## Seminar information archive

Seminar information archive ～11/07｜Today's seminar 11/08 | Future seminars 11/09～

### 2023/07/11

#### Tuesday Seminar of Analysis

16:00-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Nodal solutions for a class of degenerate BVP’s (English)

https://forms.gle/S3VgMSWg9wUP69cY6

**Julian López-Gómez**(Complutense University of Madrid)Nodal solutions for a class of degenerate BVP’s (English)

[ Abstract ]

In this talk we characterize the existence of nodal solutions for a generalized class of one-dimensional diffusive logistic type equations, including

\[−u''=\lambda u−a(x)u^3,\quad x∈[0,L],\]

under the boundary conditions $u(0)=u(L)=0$, where $\lambda$ is regarded as a bifurcation parameter, and the non-negative weight function $a(x)$ vanishes on some subinterval

\[ [\alpha,\beta]\subset (0,L)\]

with $\alpha<\beta$.

At a later stage, the general case when $a(x)$ vanishes on finitely many subintervals with the same length is analyzed. Finally, we construct some examples with classical non-degenerate weights, with $a(x)>0$ for all $x∈[0,L]$, where the BVP has an arbitrarily large number of solutions with one node in $(0,L)$. These are the first examples of this nature constructed in the literature.

References:

P. Cubillos, J. López-Gómez and A. Tellini, Multiplicity of nodal solutions in classical non-degenerate logistic equations, El. Res. Archive 30 (2022), 898—928.

J. López-Gómez, M. Molina-Meyer and P. H. Rabinowitz, Global bifurcation diagrams of one-node solutions on a class of degenerate boundary value problems, Disc. Cont. Dyn. Syst. B 22 (2017), 923—946.

J. López-Gómez and P. H. Rabinowitz, Nodal solutions for a class of degenerate one dimensional BVP’s, Top. Meth. Nonl. Anal. 49 (2017), 359—376.

J. López-Gómez and P. H. Rabinowitz, The estructure of the set of 1-node solutions for a class of degenerate BVP’s, J. Differential Equations 268 (2020), 4691—4732.

P. H. Rabinowitz, A note on a anonlinear eigenvalue problem for a class of differential equations, J. Differential Equations 9 (1971), 536—548.

[ Reference URL ]In this talk we characterize the existence of nodal solutions for a generalized class of one-dimensional diffusive logistic type equations, including

\[−u''=\lambda u−a(x)u^3,\quad x∈[0,L],\]

under the boundary conditions $u(0)=u(L)=0$, where $\lambda$ is regarded as a bifurcation parameter, and the non-negative weight function $a(x)$ vanishes on some subinterval

\[ [\alpha,\beta]\subset (0,L)\]

with $\alpha<\beta$.

At a later stage, the general case when $a(x)$ vanishes on finitely many subintervals with the same length is analyzed. Finally, we construct some examples with classical non-degenerate weights, with $a(x)>0$ for all $x∈[0,L]$, where the BVP has an arbitrarily large number of solutions with one node in $(0,L)$. These are the first examples of this nature constructed in the literature.

References:

P. Cubillos, J. López-Gómez and A. Tellini, Multiplicity of nodal solutions in classical non-degenerate logistic equations, El. Res. Archive 30 (2022), 898—928.

J. López-Gómez, M. Molina-Meyer and P. H. Rabinowitz, Global bifurcation diagrams of one-node solutions on a class of degenerate boundary value problems, Disc. Cont. Dyn. Syst. B 22 (2017), 923—946.

J. López-Gómez and P. H. Rabinowitz, Nodal solutions for a class of degenerate one dimensional BVP’s, Top. Meth. Nonl. Anal. 49 (2017), 359—376.

J. López-Gómez and P. H. Rabinowitz, The estructure of the set of 1-node solutions for a class of degenerate BVP’s, J. Differential Equations 268 (2020), 4691—4732.

P. H. Rabinowitz, A note on a anonlinear eigenvalue problem for a class of differential equations, J. Differential Equations 9 (1971), 536—548.

https://forms.gle/S3VgMSWg9wUP69cY6

### 2023/07/10

#### Seminar on Geometric Complex Analysis

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

Degenerations of Riemann surfaces and small eigenvalues of the Laplacian (日本語)

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A

**Ken-Ichi Yoshikawa**(Kyoto University)Degenerations of Riemann surfaces and small eigenvalues of the Laplacian (日本語)

[ Abstract ]

In this talk, we consider a proper surjective holomorphic map from a smooth projective surface to a compact Riemann surface. Near a singular fiber, this is viewed as a one-parameter degeneration of compact Riemann surfaces. We fix a Kähler metric on the projective surface and consider the Kähler metric on the fibers induced from this metric. In this setting, for each regular fiber, we can consider the Laplacian acting on the functions on the fiber. It is known that for any k, the k-th eigenvalue of the Laplacian extends to a continuous function on the base curve. In particular, if the singular fiber is not irreducible, some eigenvalues of the Laplacian of the regular fiber converge to zero as the regular fiber approaches to the singular fiber. We call such eigenvalues small eigenvalues. In this talk, when the singular fiber is reduced, we will explain the asymptotic behavior of the product of all small eigenvalues of the Laplacian.

[ Reference URL ]In this talk, we consider a proper surjective holomorphic map from a smooth projective surface to a compact Riemann surface. Near a singular fiber, this is viewed as a one-parameter degeneration of compact Riemann surfaces. We fix a Kähler metric on the projective surface and consider the Kähler metric on the fibers induced from this metric. In this setting, for each regular fiber, we can consider the Laplacian acting on the functions on the fiber. It is known that for any k, the k-th eigenvalue of the Laplacian extends to a continuous function on the base curve. In particular, if the singular fiber is not irreducible, some eigenvalues of the Laplacian of the regular fiber converge to zero as the regular fiber approaches to the singular fiber. We call such eigenvalues small eigenvalues. In this talk, when the singular fiber is reduced, we will explain the asymptotic behavior of the product of all small eigenvalues of the Laplacian.

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A

#### Tokyo Probability Seminar

17:00-18:30 Room #126 (Graduate School of Math. Sci. Bldg.)

孤立量子系の熱化と緩和 (日本語)

**松井 千尋**(東京大学大学院数理科学研究科)孤立量子系の熱化と緩和 (日本語)

### 2023/07/07

#### Tokyo-Nagoya Algebra Seminar

15:00-16:30 Online

クイバー表現のパーシステンス加群への応用: 区間加群による近似と分解 (Japanese)

[ Reference URL ]

http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html

**Hideto Asashiba**(Shizuoka University, Kyoto University, Osaka Metropolitan University)クイバー表現のパーシステンス加群への応用: 区間加群による近似と分解 (Japanese)

[ Reference URL ]

http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html

### 2023/07/06

#### Information Mathematics Seminar

16:50-18:35 Room #128 (Graduate School of Math. Sci. Bldg.)

Cryptographic protocols (Japanese)

**Tatsuaki Okamoto**(NTT)Cryptographic protocols (Japanese)

[ Abstract ]

Explanation of cryptographic protocols

Explanation of cryptographic protocols

### 2023/07/05

#### Number Theory Seminar

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

Duality for motivic cohomology over local fields and applications to class field theory. (English)

**Thomas Geisser**(Rikkyo University)Duality for motivic cohomology over local fields and applications to class field theory. (English)

[ Abstract ]

We give an outline a (conjectural) construction of cohomology groups for smooth and proper varieties over local fields with values in the heart of the derived category of locally compact groups.

This theory should satisfy a Pontrjagin duality theorem, and for certain weights, we give an ad hoc construction which satisfies such a duality unconditionally.

As an application we discuss class field theory for smooth and proper varieties over local fields.

We give an outline a (conjectural) construction of cohomology groups for smooth and proper varieties over local fields with values in the heart of the derived category of locally compact groups.

This theory should satisfy a Pontrjagin duality theorem, and for certain weights, we give an ad hoc construction which satisfies such a duality unconditionally.

As an application we discuss class field theory for smooth and proper varieties over local fields.

### 2023/07/04

#### Tuesday Seminar on Topology

17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)

Pre-registration required. See our seminar webpage.

Reciprocity of the Chern-Simons invariants of 3-manifolds (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Takefumi Nosaka**(Tokyo Institute of Technology)Reciprocity of the Chern-Simons invariants of 3-manifolds (JAPANESE)

[ Abstract ]

Given an oriented closed 3-manifold $M$ and a representation $\pi_1(M) \longrightarrow SL_2(\mathbb{C})$, we can define the Chern-Simons invariant and adjoint Reidemeister torsion. Recently, several physicists and topologists pose and study reciprocity conjectures of the torsions. Analogously, I pose reciprocity conjectures of the Chern-Simons invariants of 3-manifolds, and argue some supporting evidence on the conjectures. Especially, I show that the conjectures hold if Galois descent of a certain $K_3$-group is satisfied. In this talk, I will explain the backgrounds and the results in detail.

[ Reference URL ]Given an oriented closed 3-manifold $M$ and a representation $\pi_1(M) \longrightarrow SL_2(\mathbb{C})$, we can define the Chern-Simons invariant and adjoint Reidemeister torsion. Recently, several physicists and topologists pose and study reciprocity conjectures of the torsions. Analogously, I pose reciprocity conjectures of the Chern-Simons invariants of 3-manifolds, and argue some supporting evidence on the conjectures. Especially, I show that the conjectures hold if Galois descent of a certain $K_3$-group is satisfied. In this talk, I will explain the backgrounds and the results in detail.

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

### 2023/07/03

#### Seminar on Geometric Complex Analysis

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

Hyperbolicity and fundamental groups of complex quasi-projective varieties

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A

**Katsutoshi Yamanoi**(Osaka University)Hyperbolicity and fundamental groups of complex quasi-projective varieties

[ Abstract ]

This talk is based on a joint work with Benoit Cadorel and Ya Deng. arXiv:2212.12225

[ Reference URL ]This talk is based on a joint work with Benoit Cadorel and Ya Deng. arXiv:2212.12225

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A

### 2023/06/30

#### Colloquium

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

If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at https://forms.gle/z22nKn1NUrT41qiR7

Did you say $p$-adic? (English)

If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at https://forms.gle/z22nKn1NUrT41qiR7

**Guy Henniart**(Université Paris-Saclay)Did you say $p$-adic? (English)

[ Abstract ]

I am a Number Theorist and $p$ is a prime number. The $p$-adic numbers are obtained by pushing to the limit a simple idea. Suppose that you want to know which integers are sums of two squares. If an integer $x$ is odd, its square has the form $8k+1$; if $x$ is even, its square is a multiple of $4$. So the sum of two squares has the form $4k$, $4k+1$ or $4k+2$, never $4k+3$ ! More generally if a polynomial equation with integer coefficients has no integer solution if you work «modulo $N$» that is you neglect all multiples of an integer $N$, then a fortiori it has no integer solution. By the Chinese Remainder Theorem, working modulo $N$ is the same as working modulo $p^r$ where $p$ runs through prime divisors of $N$ and $p^r$ is the highest power of $p$ dividing $N$. Now work modulo $p$, modulo $p^2$, modulo $p^3$, etc. You have invented the $p$-adic integers, which are, I claim, as real as the real numbers and (nearly) as useful!

I am a Number Theorist and $p$ is a prime number. The $p$-adic numbers are obtained by pushing to the limit a simple idea. Suppose that you want to know which integers are sums of two squares. If an integer $x$ is odd, its square has the form $8k+1$; if $x$ is even, its square is a multiple of $4$. So the sum of two squares has the form $4k$, $4k+1$ or $4k+2$, never $4k+3$ ! More generally if a polynomial equation with integer coefficients has no integer solution if you work «modulo $N$» that is you neglect all multiples of an integer $N$, then a fortiori it has no integer solution. By the Chinese Remainder Theorem, working modulo $N$ is the same as working modulo $p^r$ where $p$ runs through prime divisors of $N$ and $p^r$ is the highest power of $p$ dividing $N$. Now work modulo $p$, modulo $p^2$, modulo $p^3$, etc. You have invented the $p$-adic integers, which are, I claim, as real as the real numbers and (nearly) as useful!

### 2023/06/29

#### Information Mathematics Seminar

16:50-18:35 Room #128 (Graduate School of Math. Sci. Bldg.)

Zero-knowledge proofs (Japanese)

**Tatsuaki Okamoto**(NTT)Zero-knowledge proofs (Japanese)

[ Abstract ]

Explanation of the theory of zero-knowledge proofs

Explanation of the theory of zero-knowledge proofs

### 2023/06/28

#### Algebraic Geometry Seminar

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

Preimages question and dynamical cancellation

**Yohsuke Matsuzawa**(Osaka Metropolitan University)Preimages question and dynamical cancellation

[ Abstract ]

Pulling back an invariant subvariety by a self-morphism on projective variety, you will get a tower of increasing closed subsets. Working over a number field, we expect that the set of rational points contained in this increasing subsets eventually stabilizes. I am planning to discuss several results on this problem, such as the case of etale morphisms, morphisms on the product of two P^1. I will also present some counter examples that occur when we drop some of the assumptions. This work is based on a joint work with Matt Satriano and Jason Bell, and recent work in progress with Kaoru Sano.

Pulling back an invariant subvariety by a self-morphism on projective variety, you will get a tower of increasing closed subsets. Working over a number field, we expect that the set of rational points contained in this increasing subsets eventually stabilizes. I am planning to discuss several results on this problem, such as the case of etale morphisms, morphisms on the product of two P^1. I will also present some counter examples that occur when we drop some of the assumptions. This work is based on a joint work with Matt Satriano and Jason Bell, and recent work in progress with Kaoru Sano.

#### Number Theory Seminar

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

The integral models of the RSZ Shimura varieties (日本語)

**Yuta Nakayama**(University of Tokyo)The integral models of the RSZ Shimura varieties (日本語)

[ Abstract ]

We prove that the integral models of Shimura varieties by Rapoport, Smithling and Zhang proposed to describe variants of the arithmetic Gan–Gross–Prasad conjecture are isomorphic to the models by Pappas and Rapoport. This extends our previous work that compares the former models and the Kisin–Pappas models. We rely on the construction of the models of Pappas and Rapoport, not on their characterization.

We prove that the integral models of Shimura varieties by Rapoport, Smithling and Zhang proposed to describe variants of the arithmetic Gan–Gross–Prasad conjecture are isomorphic to the models by Pappas and Rapoport. This extends our previous work that compares the former models and the Kisin–Pappas models. We rely on the construction of the models of Pappas and Rapoport, not on their characterization.

### 2023/06/27

#### Numerical Analysis Seminar

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

Solving high-dimensional partial differential equations via deep learning and probabilistic methods (Japanese)

[ Reference URL ]

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

**Toshihiro Yamada**(Hitotsubashi University)Solving high-dimensional partial differential equations via deep learning and probabilistic methods (Japanese)

[ Reference URL ]

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

### 2023/06/26

#### Tokyo Probability Seminar

17:00-18:30 Room #126 (Graduate School of Math. Sci. Bldg.)

δ次元Bessel引越過程の構成方法，サンプルパス生成方法，および汎関数期待値の数値計算法について (日本語)

**簗島 瞬**(東京都立大学)δ次元Bessel引越過程の構成方法，サンプルパス生成方法，および汎関数期待値の数値計算法について (日本語)

#### Seminar on Geometric Complex Analysis

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

Miyaoka type inequality for terminal weak Fano varieties

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A

**Masataka IWAI**(Osaka Univeristy)Miyaoka type inequality for terminal weak Fano varieties

[ Abstract ]

In this talk, we show that $c_2(X)c_1(X)^{n-2}$ is positive for any $n$-dimensional terminal weak Fano varieties $X$. As a corollary, we obtain some inequalities (Miyaoka type inequalities) with respect to $c_2(X)c_1(X)^{n-2}$ and $c_1(X)^{n}$. This is joint work with Chen Jiang and Haidong Liu (arXiv:2303.00268).

[ Reference URL ]In this talk, we show that $c_2(X)c_1(X)^{n-2}$ is positive for any $n$-dimensional terminal weak Fano varieties $X$. As a corollary, we obtain some inequalities (Miyaoka type inequalities) with respect to $c_2(X)c_1(X)^{n-2}$ and $c_1(X)^{n}$. This is joint work with Chen Jiang and Haidong Liu (arXiv:2303.00268).

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A

### 2023/06/23

#### Algebraic Geometry Seminar

13:30-15:00 Room #ハイブリッド開催/117 (Graduate School of Math. Sci. Bldg.)

Minimal log discrepnacies for quotient singularities

**Kohsuke Shibata**(Tokyo Denki University)Minimal log discrepnacies for quotient singularities

[ Abstract ]

In this talk, I will discuss recent joint work with Yusuke Nakamura on minimal log discrepancies for quotient singularities. The minimal log discrepancy is an important invariant of singularities in birational geometry. The denominator of the minimal log discrepancy of a variety depends on the Gorenstein index. On the other hand, Shokurov conjectured that the Gorenstein index of a Q-Gorenstein germ can be bounded in terms of its dimension and minimal log discrepancy. In this talk, I will explain basic properties for quotient singularities and show Shokurov's index conjecture for quotient singularities.

In this talk, I will discuss recent joint work with Yusuke Nakamura on minimal log discrepancies for quotient singularities. The minimal log discrepancy is an important invariant of singularities in birational geometry. The denominator of the minimal log discrepancy of a variety depends on the Gorenstein index. On the other hand, Shokurov conjectured that the Gorenstein index of a Q-Gorenstein germ can be bounded in terms of its dimension and minimal log discrepancy. In this talk, I will explain basic properties for quotient singularities and show Shokurov's index conjecture for quotient singularities.

### 2023/06/22

#### Applied Analysis

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

Convergence rate of periodic homogenization of forced mean curvature flow of graphs in the laminar setting (English)

https://forms.gle/BTuFtcmUVnvCLieX9

**Jiwoong Jang**(University of Wisconsin Madison)Convergence rate of periodic homogenization of forced mean curvature flow of graphs in the laminar setting (English)

[ Abstract ]

Mean curvature flow with a forcing term models the motion of a phase boundary through media with defects and heterogeneities. When the environment shows periodic patterns with small oscillations, an averaged behavior is exhibited as we zoom out, and providing mathematical treatment for the behavior has received a great attention recently. In this talk, we discuss the periodic homogenization of forced mean curvature flows, and we give a quantitative analysis for the flow starting from an entire graph in a laminated environment.

[ Reference URL ]Mean curvature flow with a forcing term models the motion of a phase boundary through media with defects and heterogeneities. When the environment shows periodic patterns with small oscillations, an averaged behavior is exhibited as we zoom out, and providing mathematical treatment for the behavior has received a great attention recently. In this talk, we discuss the periodic homogenization of forced mean curvature flows, and we give a quantitative analysis for the flow starting from an entire graph in a laminated environment.

https://forms.gle/BTuFtcmUVnvCLieX9

#### Information Mathematics Seminar

16:50-18:35 Room #128 (Graduate School of Math. Sci. Bldg.)

Lattice-based cryptography (Japanese)

**Tatsuaki Okamoto**(NTT)Lattice-based cryptography (Japanese)

[ Abstract ]

Explanation of lattice-based cryptography

Explanation of lattice-based cryptography

### 2023/06/21

#### Number Theory Seminar

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

On moduli of principal bundles under non-connected reductive groups (英語)

**Stefan Reppen**(Stockholm University)On moduli of principal bundles under non-connected reductive groups (英語)

[ Abstract ]

Let $C$ be a smooth, connected projective curve over an algebraically closed field $k$ of characteristic 0, and let $G$ be a non-connected reductive group over $k$. I will explain how to decompose the stack of $G$-bundles $\text{Bun}_G$ into open and closed substacks $X_i$ which admits finite torsors $\text{Bun}_{\mathcal{G}_i} \to X_i$, for some connected reductive group schemes $\mathcal{G}_i$ over $C$. I explain how to use this to obtain a projective good moduli space of semistable $G$-bundles over $C$, for a suitable notion of semistability. Finally, after stating a result concerning finite subgroups of connected reductive groups over $k$, I explain how to see that essentially finite $H$-bundles are not dense in the moduli space of semistable degree 0 $H$-bundles, for any connected reductive group $H$ not equal to a torus.

Let $C$ be a smooth, connected projective curve over an algebraically closed field $k$ of characteristic 0, and let $G$ be a non-connected reductive group over $k$. I will explain how to decompose the stack of $G$-bundles $\text{Bun}_G$ into open and closed substacks $X_i$ which admits finite torsors $\text{Bun}_{\mathcal{G}_i} \to X_i$, for some connected reductive group schemes $\mathcal{G}_i$ over $C$. I explain how to use this to obtain a projective good moduli space of semistable $G$-bundles over $C$, for a suitable notion of semistability. Finally, after stating a result concerning finite subgroups of connected reductive groups over $k$, I explain how to see that essentially finite $H$-bundles are not dense in the moduli space of semistable degree 0 $H$-bundles, for any connected reductive group $H$ not equal to a torus.

### 2023/06/20

#### Tuesday Seminar on Topology

17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)

Pre-registration required. See our seminar webpage.

Moduli spaces of triangle chains (ENGLISH)

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

Pre-registration required. See our seminar webpage.

**Arnaud Maret**(Sorbonne Université)Moduli spaces of triangle chains (ENGLISH)

[ Abstract ]

In this talk, I will describe a moduli space of triangle chains in the hyperbolic plane with prescribed angles. We will relate this moduli space to a specific character variety of representations of surface groups into PSL(2,R). This identification provides action-angle coordinates for the Goldman symplectic form on the character variety. If time permits, I will explain why the mapping class group action on that particular character variety is ergodic.

[ Reference URL ]In this talk, I will describe a moduli space of triangle chains in the hyperbolic plane with prescribed angles. We will relate this moduli space to a specific character variety of representations of surface groups into PSL(2,R). This identification provides action-angle coordinates for the Goldman symplectic form on the character variety. If time permits, I will explain why the mapping class group action on that particular character variety is ergodic.

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

### 2023/06/19

#### Seminar on Geometric Complex Analysis

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

A new construction method for 3-dimensional indefinite Zoll manifolds

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A

**Nobuhiro Honda**(Tokyo University of Technology)A new construction method for 3-dimensional indefinite Zoll manifolds

[ Abstract ]

The Penrose correspondence gives correspondences between special geometric structures on manifolds and complex manifolds, one of which is between Einstein-Weyl structures on 3-manifolds and complex surfaces. The latter complex surfaces are called mini-Twister spaces. In this talk, I will show that compact mini-Zeister spaces can be constructed in a natural way from hyperelliptic curves of arbitrary species, and that the resulting 3-manifolds have a remarkable geometric property called the Zoll property, which means that all geodesics are closed. A typical example is a sphere. The three-dimensional Einstein-Weyl manifold obtained in this study is indefinite, and the geodesics considered are spatial. These Einstein-Weyl manifolds can be regarded as generalizations of those given in arXiv:2208.13567.

Translated with www.DeepL.com/Translator (free version)

[ Reference URL ]The Penrose correspondence gives correspondences between special geometric structures on manifolds and complex manifolds, one of which is between Einstein-Weyl structures on 3-manifolds and complex surfaces. The latter complex surfaces are called mini-Twister spaces. In this talk, I will show that compact mini-Zeister spaces can be constructed in a natural way from hyperelliptic curves of arbitrary species, and that the resulting 3-manifolds have a remarkable geometric property called the Zoll property, which means that all geodesics are closed. A typical example is a sphere. The three-dimensional Einstein-Weyl manifold obtained in this study is indefinite, and the geodesics considered are spatial. These Einstein-Weyl manifolds can be regarded as generalizations of those given in arXiv:2208.13567.

Translated with www.DeepL.com/Translator (free version)

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A

### 2023/06/15

#### Information Mathematics Seminar

16:50-18:35 Room #128 (Graduate School of Math. Sci. Bldg.)

Cryptosystems based on elliptic curves (Japanese)

**Tatsuaki Okamoto**(NTT)Cryptosystems based on elliptic curves (Japanese)

[ Abstract ]

Explanation of crypto-systems based on elliptic curves

Explanation of crypto-systems based on elliptic curves

### 2023/06/14

#### Algebraic Geometry Seminar

14:00-15:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)

Vanishing of local cohomology modules

**Wenliang Zhang**(University of Illinois Chicago)Vanishing of local cohomology modules

[ Abstract ]

Studying the vanishing of local cohomology modules has a long and rich history, and is still an active research area. In this talk, we will discuss classic theorems (due to Grothendieck, Hartshorne, Peskine-Szpiro, and Ogus), recent developments, and some open problems.

Studying the vanishing of local cohomology modules has a long and rich history, and is still an active research area. In this talk, we will discuss classic theorems (due to Grothendieck, Hartshorne, Peskine-Szpiro, and Ogus), recent developments, and some open problems.

### 2023/06/13

#### Operator Algebra Seminars

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

Around homogeneous spaces of complex semisimple quantum groups

[ Reference URL ]

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

**Kan Kitamura**(Univ. Tokyo)Around homogeneous spaces of complex semisimple quantum groups

[ Reference URL ]

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

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

On a lower bound of the number of integers in Littlewood's conjecture (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Shunsuke Usuki**(Kyoto University)On a lower bound of the number of integers in Littlewood's conjecture (JAPANESE)

[ Abstract ]

Littlewood's conjecture is a famous and long-standing open problem on simultaneous Diophantine approximation. It is closely related to the action of diagonal matrices on ${\rm SL}(3,\mathbb{R})/{\rm SL}(3,\mathbb{Z})$, and M. Einsiedler, A. Katok and E. Lindenstrauss showed in 2000's that the exceptional set for Littlewood's conjecture has Hausdorff dimension zero by using some rigidity for invariant measures under the diagonal action. In this talk, I explain that we can obtain some quantitative result on the result of Einsiedler, Katok and Lindenstrauss by studying the empirical measures with respect to the diagonal action.

[ Reference URL ]Littlewood's conjecture is a famous and long-standing open problem on simultaneous Diophantine approximation. It is closely related to the action of diagonal matrices on ${\rm SL}(3,\mathbb{R})/{\rm SL}(3,\mathbb{Z})$, and M. Einsiedler, A. Katok and E. Lindenstrauss showed in 2000's that the exceptional set for Littlewood's conjecture has Hausdorff dimension zero by using some rigidity for invariant measures under the diagonal action. In this talk, I explain that we can obtain some quantitative result on the result of Einsiedler, Katok and Lindenstrauss by studying the empirical measures with respect to the diagonal action.

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

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