(4月25日）では、現代暗号が誕生した経緯とそれらが現在どのような形で利用されているかについて紹介する。

### 2019年04月24日(水)

#### 代数学コロキウム

17:30-18:30   数理科学研究科棟(駒場) 056号室
Joseph Ayoub 氏 (University of Zurich)
P^1-localisation and a possible definition of arithmetic Kodaira-Spencer classes (English)
[ 講演概要 ]
A^1-localisation is a universal construction which produces "cohomology theories" for which the affine line A^1 is contractible. It plays a central role in the theory of motives à la Morel-Voevodsky. In this talk, I'll discuss the analogous construction where the affine line is replaced by the projective line P^1. This is the P^1-localisation which is arguably an unnatural construction since it produces "cohomology theories" for which the projective line P^1 is contractible. Nevertheless, I'll explain a few positive results and some computations around this construction which naturally lead to a definition of Kodaira-Spencer classes of arithmetic nature. (Unfortunately, it is yet unclear if these classes are really interesting and nontrivial.)

#### 代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 118号室

Varieties of dense globally F-split type with a non-invertible polarized
endomorphism
[ 講演概要 ]
Broustet and Gongyo conjectured that if a normal projective variety X has a non-invertible polaried endomorphism, then X is of Calabi-Yau type. Furthermore, Schwede and Smith conjectured that a projective variety is of Calabi-Yau type if and only if of dense globally F-split type. Therefore it is a natural question to ask if a normal projective variety X has a non-invertible polaried endomorphism, then X is of dense globally F-split type. In this talk, I will introduce simple points and difficult points of the question. Furthermore I will give the affirmative answer of my question for 2-dimensional case.

### 2019年04月23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
Christine Vespa 氏 (Université de Strasbourg)
Higher Hochschild homology as a functor (ENGLISH)
[ 講演概要 ]
Higher Hochschild homology generalizes classical Hochschild homology for rings. Recently, Turchin and Willwacher computed higher Hochschild homology of a finite wedge of circles with coefficients in the Loday functor associated to the ring of dual numbers over the rationals. In particular, they obtained linear representations of the groups Out(F_n) which do not factorize through GL(n,Z).

In this talk, I will begin by recalling what is Hochschild homology and higher Hochschild homology. Then I will explain how viewing higher Hochschild homology of a finite wedge of circles as a functor on the category of free groups provides a conceptual framework which allows powerful tools such as exponential functors and polynomial functors to be used. In particular, this allows the generalization of the results of Turchin and Willwacher; this gives rise to new linear representations of Out(F_n) which do not factorize through GL(n,Z).

(This is joint work with Geoffrey Powell.)

### 2019年04月22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

Optimal destabilizer for a Fano manifold (Japanese)
[ 講演概要 ]
Around 2005, S. Donaldson asked whether the lower bound of the Calabi functional is achieved by a sequence of the normalized Donaldson-Futaki invariants.
For a Fano manifold we construct a sequence of multiplier ideal sheaves from a new geometric flow and answer to Donaldson's question.

#### 数値解析セミナー

16:50-18:20   数理科学研究科棟(駒場) 056号室

HDG法の超収束について (Japanese)
[ 講演概要 ]