## Seminar information archive

Seminar information archive ～09/10｜Today's seminar 09/11 | Future seminars 09/12～

### 2024/05/24

#### Algebraic Geometry Seminar

13:30-15:00 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)

Boundedness of weak Fano threefolds with fixed Gorenstein index in positive characteristic

**Kenta Sato**(Kyusyu University)Boundedness of weak Fano threefolds with fixed Gorenstein index in positive characteristic

[ Abstract ]

In this talk, we give a partial affirmative answer to the BAB conjecture for 3-folds in characteristic p>5. Specifically, we prove that a set of weak Fano 3-folds over an uncountable algebraically closed field is bounded, if each element X satisfies certain conditions regarding the Gorenstein index, a complement and Kodaira type vanishing. In the course of the proof, we also study a uniform lower bound for Seshadri constants of nef and big invertible sheaves on projective 3-folds.

In this talk, we give a partial affirmative answer to the BAB conjecture for 3-folds in characteristic p>5. Specifically, we prove that a set of weak Fano 3-folds over an uncountable algebraically closed field is bounded, if each element X satisfies certain conditions regarding the Gorenstein index, a complement and Kodaira type vanishing. In the course of the proof, we also study a uniform lower bound for Seshadri constants of nef and big invertible sheaves on projective 3-folds.

### 2024/05/23

#### Applied Analysis

16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Homogenization of nonlocal Hamilton Jacobi equations (English)

**Adina Ciomaga**(University Paris Cité (Laboratoire Jacques Louis Lions), France “O Mayer” Institute of the Romanian Academy, Iasi, Roumania)Homogenization of nonlocal Hamilton Jacobi equations (English)

[ Abstract ]

I will present the framework of periodic homogenisation of nonlocal Hamilton-Jacobi equations, associated with Levy-Itô integro-differential operators. A typical equation is the fractional diffusion coupled with a transport term, where the diffusion is only weakly elliptical. Homogenization is established in two steps: (i) the resolution of a cellular problem - where Lipshitz regularity of the corrector plays a key role and (ii) the convergence of the oscillating solutions towards an averaged profile - where comparison principles are involved. I shall discuss recent results on the regularity of solutions and comparison principles for nonlocal equations, and the difficulties we face when compared with local PDEs. The talked is based on recent developments obtained in collaboration with D. Ghilli, O.Ley, E. Topp, T. Minh Le.

I will present the framework of periodic homogenisation of nonlocal Hamilton-Jacobi equations, associated with Levy-Itô integro-differential operators. A typical equation is the fractional diffusion coupled with a transport term, where the diffusion is only weakly elliptical. Homogenization is established in two steps: (i) the resolution of a cellular problem - where Lipshitz regularity of the corrector plays a key role and (ii) the convergence of the oscillating solutions towards an averaged profile - where comparison principles are involved. I shall discuss recent results on the regularity of solutions and comparison principles for nonlocal equations, and the difficulties we face when compared with local PDEs. The talked is based on recent developments obtained in collaboration with D. Ghilli, O.Ley, E. Topp, T. Minh Le.

### 2024/05/22

#### Number Theory Seminar

17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)

On the (φ,Γ)-modules corresponding to crystalline representations and semi-stable representations

**Takumi Watanabe**(University of Tokyo)On the (φ,Γ)-modules corresponding to crystalline representations and semi-stable representations

[ Abstract ]

From the 1980s to the 1990s, J.-M. Fontaine constructed an equivalence of categories between the category of (φ, Γ)-modules and the category of p-adic Galois representations. After recalling it, I will present my result on the (φ, Γ)-modules corresponding to crystalline representations and semi-stable representations. As for the crystalline case, this can be seen, in a sense, as a generalization of Wach module in the ramified case. If time permits, I will explain my ongoing research on the (φ, Γ)-modules corresponding to de Rham representations.

From the 1980s to the 1990s, J.-M. Fontaine constructed an equivalence of categories between the category of (φ, Γ)-modules and the category of p-adic Galois representations. After recalling it, I will present my result on the (φ, Γ)-modules corresponding to crystalline representations and semi-stable representations. As for the crystalline case, this can be seen, in a sense, as a generalization of Wach module in the ramified case. If time permits, I will explain my ongoing research on the (φ, Γ)-modules corresponding to de Rham representations.

### 2024/05/21

#### Tuesday Seminar on Topology

17:30-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)

Pre-registration required. See our seminar webpage.

γ-supports and sheaves (JAPANESE)

https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

Pre-registration required. See our seminar webpage.

**Yuichi Ike**(Institute of Mathematics for Industry, Kyushu University)γ-supports and sheaves (JAPANESE)

[ Abstract ]

The space of smooth compact exact Lagrangians of a cotangent bundle carries the spectral metric γ, and we consider its completion. With an element of the completion, Viterbo associated a closed subset called γ-support. In this talk, I will explain how we can use sheaf-theoretic methods to explore the completion and γ-supports. I will show that we can associate a sheaf with an element of the completion, and its (reduced) microsupport is equal to the γ-support through the correspondence. With this equality, I will also show several properties of γ-supports. This is joint work with Tomohiro Asano (RIMS), Stéphane Guillermou (Nantes Université), Vincent Humilière (Sorbonne Université), and Claude Viterbo (Université Paris-Saclay).

[ Reference URL ]The space of smooth compact exact Lagrangians of a cotangent bundle carries the spectral metric γ, and we consider its completion. With an element of the completion, Viterbo associated a closed subset called γ-support. In this talk, I will explain how we can use sheaf-theoretic methods to explore the completion and γ-supports. I will show that we can associate a sheaf with an element of the completion, and its (reduced) microsupport is equal to the γ-support through the correspondence. With this equality, I will also show several properties of γ-supports. This is joint work with Tomohiro Asano (RIMS), Stéphane Guillermou (Nantes Université), Vincent Humilière (Sorbonne Université), and Claude Viterbo (Université Paris-Saclay).

https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

#### Operator Algebra Seminars

16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)

Optimal version of the fundamental theorem of chronogeometry

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

**Michiya Mori**(Univ．Tokyo)Optimal version of the fundamental theorem of chronogeometry

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

### 2024/05/20

#### Seminar on Geometric Complex Analysis

10:50-12:20 Room #128 (Graduate School of Math. Sci. Bldg.)

Kähler metrics in the Siegel domain (Japanese)

https://forms.gle/gTP8qNZwPyQyxjTj8

**Lijie Sun**(Yamaguchi Univ.)Kähler metrics in the Siegel domain (Japanese)

[ Abstract ]

The Siegel domain is endowed with an intrinsic Kähler structure, making it an exemplary model for the complex hyperbolic plane. Its boundary, characterized as the one-point compactification of the Heisenberg group, plays an important role in studying the geometry of the Siegel domain. In this talk, using the CR structure of the Heisenberg group we introduce a variety of Kähler structures within the Siegel domain. We conclude by demonstrating that all these metrics are PCR-Kähler equivalent, that is, essentially the same when confined to the CR structure. This talk is based on a joint work with Ioannis Platis and Joonhyung Kim.

[ Reference URL ]The Siegel domain is endowed with an intrinsic Kähler structure, making it an exemplary model for the complex hyperbolic plane. Its boundary, characterized as the one-point compactification of the Heisenberg group, plays an important role in studying the geometry of the Siegel domain. In this talk, using the CR structure of the Heisenberg group we introduce a variety of Kähler structures within the Siegel domain. We conclude by demonstrating that all these metrics are PCR-Kähler equivalent, that is, essentially the same when confined to the CR structure. This talk is based on a joint work with Ioannis Platis and Joonhyung Kim.

https://forms.gle/gTP8qNZwPyQyxjTj8

#### Tokyo Probability Seminar

16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)

We are having teatime from 15:15 in the common room on the second floor. Please join us.

2曲線間に制限されたパス空間上でのWiener測度に対する高階の部分積分公式 (日本語)

We are having teatime from 15:15 in the common room on the second floor. Please join us.

**Soma Nishino**(Tokyo Metropolitan University)2曲線間に制限されたパス空間上でのWiener測度に対する高階の部分積分公式 (日本語)

[ Abstract ]

2曲線間に制限されたパス空間上でのWiener測度に対する1階微分の部分積分公式は既に知られている。本講演では、この結果を高階微分の部分積分公式に拡張する。高階微分の部分積分公式においては、従来の1階微分の場合にはない非自明な境界項が追加で現れ、さらに、その証明において、Brownian excursionやBrownian house-movingと呼ばれる確率過程のランダムウォーク近似による構成方法が新たに必要となる。また、証明の中で、1次および2次の無限小確率の概念を導入する。この概念を導入することで、部分積分公式の各項に現れる数式に対して確率論的な解釈が可能となり、部分積分公式を整理する上で有益な概念であることを説明する。なお、本講演内容は、東京都立大学の石谷謙介氏との共同研究(arXiv:2405.05595)に基づく。

2曲線間に制限されたパス空間上でのWiener測度に対する1階微分の部分積分公式は既に知られている。本講演では、この結果を高階微分の部分積分公式に拡張する。高階微分の部分積分公式においては、従来の1階微分の場合にはない非自明な境界項が追加で現れ、さらに、その証明において、Brownian excursionやBrownian house-movingと呼ばれる確率過程のランダムウォーク近似による構成方法が新たに必要となる。また、証明の中で、1次および2次の無限小確率の概念を導入する。この概念を導入することで、部分積分公式の各項に現れる数式に対して確率論的な解釈が可能となり、部分積分公式を整理する上で有益な概念であることを説明する。なお、本講演内容は、東京都立大学の石谷謙介氏との共同研究(arXiv:2405.05595)に基づく。

### 2024/05/17

#### Algebraic Geometry Seminar

13:30-15:00 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)

非分離Kummer曲面 (日本語)

**Yuya Matsumoto**(Tokyo University of Science)非分離Kummer曲面 (日本語)

[ Abstract ]

Kummer曲面Km(A)とは，+-1倍写像によるアーベル曲面Aの商の最小特異点解消として得られる曲面である．Aが標数≠2の場合（resp. 標数2で，超特異ではない場合）は，Km(A)はK3曲面であり，例外曲線は互いに交わらない（resp. 所定の交わり方をする）16本の有理曲線である．Aが標数2で超特異の場合はKm(A)はK3曲面にならない．また，Km(A)が標数2の超特異K3曲面になることはない．

本講演では，標数2の超特異K3曲面とその上の16本の有理曲線で所定の交わり方をするものに対し，非分離2重被覆Aを構成することができること，Aは非特異部分に群構造が入り「アーベル曲面もどき」になることを示す．Aの分類のために，RDP K3曲面のRDPの補集合から最小特異点解消への B_n \Omega^1（Cartier作用素を何回か適用すると消える1次微分形式の層）の延長に関する結果を用いるので，これにも言及したい．

プレプリントは https://arxiv.org/abs/2403.02770 でご覧いただけます．

Kummer曲面Km(A)とは，+-1倍写像によるアーベル曲面Aの商の最小特異点解消として得られる曲面である．Aが標数≠2の場合（resp. 標数2で，超特異ではない場合）は，Km(A)はK3曲面であり，例外曲線は互いに交わらない（resp. 所定の交わり方をする）16本の有理曲線である．Aが標数2で超特異の場合はKm(A)はK3曲面にならない．また，Km(A)が標数2の超特異K3曲面になることはない．

本講演では，標数2の超特異K3曲面とその上の16本の有理曲線で所定の交わり方をするものに対し，非分離2重被覆Aを構成することができること，Aは非特異部分に群構造が入り「アーベル曲面もどき」になることを示す．Aの分類のために，RDP K3曲面のRDPの補集合から最小特異点解消への B_n \Omega^1（Cartier作用素を何回か適用すると消える1次微分形式の層）の延長に関する結果を用いるので，これにも言及したい．

プレプリントは https://arxiv.org/abs/2403.02770 でご覧いただけます．

### 2024/05/15

#### Numerical Analysis Seminar

16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Regularization via Bregman divergence for the discrete optimal transport problem (Japanese)

[ Reference URL ]

https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/

**Koya Sakakibara**(Kanazawa University)Regularization via Bregman divergence for the discrete optimal transport problem (Japanese)

[ Reference URL ]

https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/

#### Number Theory Seminar

17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)

Equidimensionality of affine Deligne-Lusztig varieties in mixed characteristic (日本語)

**Yuta Takaya**(University of Tokyo)Equidimensionality of affine Deligne-Lusztig varieties in mixed characteristic (日本語)

[ Abstract ]

Shimura varieties are of central interest in arithmetic geometry and affine Deligne-Lusztig varieties are closely related to their special fibers. These varieties are group-theoretical objects and can be defined even for non-miniscule local Shimura data. In this talk, I will explain the proof of the equidimensionality of affine Deligne-Lusztig varieties in mixed characteristic.

The main ingredient is a local foliation of affine Deligne-Lusztig varieties in mixed characteristic. In equal characteristic, this local structure was previously introduced by Hartl and Viehmann.

Shimura varieties are of central interest in arithmetic geometry and affine Deligne-Lusztig varieties are closely related to their special fibers. These varieties are group-theoretical objects and can be defined even for non-miniscule local Shimura data. In this talk, I will explain the proof of the equidimensionality of affine Deligne-Lusztig varieties in mixed characteristic.

The main ingredient is a local foliation of affine Deligne-Lusztig varieties in mixed characteristic. In equal characteristic, this local structure was previously introduced by Hartl and Viehmann.

### 2024/05/14

#### Tuesday Seminar of Analysis

16:00-18:15 Room #128 (Graduate School of Math. Sci. Bldg.)

The Energy of Heavy Atoms: Density Functionals (English)

https://forms.gle/ZEyVso6wa9QpNfxH7

Well-posedness for Semilinear Heat Equations in Orlicz Spaces (English)

https://forms.gle/ZEyVso6wa9QpNfxH7

**Heinz Siedentop**(LMU University of Munich) 16:00-17:00The Energy of Heavy Atoms: Density Functionals (English)

[ Abstract ]

Since computing the energy of a system with $N$ particles requires solving a $4^N$ dimensional system of (pseudo-)differential equations in $3N$ independent variables, an analytic solution is practically impossible. Therefore density functionals, i.e., functionals that depend on the particle density (3 variables) only and yield the energy upon minimization, are of great interest.

This concept has been applied successfully in non-relativistic quantum mechanics. However, in relativistic quantum mechanics even the simple analogue of the Thomas-Fermi functional is not bounded from below for Coulomb potential. This problem was addressed eventually by Engel and Dreizler who derived a functional from QED. I will review some known mathematical properties of this functional and show that it yields basic features of physics, such as asymptotic correct energy, stability of matter, and boundedness of the excess charge.

[ Reference URL ]Since computing the energy of a system with $N$ particles requires solving a $4^N$ dimensional system of (pseudo-)differential equations in $3N$ independent variables, an analytic solution is practically impossible. Therefore density functionals, i.e., functionals that depend on the particle density (3 variables) only and yield the energy upon minimization, are of great interest.

This concept has been applied successfully in non-relativistic quantum mechanics. However, in relativistic quantum mechanics even the simple analogue of the Thomas-Fermi functional is not bounded from below for Coulomb potential. This problem was addressed eventually by Engel and Dreizler who derived a functional from QED. I will review some known mathematical properties of this functional and show that it yields basic features of physics, such as asymptotic correct energy, stability of matter, and boundedness of the excess charge.

https://forms.gle/ZEyVso6wa9QpNfxH7

**Robert Laister**(University of the West of England) 17:15-18:15Well-posedness for Semilinear Heat Equations in Orlicz Spaces (English)

[ Abstract ]

We consider the local well-posedness of semilinear heat equations in Orlicz spaces, the latter prescribed via a Young function $\Phi$. Many existence-uniqueness results exist in the literature for power-like or exponential-like nonlinearities $f$, where the natural setting is an Orlicz space of corresponding type; i.e. if $f$ is power-like then $\Phi$ is power-like (Lebesgue space), if $f$ is exponential-like then $\Phi$ is exponential-like. However, the general problem of prescribing a suitable $\Phi$ for a given, otherwise arbitrary $f$ is open. Our goal is to provide a suitable framework to resolve this problem and I will present some recent results in this direction. The key is a new (to the best of our knowledge) smoothing estimate for the heat semigroup between two arbitrary Orlicz spaces. Existence then follows familiar lines via monotonicity or contraction mapping arguments. Global solutions are also presented under additional assumptions. This work is part of a collaborative project with Prof Kazuhiro Ishige, Dr Yohei Fujishima and Dr Kotaro Hisa.

[ Reference URL ]We consider the local well-posedness of semilinear heat equations in Orlicz spaces, the latter prescribed via a Young function $\Phi$. Many existence-uniqueness results exist in the literature for power-like or exponential-like nonlinearities $f$, where the natural setting is an Orlicz space of corresponding type; i.e. if $f$ is power-like then $\Phi$ is power-like (Lebesgue space), if $f$ is exponential-like then $\Phi$ is exponential-like. However, the general problem of prescribing a suitable $\Phi$ for a given, otherwise arbitrary $f$ is open. Our goal is to provide a suitable framework to resolve this problem and I will present some recent results in this direction. The key is a new (to the best of our knowledge) smoothing estimate for the heat semigroup between two arbitrary Orlicz spaces. Existence then follows familiar lines via monotonicity or contraction mapping arguments. Global solutions are also presented under additional assumptions. This work is part of a collaborative project with Prof Kazuhiro Ishige, Dr Yohei Fujishima and Dr Kotaro Hisa.

https://forms.gle/ZEyVso6wa9QpNfxH7

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Exotic 4-manifolds with signature zero (JAPANESE)

https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

Pre-registration required. See our seminar webpage.

**Noriyuki Hamada**(Institute of Mathematics for Industry, Kyushu University)Exotic 4-manifolds with signature zero (JAPANESE)

[ Abstract ]

We will talk about our novel examples of symplectic 4-manifolds, which are homeomorphic but not diffeomorphic to the standard simply-connected closed 4-manifolds with signature zero. In particular, they provide such examples with the smallest Euler characteristics known to date. Our method employs the time-honored approach of reverse-engineering, while the key new ingredients are the model manifolds that we build from scratch as Lefschetz fibrations. Notably, our method greatly simplifies pi_1 calculations, typically the most intricate aspect in existing literature.

This is joint work with Inanc Baykur (University of Massachusetts Amherst).

[ Reference URL ]We will talk about our novel examples of symplectic 4-manifolds, which are homeomorphic but not diffeomorphic to the standard simply-connected closed 4-manifolds with signature zero. In particular, they provide such examples with the smallest Euler characteristics known to date. Our method employs the time-honored approach of reverse-engineering, while the key new ingredients are the model manifolds that we build from scratch as Lefschetz fibrations. Notably, our method greatly simplifies pi_1 calculations, typically the most intricate aspect in existing literature.

This is joint work with Inanc Baykur (University of Massachusetts Amherst).

https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

#### Operator Algebra Seminars

16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)

Completely rational conformal nets and modular tensor categories

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

**Ziyun Xu**(Univ. Tokyo)Completely rational conformal nets and modular tensor categories

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

### 2024/05/13

#### Tokyo Probability Seminar

16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)

We are having teatime from 15:15 in the common room on the second floor. Please join us.

Brownian motion with darning and its related open problem (English)

We are having teatime from 15:15 in the common room on the second floor. Please join us.

**Shuwen Lou**(University of Illinois)Brownian motion with darning and its related open problem (English)

[ Abstract ]

In this talk, I will discuss some existing results about Brownian motion with darning, including its HKE and discrete approximate by random walks, along with an open problem: What is the relationship between (a) subordinated BM with darning, and (b) the process obtained by darning together two subordinated reflected BM. This is an ongoing collaboration with Zhen-Qing Chen.

In this talk, I will discuss some existing results about Brownian motion with darning, including its HKE and discrete approximate by random walks, along with an open problem: What is the relationship between (a) subordinated BM with darning, and (b) the process obtained by darning together two subordinated reflected BM. This is an ongoing collaboration with Zhen-Qing Chen.

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

(Japanese)

[ Reference URL ]

https://forms.gle/gTP8qNZwPyQyxjTj8

**Yu Kawakami**(Kanazawa Univ.)(Japanese)

[ Reference URL ]

https://forms.gle/gTP8qNZwPyQyxjTj8

### 2024/05/08

#### Number Theory Seminar

17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)

The pro-modularity in the residually reducible case (English)

**Xinyao Zhang**(University of Tokyo)The pro-modularity in the residually reducible case (English)

[ Abstract ]

For a continuous odd two dimensional Galois representation over a finite field of characteristic p, it is conjectured that its universal deformation ring is isomorphic to some p-adic big Hecke algebra, called the big R=T theorem. Recently, Deo explored the residually reducible case and proved a big R=T theorem for Q under the assumption of the cyclicity of some cohomology group. However, his method is unavailable for totally real fields since the assumption does not hold any longer. In this talk, we follow the strategy of the work from Skinner-Wiles and Pan on the Fontaine-Mazur conjecture and give a pro-modularity result for some totally real fields, which is an analogue to the big R=T theorem.

For a continuous odd two dimensional Galois representation over a finite field of characteristic p, it is conjectured that its universal deformation ring is isomorphic to some p-adic big Hecke algebra, called the big R=T theorem. Recently, Deo explored the residually reducible case and proved a big R=T theorem for Q under the assumption of the cyclicity of some cohomology group. However, his method is unavailable for totally real fields since the assumption does not hold any longer. In this talk, we follow the strategy of the work from Skinner-Wiles and Pan on the Fontaine-Mazur conjecture and give a pro-modularity result for some totally real fields, which is an analogue to the big R=T theorem.

### 2024/05/07

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

The Thurston spine and the Systole function of Teichmüller space (ENGLISH)

https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

Pre-registration required. See our seminar webpage.

**Ingrid Irmer**(Southern University of Science and Technology)The Thurston spine and the Systole function of Teichmüller space (ENGLISH)

[ Abstract ]

The systole function $f_{sys}$ on Teichm\"uller space $\mathcal{T}_{g}$ of a closed genus $g$ surface is a piecewise-smooth map $\mathcal{T}_{g}\rightarrow \mathbb{R}$ whose value at any point is the length of the shortest geodesic on the corresponding hyperbolic surface. It is known that $f_{sys}$ gives a mapping class group-equivariant handle decomposition of $\mathcal{T}_{g}$ via an analogue of Morse Theory. This talk explains the relationship between this handle decomposition and the Thurston spine of $\mathcal{T}_{g}$.

[ Reference URL ]The systole function $f_{sys}$ on Teichm\"uller space $\mathcal{T}_{g}$ of a closed genus $g$ surface is a piecewise-smooth map $\mathcal{T}_{g}\rightarrow \mathbb{R}$ whose value at any point is the length of the shortest geodesic on the corresponding hyperbolic surface. It is known that $f_{sys}$ gives a mapping class group-equivariant handle decomposition of $\mathcal{T}_{g}$ via an analogue of Morse Theory. This talk explains the relationship between this handle decomposition and the Thurston spine of $\mathcal{T}_{g}$.

https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

#### Operator Algebra Seminars

16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)

Harmonic measures in percolation clusters on hyperbolic groups

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

**Kohki Sakamoto**(Univ. Tokyo)Harmonic measures in percolation clusters on hyperbolic groups

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

### 2024/05/01

#### Number Theory Seminar

17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)

On the potential automorphy and the local-global compatibility for the monodromy operators at p ≠ l over CM fields. (日本語)

**Kojiro Matsumoto**(University of Tokyo)On the potential automorphy and the local-global compatibility for the monodromy operators at p ≠ l over CM fields. (日本語)

[ Abstract ]

Let F be a totally real field or CM field, n be a positive integer, l be a prime, π be a cohomological cuspidal automorphic representation of GLn over F and v be a non-l-adic finite place of F. In 2014, Harris-Lan-Taylor-Thorne constructed the l-adic Galois representation corresponding to π. (Scholze also constructed this by another method.) The compatibility of this construction and the local Langlands correspondence at v was proved up to semisimplification by Ila Varma(2014), but the compatibility for the monodromy operators was known only in conjugate self-dual cases and some special 2-dimensional cases. In this talk, we will prove the local-global compatibility in some self-dual cases and sufficiently regular weight cases by using some new potential automorphy theorems. Moreover, if we have time, we will also prove the Ramanujan conjecture for the cohomological cuspidal automorphic representations of GL2 over F, which was proved in parallel weight cases by Boxer-Calegari-Gee-Newton-Thorne (2023).

Let F be a totally real field or CM field, n be a positive integer, l be a prime, π be a cohomological cuspidal automorphic representation of GLn over F and v be a non-l-adic finite place of F. In 2014, Harris-Lan-Taylor-Thorne constructed the l-adic Galois representation corresponding to π. (Scholze also constructed this by another method.) The compatibility of this construction and the local Langlands correspondence at v was proved up to semisimplification by Ila Varma(2014), but the compatibility for the monodromy operators was known only in conjugate self-dual cases and some special 2-dimensional cases. In this talk, we will prove the local-global compatibility in some self-dual cases and sufficiently regular weight cases by using some new potential automorphy theorems. Moreover, if we have time, we will also prove the Ramanujan conjecture for the cohomological cuspidal automorphic representations of GL2 over F, which was proved in parallel weight cases by Boxer-Calegari-Gee-Newton-Thorne (2023).

#### Discrete mathematical modelling seminar

13:00-15:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Semitoric systems and their symplectic invariants (English)

**Jaume Alonso**(Technische Universität Berlin)Semitoric systems and their symplectic invariants (English)

[ Abstract ]

Semitoric systems are a special class of completely integrable systems defined on four-dimensional symplectic manifolds. One of the reasons that make these systems interesting is their classification in terms of five symplectic invariants proposed by Pelayo and Vũ Ngọc. In the last years, many efforts have been made in order to extend this classification to broader settings, to generate more examples and to compute their invariants. In this talk we will discuss some of the most important properties of semitoric systems and introduce some families of systems with one and more focus-focus singularities. We will also show how the symplectic invariants of these systems change as we move the parameters of the families and how they can be computed using mathematical software.

This is a joint work with H. Dullin, S. Hohloch and J. Palmer.

Semitoric systems are a special class of completely integrable systems defined on four-dimensional symplectic manifolds. One of the reasons that make these systems interesting is their classification in terms of five symplectic invariants proposed by Pelayo and Vũ Ngọc. In the last years, many efforts have been made in order to extend this classification to broader settings, to generate more examples and to compute their invariants. In this talk we will discuss some of the most important properties of semitoric systems and introduce some families of systems with one and more focus-focus singularities. We will also show how the symplectic invariants of these systems change as we move the parameters of the families and how they can be computed using mathematical software.

This is a joint work with H. Dullin, S. Hohloch and J. Palmer.

### 2024/04/30

#### Operator Algebra Seminars

16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)

Non-semisimple modular tensor categories via local modules

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

**Harshit Yadav**(Univ. Alberta)Non-semisimple modular tensor categories via local modules

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

### 2024/04/26

#### Algebraic Geometry Seminar

14:00-15:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Frobenius stable Grauert-Riemenschneider vanishing fails (日本語)

**Tatsuro Kawakami**(Kyoto University)Frobenius stable Grauert-Riemenschneider vanishing fails (日本語)

[ Abstract ]

We show that the Frobenius stable version of Grauert-Riemenschneider vanishing fails for a terminal 3-fold in characteristic 2. To prove this, we introduce the notion of $F_p$-rationality for singularities in positive characteristic, and prove that 3-dimensional klt singularities are $F_p$-rational. I will also talk about the vanishing of $F_p$-cohomologies of log Fano threefolds. This is joint work with Jefferson Baudin and Fabio Bernasconi.

We show that the Frobenius stable version of Grauert-Riemenschneider vanishing fails for a terminal 3-fold in characteristic 2. To prove this, we introduce the notion of $F_p$-rationality for singularities in positive characteristic, and prove that 3-dimensional klt singularities are $F_p$-rational. I will also talk about the vanishing of $F_p$-cohomologies of log Fano threefolds. This is joint work with Jefferson Baudin and Fabio Bernasconi.

#### Colloquium

15:30-16:30 Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)

Riemannian manifolds and their limit spaces (JAPANESE)

**Shouhei Honda**(Graduate School of Mathematical Sciences, University of Tokyo)Riemannian manifolds and their limit spaces (JAPANESE)

[ Abstract ]

The Gromov-Hausdorff (GH) distance defines a distance on the set A of all isometry classes of Riemannian manifolds. Gromov established a precompactness result with respect to the GH distance, under assuming a lower bound on Ricci curvature. In particular we are able to discuss limit nonsmooth spaces of Riemannian manifolds with Ricci curvature bounded below. In this talk, we explain recent developments about this topic.

The Gromov-Hausdorff (GH) distance defines a distance on the set A of all isometry classes of Riemannian manifolds. Gromov established a precompactness result with respect to the GH distance, under assuming a lower bound on Ricci curvature. In particular we are able to discuss limit nonsmooth spaces of Riemannian manifolds with Ricci curvature bounded below. In this talk, we explain recent developments about this topic.

### 2024/04/24

#### Numerical Analysis Seminar

16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Generalization analysis of neural networks based on Koopman operators

(Japanese)

[ Reference URL ]

https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/

**Yuka Hashimoto**(NTT Network Service Systems Laboratories)Generalization analysis of neural networks based on Koopman operators

(Japanese)

[ Reference URL ]

https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/

#### FJ-LMI Seminar

15:00-16:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Some aspects of Schrödinger models (英語)

https://fj-lmi.cnrs.fr/seminars/

**Laurent Di Menza**(Université de Reims Champagne-Ardenne, CNRS)Some aspects of Schrödinger models (英語)

[ Abstract ]

In this talk, we focus on basic facts about the Schrödinger equation that arises in various physical contexts, from quantum mechanics to gravita-tional systems. This kind of equation has been intensively studied in the literature and many properties are known, either from a qualitative and quantitative point of view. The goal of this presentation is to give basic properties of solutions in different regimes. A particular effort will be paid for the numerical computation of solitons that consist in solutions that propagate with shape invariance.

[ Reference URL ]In this talk, we focus on basic facts about the Schrödinger equation that arises in various physical contexts, from quantum mechanics to gravita-tional systems. This kind of equation has been intensively studied in the literature and many properties are known, either from a qualitative and quantitative point of view. The goal of this presentation is to give basic properties of solutions in different regimes. A particular effort will be paid for the numerical computation of solitons that consist in solutions that propagate with shape invariance.

https://fj-lmi.cnrs.fr/seminars/

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