## Seminar information archive

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

### 2023/08/07

#### Tokyo Probability Seminar

17:00-18:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Approximation of Random Variables by Elements that are independent of a given sigma algebra (English)

**Freddy Delbaen**(Professor emeritus at ETH Zurich)Approximation of Random Variables by Elements that are independent of a given sigma algebra (English)

[ Abstract ]

Given a square integrable m-dimensional random variable $X$ on a probability space $(\Omega,\mathcal{F},\mathbb{P})$ and a sub sigma algebra $\mathcal{A}$, we show that there exists another m-dimensional random variable $Y$, independent of $\mathcal{A}$ and minimising the $L^2$ distance to $X$. Such results have an importance to fairness and bias reduction in Artificial Intelligence, Machine Learning and Network Theory. The proof needs elements from transportation theory, a parametric version due to Dudley and Blackwell of the Skorohod theorem, selection theorems, … The problem also triggers other approximation problems. (joint work with C. Majumdar)

Given a square integrable m-dimensional random variable $X$ on a probability space $(\Omega,\mathcal{F},\mathbb{P})$ and a sub sigma algebra $\mathcal{A}$, we show that there exists another m-dimensional random variable $Y$, independent of $\mathcal{A}$ and minimising the $L^2$ distance to $X$. Such results have an importance to fairness and bias reduction in Artificial Intelligence, Machine Learning and Network Theory. The proof needs elements from transportation theory, a parametric version due to Dudley and Blackwell of the Skorohod theorem, selection theorems, … The problem also triggers other approximation problems. (joint work with C. Majumdar)

### 2023/07/31

#### Operator Algebra Seminars

16:45-18:15 Room #128 (Graduate School of Math. Sci. Bldg.)

Operator Algebras and Quantum Field Theory: introductory elements

[ Reference URL ]

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

**Roberto Longo**(Univ. Rome, ”Tor Vergata”)Operator Algebras and Quantum Field Theory: introductory elements

[ Reference URL ]

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

### 2023/07/28

#### Algebraic Geometry Seminar

13:30-15:00 Room #ハイブリッド開催/002 (Graduate School of Math. Sci. Bldg.)

TBA

**Shihoko Ishii**(The University of Tokyo)TBA

### 2023/07/21

#### Algebraic Geometry Seminar

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

The Demailly--Peternell--Schneider conjecture is true in positive characteristic

**Sho Ejiri**(Osaka Metropolitan University)The Demailly--Peternell--Schneider conjecture is true in positive characteristic

[ Abstract ]

In 1993, Demailly, Peternell and Schneider conjectured that the Albanese morphism of a compact K\"{a}hler manifold with nef anti-canonical divisor is surjective. For smooth projective varieties of characteristic zero, the conjecture was verified by Zhang in 1996. In positive characteristic, the conjecture was solved under the assumption that the geometric generic fiber F of the Albanese morphism has only mild singularities. However, F may have bad singularities even if we restrict ourselves to the case when the anti-canonical divisor is nef. In this talk, we prove the conjecture in positive characteristic without any extra assumption. We also discuss properties of the Albanese morphism, such as flatness or local isotriviality. This talk is based on joint work with Zsolt Patakfalvi.

In 1993, Demailly, Peternell and Schneider conjectured that the Albanese morphism of a compact K\"{a}hler manifold with nef anti-canonical divisor is surjective. For smooth projective varieties of characteristic zero, the conjecture was verified by Zhang in 1996. In positive characteristic, the conjecture was solved under the assumption that the geometric generic fiber F of the Albanese morphism has only mild singularities. However, F may have bad singularities even if we restrict ourselves to the case when the anti-canonical divisor is nef. In this talk, we prove the conjecture in positive characteristic without any extra assumption. We also discuss properties of the Albanese morphism, such as flatness or local isotriviality. This talk is based on joint work with Zsolt Patakfalvi.

#### 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 [Reference URL].

Quantum Field Theory in Mathematics (JAPANESE)

https://forms.gle/igR5ZB5AwginXBt49

If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].

**Masahito Yamazaki**(Kavli Institute for the Physics and Mathematics of the Uniiverse, the University of Tokyo)Quantum Field Theory in Mathematics (JAPANESE)

[ Abstract ]

While quantum field theory has primarily been a theory in physics, it has also been a source of new ideas in mathematics, and has facilitated interactions between different branches of mathematics. There have also been many attempts to formulate quantum field theories themselves rigorously in mathematics. In this lecture we will discuss some examples of research in knot invariants and integrable models, to illustrate the impact of quantum field theories and string theory in modern mathematics.

[ Reference URL ]While quantum field theory has primarily been a theory in physics, it has also been a source of new ideas in mathematics, and has facilitated interactions between different branches of mathematics. There have also been many attempts to formulate quantum field theories themselves rigorously in mathematics. In this lecture we will discuss some examples of research in knot invariants and integrable models, to illustrate the impact of quantum field theories and string theory in modern mathematics.

https://forms.gle/igR5ZB5AwginXBt49

### 2023/07/19

#### thesis presentations

9:15-10:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Graded modules associated with permissible C∞-divisors on tropical manifolds

(トロピカル多様体上の可容C∞因子に付随した次数付き加群)

**TSUTSUI Yuki**(Graduate School of Mathematical Sciences University of Tokyo)Graded modules associated with permissible C∞-divisors on tropical manifolds

(トロピカル多様体上の可容C∞因子に付随した次数付き加群)

#### thesis presentations

10:30-11:45 Room #117 (Graduate School of Math. Sci. Bldg.)

A regularity theory for perturbed singular elliptic and parabolic equations

(摂動特異楕円型および放物型方程式に対する正則性理論)

**TSUBOUCHI Shuntaro**( Graduate School of Mathematical Sciences University of Tokyo)A regularity theory for perturbed singular elliptic and parabolic equations

(摂動特異楕円型および放物型方程式に対する正則性理論)

#### thesis presentations

10:45-12:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Elliptic genera of complete intersection Calabi-Yau 17-folds in F4-Grassmannians

(F4型グラスマン多様体内の17次元完全交叉カラビ・ヤウ多様体の楕円種数)

**KOBAYASHI Kenta**(Graduate School of Mathematical Sciences University of Tokyo)Elliptic genera of complete intersection Calabi-Yau 17-folds in F4-Grassmannians

(F4型グラスマン多様体内の17次元完全交叉カラビ・ヤウ多様体の楕円種数)

### 2023/07/14

#### Tokyo-Nagoya Algebra Seminar

10:30-12:00 Online

Local Forms of Noncommutative Functions and Applications (English)

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

**Michael Wemyss**(University of Glasgow)Local Forms of Noncommutative Functions and Applications (English)

[ Abstract ]

This talk will explain how Arnold's results for commutative singularities can be extended into the noncommutative setting, with the main result being a classification of certain Jacobi algebras

arising from (complete) free algebras. This class includes finite dimensional Jacobi algebras, and also Jacobi algebras of GK dimension one, suitably interpreted. The surprising thing is that a classification should exist at all, and it is even more surprising that ADE enters.

I will spend most of my time explaining what the algebras are, what they classify, and how to intrinsically extract ADE information from them. At the end, I'll explain why I'm really interested in this problem, an update including results on different quivers, and the applications of the above classification to curve counting and birational geometry. This is joint work with Gavin Brown.

Meeting ID: 863 9598 8196

passcode: 423160

[ Reference URL ]This talk will explain how Arnold's results for commutative singularities can be extended into the noncommutative setting, with the main result being a classification of certain Jacobi algebras

arising from (complete) free algebras. This class includes finite dimensional Jacobi algebras, and also Jacobi algebras of GK dimension one, suitably interpreted. The surprising thing is that a classification should exist at all, and it is even more surprising that ADE enters.

I will spend most of my time explaining what the algebras are, what they classify, and how to intrinsically extract ADE information from them. At the end, I'll explain why I'm really interested in this problem, an update including results on different quivers, and the applications of the above classification to curve counting and birational geometry. This is joint work with Gavin Brown.

Meeting ID: 863 9598 8196

passcode: 423160

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

### 2023/07/13

#### Information Mathematics Seminar

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

Fully Homorphic Encryption and Functional Encryption (Japanese)

**Tatsuaki Okamoto**(NTT)Fully Homorphic Encryption and Functional Encryption (Japanese)

[ Abstract ]

Explanation of fully homorphic encryption and functional encryption

Explanation of fully homorphic encryption and functional encryption

#### Discrete mathematical modelling seminar

17:30-18:30 Online

This seminar will be held using Zoom. If you wish to participate, please contact R. Willox by email.

On the Painlevé XXV - Ermakov equation (English)

This seminar will be held using Zoom. If you wish to participate, please contact R. Willox by email.

**Galina Filipuk**(University of Warsaw)On the Painlevé XXV - Ermakov equation (English)

[ Abstract ]

We study a nonlinear second order ordinary differential equation which we call the Ermakov-Painlevé XXV equation since under certain restrictions on its coefficients it can be reduced to the Ermakov or the Painlevé XXV equation. The Ermakov-Painlevé XXV equation also arises from a generalized Riccati equation and the related third order linear differential equation via the Schwarzian derivative. Starting from the Riccati equation and the second-order element of the Riccati chain as the simplest examples of linearizable equations, by introducing a suitable change of variables, it is shown how the Schwarzian derivative represents a key tool in the construction of solutions. Two families of Bäcklund transformations, which link the linear and nonlinear equations under investigation, are obtained. Some analytical examples will be given and discussed.

The talk will be mainly based on the paper

S. Carillo, A. Chichurin, G. Filipuk, F. Zullo, Schwarzian derivative, Painleve XXV--Ermakov equation and Backlund transformations, accepted in Mathematische Nachrichten, https://doi.org/10.1002/mana.202200180, available at arXiv:2201.02267 [nlin.SI].

We study a nonlinear second order ordinary differential equation which we call the Ermakov-Painlevé XXV equation since under certain restrictions on its coefficients it can be reduced to the Ermakov or the Painlevé XXV equation. The Ermakov-Painlevé XXV equation also arises from a generalized Riccati equation and the related third order linear differential equation via the Schwarzian derivative. Starting from the Riccati equation and the second-order element of the Riccati chain as the simplest examples of linearizable equations, by introducing a suitable change of variables, it is shown how the Schwarzian derivative represents a key tool in the construction of solutions. Two families of Bäcklund transformations, which link the linear and nonlinear equations under investigation, are obtained. Some analytical examples will be given and discussed.

The talk will be mainly based on the paper

S. Carillo, A. Chichurin, G. Filipuk, F. Zullo, Schwarzian derivative, Painleve XXV--Ermakov equation and Backlund transformations, accepted in Mathematische Nachrichten, https://doi.org/10.1002/mana.202200180, available at arXiv:2201.02267 [nlin.SI].

### 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)

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