## 過去の記録

### 2023年01月26日(木)

#### 博士論文発表会

9:15-10:30   数理科学研究科棟(駒場) 122号室号室

Fourier-Mukai transforms for non-commutative complex tori
(非可換複素トーラスのフーリエ・向井変換)

#### 博士論文発表会

11:00-12:15   数理科学研究科棟(駒場) 122号室

Earthquake theorem and cluster algebras
(地震定理とクラスター代数)

#### 博士論文発表会

11:00-12:15   数理科学研究科棟(駒場) 126号室

On universality of the Kardar-Parisi-Zhang equation in high temperature regime
(高温相におけるKardar-Parisi-Zhang 方程式の普遍性について)

#### 博士論文発表会

13:00-14:15   数理科学研究科棟(駒場) 118号室

Studies on the Cone Conjecture, Automorphisms, and Arithmetic Degrees
(錐予想, 自己同型と算術次数の研究)

#### 博士論文発表会

13:00-14:15   数理科学研究科棟(駒場) 122号室
キム　ミンギュ 氏 (東京大学大学院数理科学研究科)
Finite path integral model and toric code based on homological algebra
(ホモロジー代数に基づく有限経路積分モデルとトーリックコード)

#### 博士論文発表会

14:45-16:00   数理科学研究科棟(駒場) 118号室

Irreducible module decompositions of rank 2 symmetric hyperbolic Kac-Moody Lie algebras by sl2 subalgebras which are generalizations of principal sl2 subalgebras
(主sl2部分代数の一般化であるsl2部分代数によるrank2対称双曲型Kac-Moody Lie 代数の既約分解)

### 2023年01月20日(金)

#### 談話会・数理科学講演会

15:30-16:30   ハイブリッド開催

Mikhail Bershtein 氏 (HSE大学, Skoltech)
Kyiv formula and its applications (ENGLISH)
[ 講演概要 ]
The Kyiv formula gives the generic tau function of Painleve' equation (and more generally isomonodromy deformation equations) in terms of conformal blocks or Nekrasov partition function. I will explain the statement, examples and different approaches to the proof. If time permits, I will discuss some applications of this formula.
[ 参考URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZUrduioqjouG9wBfhl35VPxN_K92oa1wB4P

#### 東京名古屋代数セミナー

10:30-12:00   オンライン開催
オンライン開催の詳細は講演参考URLをご覧ください。

Tropical cluster transformations and train track splittings (Japanese)
[ 講演概要 ]
Fock-Goncharovは箙に対し、クラスター代数と呼ばれる組み合わせ構造を持つような概形であるクラスター多様体を定義した。
この概形は良い正値性を持つことから、半体値集合を考えることができる。

クラスター多様体のトロピカル半体値集合はクラスター構造から定まるPL構造を持つが、一方で曲面の測度付き葉層構造の空間にはトレイントラックと呼ばれるグラフを用いたPL構造が定まることが知られている。

またこれの応用として、一般の擬Anosov写像類が符号安定性と呼ばれる性質を持つことを説明する。

ミーティングID: 820 6834 6105
パスコード: 039914
[ 参考URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html

### 2023年01月19日(木)

#### 情報数学セミナー

16:50-18:35   数理科学研究科棟(駒場) 123号室

[ 講演概要 ]

### 2023年01月18日(水)

#### 代数学コロキウム

17:00-18:00   ハイブリッド開催
Kestutis Cesnavicius 氏 (Paris-Saclay University)
The affine Grassmannian as a presheaf quotient (English)
[ 講演概要 ]
The affine Grassmannian of a reductive group G is usually defined as the étale sheafification of the quotient of the loop group LG by the positive loop subgroup. I will discuss various triviality results for G-torsors which imply that this sheafification is often not necessary.

### 2023年01月17日(火)

#### トポロジー火曜セミナー

17:00-18:00   オンライン開催

Chenghan Zha 氏 (東京大学大学院数理科学研究科)
Integral structures in the local algebra of a singularity (ENGLISH)
[ 講演概要 ]
We compute the image of the Milnor lattice of an ADE singularity under a period map. We also prove that the Milnor lattice can be identified with an appropriate relative K-group defined through the Berglund-Huebsch dual of the corresponding singularity. Furthermore, we figure out the image of the Milnor lattice of the singularity of an invertible polynomial of chain type using the basis of middle homology constructed by Otani-Takahashi. We calculated the Seifert form of the basis as well.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

### 2023年01月16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

Holomorphic foliation associated with a semi-positive class of numerical dimension one (Japanese)
[ 講演概要 ]
Let $X$ be a compact Kähler manifold and $\alpha$ be a Dolbeault cohomology class of bidegree $(1,1)$ on $X$.
When the numerical dimension of $\alpha$ is one and $\alpha$ admits at least two smooth semi-positive representatives, we show the existence of a family of real analytic Levi-flat hypersurfaces in $X$ and a holomorphic foliation on a suitable domain of $X$ along whose leaves any semi-positive representative of $\alpha$ is zero.

As an application, we give the affirmative answer to a conjecture on the relation between the semi-positivity of the line bundle $[Y]$ and the analytic structure of a neighborhood of $Y$ for a smooth connected hypersurface $Y$ of $X$.
[ 参考URL ]
https://forms.gle/hYT2hVhDE3q1wDSh6

### 2023年01月13日(金)

#### 離散数理モデリングセミナー

13:15-14:45   数理科学研究科棟(駒場) 126号室
Andy Hone 氏 (University of Kent)
An infinite sequence of Heron triangles with two rational medians (English)
[ 講演概要 ]
Triangles with integer length sides and integer area are known as Heron triangles. Taking rescaling freedom into account, one can apply the same name when all sides and the area are rational numbers. A perfect triangle is a Heron triangle with all three medians being rational, and it is a longstanding conjecture that no such triangle exists. However, despite an assertion by Schubert that even two rational medians are impossible, Buchholz and Rathbun showed that there are infinitely many Heron triangles with two rational medians, an infinite subset of which are associated with rational points on an elliptic curve E(Q) with Mordell-Weil group Z x Z/2Z, and they observed a connection with a pair of Somos-5 sequences. Here we make the latter connection more precise by providing explicit formulae for the integer side lengths, the two rational medians, and the area in this infinite family of Heron triangles. The proof uses a combined approach to Somos-5 sequences and associated Quispel-Roberts-Thompson (QRT) maps in the plane, from several different viewpoints: complex analysis, real dynamics, and reduction modulo a prime.

### 2023年01月12日(木)

#### 情報数学セミナー

16:50-18:35   数理科学研究科棟(駒場) 123号室

[ 講演概要 ]

#### 講演会

16:00-17:00   オンライン開催
Prof. Yi-Hsuan Lin 氏 (National Yang Ming Chiao Tung University, Taiwan)
The Calder'on problem for nonlocal parabolic operators (English)
[ 講演概要 ]
We investigate inverse problems in the determination of leading coefficients for nonlocal parabolic operators, by knowing the corresponding Cauchy data in the exterior space-time domain. The key contribution is that we reduce nonlocal parabolic inverse problems to the corresponding local inverse problems with the lateral boundary Cauchy data. In addition, we derive a new equation and offer a novel proof of the unique continuation property for this new equation. We also build both uniqueness and non-uniqueness results for both nonlocal isotropic and anisotropic parabolic Calder'on problems, respectively.
This is a joint work with Ching-Lung Lin and Gunther Uhlmann.
[ 参考URL ]
https://u-tokyo-ac-jp.zoom.us/j/82806510515?pwd=NEk1RDlMVEFOTEg4WE1MekRySlJpdz09

### 2023年01月11日(水)

#### 離散数理モデリングセミナー

13:15-16:45   数理科学研究科棟(駒場) 056号室
Joe Harrow 氏 (University of Kent) 13:15-14:45
Determinantal expressions for Ohyama polynomials (English)
[ 講演概要 ]
The Ohyama polynomials provide algebraic solutions of the D7 case of the Painleve III equation at a particular sequence of parameter values. It is known that many special function solutions of Painleve equations are expressed in terms of tau functions that can be written in the form of determinants, but until now such a representation for the Ohyama polynomials was not known. Here we present two different determinantal formulae for these polynomials: the first, in terms of Wronskian determinants related to a Darboux transformation for a Lax pair of KdV type; and the second, in terms of Hankel determinants, which is related to the Toda lattice. If time permits, then connections with orthogonal polynomials, and with the recent Riemann-Hilbert approach of Buckingham & Miller, will briefly be mentioned.
Andy Hone 氏 (University of Kent) 15:15-16:45
Discrete dynamics, continued fractions and hyperelliptic curves (English)
[ 講演概要 ]
After reviewing some standard facts about continued fractions for quadratic irrationals, we switch from the real numbers to the field of Laurent series, and describe some classical and more recent results on continued fraction expansions for the square root of an even degree polynomial, and other functions defined on the associated hyperelliptic curve. In the latter case, we extend results of van der Poorten on continued fractions of Jacobi type (J-fractions), and explain the connection with a family of discrete integrable systems (including Quispel-Roberts-Thompson maps and Somos sequences), orthogonal polynomials, and the Toda lattice. If time permits, we will make some remarks on current work with John Roberts and Pol Vanhaecke, concerning expansions involving the square root of an odd degree polynomial, Stieltjes continued fractions, and the Volterra lattice.

### 2023年01月10日(火)

#### 代数幾何学セミナー

10:30-12:00   数理科学研究科棟(駒場) ハイブリッド開催/002号室

Toric Fano varieties arising from posets and their combinatorial mutation equivalence (日本語)
[ 講演概要 ]
In 1986, Stanley introduced two polytopes arising from posets, called order polytopes and chain polytopes. Since then, those polytopes have been studied from viewpoints of combinatorics. Projective toric varieties arising from order polytopes are called Hibi toric varieties in these days. On the other hand, combinatorial mutations were introduced by Akhtar-Coates-Galkin-Kasprzyk in 2012 in the context of the classification problem of Fano varieties using mirror symmetry.
In this talk, after surveying two poset polytopes and combinatorial mutations, we discuss the combinatorial mutation equivalence of two poset polytopes. Those equivalence implies qG-deformation equivalence of projective toric varieties arising from two poset polytopes.
Moreover, it turns out that order polytopes, chain polytopes and their intermediate polytopes correspond to some toric Fano varieties.

#### 講演会

16:00-17:00   オンライン開催
Logarithmic convexity of semigroups and inverse problems for parabolic equations (English)
[ 参考URL ]
https://u-tokyo-ac-jp.zoom.us/j/83149935801?pwd=OE5aanNBVGxvajNycXgyb2RKcW1kZz09

#### トポロジー火曜セミナー

17:00-18:00   オンライン開催

Some calculations of an earthquake map in the cross ratio coordinates and the earthquake theorem of cluster algebras of finite type (JAPANESE)
[ 講演概要 ]
Thurston defined an earthquake, which cuts the Poincaré half-plane model and shifts it. Though it is a discontinuous bijective map, it can be extended to a homeomorphism of a circumference. Also, if an earthquake is equivalent relative to a Fuchsian group, the homeomorphism is equivalent, too. Moreover, Thurston proved the earthquake theorem saying that there uniquely exists an earthquake for any orient-preserving homeomorphism of a circumference, and Bonsante-Krasnov-Schlenker extended it to the case of marked surfaces. We calculate some earthquake maps by the cross ratio coordinates. The cross ratio coordinates are deeply related by the cluster algebra (Fock-Goncharov). We prove the earthquake theorem of cluster algebras of finite type. It is a joint work with Tsukasa Ishibashi and Shunsuke Kano.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

#### 統計数学セミナー

10:50-11:30   数理科学研究科棟(駒場) 号室

Parameter Estimation with Increased Precision for Elliptic and Hypo-elliptic Diffusions

[ 講演概要 ]
Parametric inference for multi-dimensional diffusion processes has been studied over the past decades. Established approaches for likelihood-based estimation invoke a numerical time-discretisation scheme for the approximation of the (typically intractable) transition dynamics of the Stochastic Differential Equation (SDE) over finite time periods. Especially in the setting of some class of hypo-elliptic models, recent research (Ditlevsen and Samson 2019, Gloter and Yoshida 2021) has highlighted the critical effect of the choice of numerical scheme on the behaviour of derived parameter estimates. In our work, first, we develop two weak second order ‘sampling schemes' (to cover both the hypo-elliptic and elliptic classes) and generate accompanying ‘transition density schemes' of the SDE (i.e., approximations of the SDE transition density). Then, we produce a collection of analytic results, providing a complete theoretical framework that solidifies the proposed schemes and showcases advantages from their incorporation within SDE calibration methods, in both high and low frequency observations regime. We also present numerical results from carrying out classical or Bayesian inference. This is a joint work with Alexandros Beskos and Matthew Graham, and the preprint is available at https://arxiv.org/abs/2211.16384.
[ 参考URL ]

### 2023年01月04日(水)

#### 代数学コロキウム

17:00-18:00   ハイブリッド開催

G-displays over prisms and deformation theory (Japanese)
[ 講演概要 ]
The notion of display, which was introduced by Zink, has been successfully applied to the deformation theory of p-divisible groups. Recently, for a reductive group G over the ring of p-adic integers, Lau introduced the notion of G-display. In this talk, following the approach of Lau, we study displays and G-displays over the prismatic site of Bhatt-Scholze, and explain the deformation theory for them. As an application, we give an alternative proof of the classification of p-divisible groups over a complete discrete valuation ring of mixed characteristic (0, p) with perfect residue field, using our deformation theory.

#### 講演会

17:00-18:00   オンライン開催
Professor Debora Presti 氏 (Messina University)
On the source of the catastrophic 1908 Messina tsunami, southern Italy (English)
[ 参考URL ]
https://u-tokyo-ac-jp.zoom.us/j/81296515694?pwd=dlNZY2dZWDRENmdscjRWcFM1MjRCQT09

### 2022年12月27日(火)

#### 講演会

16:00-17:00   オンライン開催
Controllability and inverse problems for parabolic equations with dynamic boundary conditions. (English)
[ 参考URL ]
https://u-tokyo-ac-jp.zoom.us/j/83149935801?pwd=OE5aanNBVGxvajNycXgyb2RKcW1kZz09

### 2022年12月22日(木)

#### 情報数学セミナー

16:50-18:35   数理科学研究科棟(駒場) 123号室
12月15日（木）は講演なし

[ 講演概要 ]

### 2022年12月21日(水)

#### 代数幾何学セミナー

13:00-14:00 or 14:30   数理科学研究科棟(駒場) ハイブリッド開催/056号室
いつもと部屋が異なります. 京大代数幾何セミナーと共催です.
Hsueh-Yung Lin 氏 (NTU)
Towards a geometric origin of the dynamical filtrations (English)
[ 講演概要 ]
Let X be a smooth projective variety with an automorphism f. When X is a threefold, Serge Cantat asked whether X has a non-trivial equivariant rational fibration, if the action of f on the Néron-Severi space is non-trivial and unipotent. We will propose a precise conjecture related to Cantat's question for minimal varieties in arbitrary dimension, in light of the "dynamical filtrations" arising in the study of zero entropy group actions. This conjecture also suggests a geometric origin of dynamical filtrations, whose definition is purely cohomological. We will provide some heuristic evidence from the relative abundance conjecture.
If time permits, we will also explain how the study of dynamical filtrations leads to new results about solvable group actions, which are not necessarily of zero entropy.