## Seminar information archive

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

#### Lie Groups and Representation Theory

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

Discrete branching laws of derived functor modules (Japanese)

**Yoshiki Oshima**(The University of Tokyo)Discrete branching laws of derived functor modules (Japanese)

[ Abstract ]

We consider the restriction of Zuckerman's derived functor modules for symmetric pairs of real reductive groups assuming that it is discretely decomposable in the sense of Kobayashi. By using a classification result, it can be shown that the restriction decomposes as a direct sum of Zuckerman's derived functor modules for the subgroup. In this talk, we would like to discuss how to obtain explicit branching formulas for some examples.

We consider the restriction of Zuckerman's derived functor modules for symmetric pairs of real reductive groups assuming that it is discretely decomposable in the sense of Kobayashi. By using a classification result, it can be shown that the restriction decomposes as a direct sum of Zuckerman's derived functor modules for the subgroup. In this talk, we would like to discuss how to obtain explicit branching formulas for some examples.

### 2023/05/29

#### Seminar on Geometric Complex Analysis

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

On dynamical degrees of birational maps

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

**Takato UEHARA**(Okayama University)On dynamical degrees of birational maps

[ Abstract ]

A birational map on a projective surface defines its dynamical degree, which measures the complexity of dynamical behavior of the map. The set of dynamical degrees, called the dynamical spectrum, has properties similar to that of volumes of hyperbolic 3-manifolds, shown by Thurston. In this talk, we will explain the properties of the dynamical spectrum.

[ Reference URL ]A birational map on a projective surface defines its dynamical degree, which measures the complexity of dynamical behavior of the map. The set of dynamical degrees, called the dynamical spectrum, has properties similar to that of volumes of hyperbolic 3-manifolds, shown by Thurston. In this talk, we will explain the properties of the dynamical spectrum.

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

### 2023/05/26

#### Algebraic Geometry Seminar

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

Varieties in positive characteristic with numerically flat tangent bundle

**Shou Yoshikawa**(Tokyo Institute of Technology, RIKEN)Varieties in positive characteristic with numerically flat tangent bundle

[ Abstract ]

The positivity condition imposed on the tangent bundle of a smooth projective variety is known to restrict the geometric structure of the variety. Demailly, Peternell and Schneider established a decomposition theorem for a smooth projective complex variety with nef tangent bundle. The theorem states that, up to an etale cover, such a variety has a smooth fibration admitting a smooth algebraic fiber space over an abelian variety whose fibers are Fano varieties, so one can say that such a variety decomposes into the "positive” part and the "flat” part. A positive characteristic analog of the above decomposition theorem was proved by Kanemitsu and Watanabe. The "flat” part of their theorem is a smooth projective variety with numerically flat tangent bundle. In this talk, I will introduce the result that every ordinary variety with numerically flat tangent bundle is an etale quotient of an ordinary Abelian variety. In particular, we obtain the decomposition theorem for Frobenius splitting varieties with nef tangent bundle. This talk is based on joint work with Sho Ejiri.

The positivity condition imposed on the tangent bundle of a smooth projective variety is known to restrict the geometric structure of the variety. Demailly, Peternell and Schneider established a decomposition theorem for a smooth projective complex variety with nef tangent bundle. The theorem states that, up to an etale cover, such a variety has a smooth fibration admitting a smooth algebraic fiber space over an abelian variety whose fibers are Fano varieties, so one can say that such a variety decomposes into the "positive” part and the "flat” part. A positive characteristic analog of the above decomposition theorem was proved by Kanemitsu and Watanabe. The "flat” part of their theorem is a smooth projective variety with numerically flat tangent bundle. In this talk, I will introduce the result that every ordinary variety with numerically flat tangent bundle is an etale quotient of an ordinary Abelian variety. In particular, we obtain the decomposition theorem for Frobenius splitting varieties with nef tangent bundle. This talk is based on joint work with Sho Ejiri.

### 2023/05/25

#### Information Mathematics Seminar

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

Security, construction, and proof of public-key encryption (2) (Japanese)

**Tatsuaki Okamoto**(NTT)Security, construction, and proof of public-key encryption (2) (Japanese)

[ Abstract ]

Explanation of security, construction and proof of public-key encryption

Explanation of security, construction and proof of public-key encryption

### 2023/05/23

#### Numerical Analysis Seminar

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

Theory of Deep Learning and Over-Parameterization (Japanese)

[ Reference URL ]

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

**Masaaki Imaizumi**(The University of Tokyo)Theory of Deep Learning and Over-Parameterization (Japanese)

[ Reference URL ]

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

#### Operator Algebra Seminars

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

Magnetic monopole and domain-wall fermion Dirac operator (English)

[ Reference URL ]

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

**Hidenori Fukaya**(Osaka University)Magnetic monopole and domain-wall fermion Dirac operator (English)

[ Reference URL ]

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

#### Lie Groups and Representation Theory

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

Deformation of the heat kernel and the Wiener measure from the viewpoint of Laguerre semigroup theory (Japanese)

**Temma Aoyama**(The University of Tokyo)Deformation of the heat kernel and the Wiener measure from the viewpoint of Laguerre semigroup theory (Japanese)

[ Abstract ]

I talk about basic properties of generalized heat kernels and a construction of generalized Wiener measures form the viewpoint of Laguerre semigroup theory and generalized Fourier analysis introduced by B. Saïd--T. Kobayashi--B. Ørsted.

I talk about basic properties of generalized heat kernels and a construction of generalized Wiener measures form the viewpoint of Laguerre semigroup theory and generalized Fourier analysis introduced by B. Saïd--T. Kobayashi--B. Ørsted.

### 2023/05/22

#### Seminar on Geometric Complex Analysis

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

A residue formula for meromorphic connections and applications to stable sets of foliations

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

**Masanari Adachi**(Shizuoka Univeristy)A residue formula for meromorphic connections and applications to stable sets of foliations

[ Abstract ]

We discuss a proof for Brunella’s conjecture: a codimension one holomorphic foliation on a compact complex manifold of dimension > 2 has no exceptional minimal set if its normal bundle is ample. The main idea is the localization of the first Chern class of the normal bundle of the foliation via a holomorphic connection. Although this localization was done via that of the first Atiyah class in our previous proof, we shall explain that this can be shown more directly by a residue formula. If time permits, we also discuss a nonexistence result of Levi flat hypersurfaces with transversely affine Levi foliation. This talk is based on joint works

with S. Biard and J. Brinkschulte.

[ Reference URL ]We discuss a proof for Brunella’s conjecture: a codimension one holomorphic foliation on a compact complex manifold of dimension > 2 has no exceptional minimal set if its normal bundle is ample. The main idea is the localization of the first Chern class of the normal bundle of the foliation via a holomorphic connection. Although this localization was done via that of the first Atiyah class in our previous proof, we shall explain that this can be shown more directly by a residue formula. If time permits, we also discuss a nonexistence result of Levi flat hypersurfaces with transversely affine Levi foliation. This talk is based on joint works

with S. Biard and J. Brinkschulte.

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

### 2023/05/19

#### Colloquium

15:30-16:30 Room #大講義室 (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/J4Wo8N6CbLmYiprUA.

Locally stable regression (日本語)

If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at https://forms.gle/J4Wo8N6CbLmYiprUA.

**Hiroki Masuda**(Graduate School of Mathematical Sciences, the University of Tokyo)Locally stable regression (日本語)

[ Abstract ]

A non-ergodic model structure naturally emerges in estimating a stochastic process model observed at high frequency over a fixed period. The probability structure of the driving noise determines whether or not the characteristics of the model can be statistically estimated. However, it is difficult to describe the possible phenomena in general when the noise is non-Gaussian. Building on such backgrounds, we will present some recent results on non-ergodic regression modeling driven by a locally stable Lévy process: the construction of an explicit non-Gaussian quasi-maximum likelihood and the asymptotic distribution of the corresponding estimator. We will also present a method for relative model comparison and its theoretical property.

A non-ergodic model structure naturally emerges in estimating a stochastic process model observed at high frequency over a fixed period. The probability structure of the driving noise determines whether or not the characteristics of the model can be statistically estimated. However, it is difficult to describe the possible phenomena in general when the noise is non-Gaussian. Building on such backgrounds, we will present some recent results on non-ergodic regression modeling driven by a locally stable Lévy process: the construction of an explicit non-Gaussian quasi-maximum likelihood and the asymptotic distribution of the corresponding estimator. We will also present a method for relative model comparison and its theoretical property.

### 2023/05/18

#### Applied Analysis

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

On the wellposedness of generalized SQG equation in a half-plane (English)

https://forms.gle/Cezz3sicY7izDPfq8

**Junha Kim**(Korea Institute for Advanced Study)On the wellposedness of generalized SQG equation in a half-plane (English)

[ Abstract ]

In this talk, we investigate classical solutions to the $\alpha$-SQG in a half-plane, which reduces to the 2D Euler equations and SQG equation for $\alpha=0$ and $\alpha=1$, respectively. When $\alpha \in (0,1/2]$, we establish that $\alpha$-SQG is well-posed in appropriate anisotropic Lipschitz spaces. Moreover, we prove that every solution with smooth initial data that is compactly supported and not vanishing on the boundary has infinite $C^{\beta}$-norm instantaneously where $\beta > 1-\alpha$. In the case of $\alpha \in (1/2,1]$, we show the nonexistence of solutions in $C^{\alpha}$. This is a joint work with In-Jee Jeong and Yao Yao.

[ Reference URL ]In this talk, we investigate classical solutions to the $\alpha$-SQG in a half-plane, which reduces to the 2D Euler equations and SQG equation for $\alpha=0$ and $\alpha=1$, respectively. When $\alpha \in (0,1/2]$, we establish that $\alpha$-SQG is well-posed in appropriate anisotropic Lipschitz spaces. Moreover, we prove that every solution with smooth initial data that is compactly supported and not vanishing on the boundary has infinite $C^{\beta}$-norm instantaneously where $\beta > 1-\alpha$. In the case of $\alpha \in (1/2,1]$, we show the nonexistence of solutions in $C^{\alpha}$. This is a joint work with In-Jee Jeong and Yao Yao.

https://forms.gle/Cezz3sicY7izDPfq8

#### Information Mathematics Seminar

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

Security, construction, and proof of public-key encryption (1) (Japanese)

**Tatsuaki Okamoto**(NTT)Security, construction, and proof of public-key encryption (1) (Japanese)

[ Abstract ]

Explanation on security, construction, and proof of public-key encryption

Explanation on security, construction, and proof of public-key encryption

### 2023/05/17

#### Number Theory Seminar

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

Indecomposable higher Chow cycles on Kummer surfaces (日本語)

**Ken Sato**(Tokyo Institute of Technology)Indecomposable higher Chow cycles on Kummer surfaces (日本語)

[ Abstract ]

The higher Chow group $\mathrm{CH}^p(X,q)$ introduced by Bloch is a generalization of the classical Chow groups. It satisfies many interesting properties, but its structure is still mysterious for almost all varieties when $p$ is greater than 1. In this talk, I will explain the explicit construction of higher Chow cycles in $\mathrm{CH}^2(X,1)$ on a family of Kummer surfaces. By computing their images under the Beilinson regulator map, in very general cases, these cycles generate at least rank 18 subgroup of $\mathrm{CH}^2(X,1)_{\mathrm{ind}}$, which is the quotient of $\mathrm{CH}^2(X,1)$ by the images of the intersection product maps. To compute the images under the regulator map, we use automorphisms of the family and the explicit description of the action of the automorphisms on the Picard-Fuchs differential equations of the family.

The higher Chow group $\mathrm{CH}^p(X,q)$ introduced by Bloch is a generalization of the classical Chow groups. It satisfies many interesting properties, but its structure is still mysterious for almost all varieties when $p$ is greater than 1. In this talk, I will explain the explicit construction of higher Chow cycles in $\mathrm{CH}^2(X,1)$ on a family of Kummer surfaces. By computing their images under the Beilinson regulator map, in very general cases, these cycles generate at least rank 18 subgroup of $\mathrm{CH}^2(X,1)_{\mathrm{ind}}$, which is the quotient of $\mathrm{CH}^2(X,1)$ by the images of the intersection product maps. To compute the images under the regulator map, we use automorphisms of the family and the explicit description of the action of the automorphisms on the Picard-Fuchs differential equations of the family.

### 2023/05/16

#### Operator Algebra Seminars

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

Group actions on bimodules and equivariant $\alpha$-induction

[ Reference URL ]

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

**Mizuki Oikawa**(Univ. Tokyo)Group actions on bimodules and equivariant $\alpha$-induction

[ Reference URL ]

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

#### Numerical Analysis Seminar

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

Numerical analysis of the Plateau problem by the method of fundamental solutions (Japanese)

[ Reference URL ]

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

**Yuuki Shimizu**(The University of Tokyo)Numerical analysis of the Plateau problem by the method of fundamental solutions (Japanese)

[ Reference URL ]

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

#### 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.

Anderson self-duality of topological modular forms and heretoric string theory (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Mayuko Yamashita**(Kyoto University)Anderson self-duality of topological modular forms and heretoric string theory (JAPANESE)

[ Abstract ]

Topological Modular Forms (TMF) is an E-infinity ring spectrum which is conjectured by Stolz-Teichner to classify two-dimensional supersymmetric quantum field theories in physics. In the previous work with Y. Tachikawa, we proved the vanishing of anomalies in heterotic string theory mathematically by using TMF. In this talk, I explain our recent update on the previous work. Because of the vanishing result, we can consider a secondary transformation of spectra, which is shown to coincide with the Anderson self-duality morphism of TMF. This allows us to detect subtle torsion phenomena in TMF by differential-geometric ways.

[ Reference URL ]Topological Modular Forms (TMF) is an E-infinity ring spectrum which is conjectured by Stolz-Teichner to classify two-dimensional supersymmetric quantum field theories in physics. In the previous work with Y. Tachikawa, we proved the vanishing of anomalies in heterotic string theory mathematically by using TMF. In this talk, I explain our recent update on the previous work. Because of the vanishing result, we can consider a secondary transformation of spectra, which is shown to coincide with the Anderson self-duality morphism of TMF. This allows us to detect subtle torsion phenomena in TMF by differential-geometric ways.

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

#### Tokyo-Nagoya Algebra Seminar

15:00-16:30 Online

Cluster-additive functions and frieze patterns with coefficients (English)

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

**Antoine de Saint Germain**(University of Hong Kong)Cluster-additive functions and frieze patterns with coefficients (English)

[ Abstract ]

In his study of combinatorial features of cluster categories and cluster-tilted algebras, Ringel introduced an analogue of additive functions of stable translation quivers called cluster-additive functions.

In the first part of this talk, we will define cluster-additive functions associated to any acyclic mutation matrix, relate them to mutations of the cluster X variety, and realise their values as certain compatibility degrees between functions on the cluster A variety associated to the Langlands dual mutation matrix (in accordance with the philosophy of Fock-Goncharov). This is based on joint work with Peigen Cao and Jiang-Hua Lu. In the second part of this talk, we will introduce the notion of frieze patterns with coefficients based on joint work with Min Huang and Jiang-Hua Lu. We will then discuss their connection with cluster-additive functions.

ミーティングID: 815 4247 1556

パスコード: 742240

[ Reference URL ]In his study of combinatorial features of cluster categories and cluster-tilted algebras, Ringel introduced an analogue of additive functions of stable translation quivers called cluster-additive functions.

In the first part of this talk, we will define cluster-additive functions associated to any acyclic mutation matrix, relate them to mutations of the cluster X variety, and realise their values as certain compatibility degrees between functions on the cluster A variety associated to the Langlands dual mutation matrix (in accordance with the philosophy of Fock-Goncharov). This is based on joint work with Peigen Cao and Jiang-Hua Lu. In the second part of this talk, we will introduce the notion of frieze patterns with coefficients based on joint work with Min Huang and Jiang-Hua Lu. We will then discuss their connection with cluster-additive functions.

ミーティングID: 815 4247 1556

パスコード: 742240

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

#### Lie Groups and Representation Theory

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

Integral expression of the $(k,a)$-generalized Laguerre semigroup

(Japanese)

**Hiroyoshi TAMORI**(Shibaura institute of technology)Integral expression of the $(k,a)$-generalized Laguerre semigroup

(Japanese)

[ Abstract ]

The $(k,a)$-generalized Laguerre semigroup was introduced by Ben

Sa\"{\i}d--Kobayashi-{\O}rsted as an interpolation of the Hermite semigroup (the k=0, a=2 case) and the Laguerre semigroup (the k=0, a=1 case). Based on a joint work with Kouichi Taira (Ritsumeikan University), I will explain an integral expression of the semigroup and an upper estimate of the integral kernel, which leads to Strichartz estimates for operators $|x|^{2-a}\Delta_{k}-|x|^a$ and $|x|^{2-a}\Delta_{k}$ ($\Delta_k$ denotes the Dunkl Laplacian) under some condition on the deformation parameter $(k,a)$.

The $(k,a)$-generalized Laguerre semigroup was introduced by Ben

Sa\"{\i}d--Kobayashi-{\O}rsted as an interpolation of the Hermite semigroup (the k=0, a=2 case) and the Laguerre semigroup (the k=0, a=1 case). Based on a joint work with Kouichi Taira (Ritsumeikan University), I will explain an integral expression of the semigroup and an upper estimate of the integral kernel, which leads to Strichartz estimates for operators $|x|^{2-a}\Delta_{k}-|x|^a$ and $|x|^{2-a}\Delta_{k}$ ($\Delta_k$ denotes the Dunkl Laplacian) under some condition on the deformation parameter $(k,a)$.

### 2023/05/15

#### Seminar on Geometric Complex Analysis

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

$\mathcal{I}'$-curvatures and the Hirachi conjecture (Japanese)

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

**Yuya Takeuchi**(Tsukuba Univeristy)$\mathcal{I}'$-curvatures and the Hirachi conjecture (Japanese)

[ Abstract ]

Hirachi conjecture deals with a relation between the integrals of local pseudo-Hermitian invariants and global CR invariants. This is a CR analogue of the Deser-Schwimmer conjceture, which was proved by Alexakis. In this talk, I would like to explain some results on the Hirachi conjecture. In particular, I'll introduce the $\mathcal{I}'$-curvatures and prove that these produce counterexamples to the Hirachi conjecture in higher dimensions. This talk is based on joint work with Jeffrey S. Case.

[ Reference URL ]Hirachi conjecture deals with a relation between the integrals of local pseudo-Hermitian invariants and global CR invariants. This is a CR analogue of the Deser-Schwimmer conjceture, which was proved by Alexakis. In this talk, I would like to explain some results on the Hirachi conjecture. In particular, I'll introduce the $\mathcal{I}'$-curvatures and prove that these produce counterexamples to the Hirachi conjecture in higher dimensions. This talk is based on joint work with Jeffrey S. Case.

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.)

Capacity of the range of random walk (JAPANESE)

**岡田いず海**(千葉大学)Capacity of the range of random walk (JAPANESE)

[ Abstract ]

We study the capacity of the range of a simple random walk in three and higher dimensions. It is known that the order of the capacity of the random walk range in n dimensions is similar to that of the volume of the random walk range in n-2 dimensions. We show that this correspondence breaks down for the law of the iterated logarithm for the capacity of the random walk range in three dimensions. We also prove the law of the iterated logarithm in higher dimensions. This is joint work with Amir Dembo.

We study the capacity of the range of a simple random walk in three and higher dimensions. It is known that the order of the capacity of the random walk range in n dimensions is similar to that of the volume of the random walk range in n-2 dimensions. We show that this correspondence breaks down for the law of the iterated logarithm for the capacity of the random walk range in three dimensions. We also prove the law of the iterated logarithm in higher dimensions. This is joint work with Amir Dembo.

### 2023/05/11

#### Information Mathematics Seminar

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

The security definition and proof of symmetric key encryption and public key encryption (Japanese)

**Tatsuaki Okamoto**(NTT)The security definition and proof of symmetric key encryption and public key encryption (Japanese)

[ Abstract ]

Explanation of the security definition and proof of symmetric key encryption and public key encryption

Explanation of the security definition and proof of symmetric key encryption and public key encryption

### 2023/05/10

#### Number Theory Seminar

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

Swan exponent of Galois representations and fonctoriality for classical groups over p-adic fields (English)

**Guy Henniart**(Paris-Sud University)Swan exponent of Galois representations and fonctoriality for classical groups over p-adic fields (English)

[ Abstract ]

This is joint work with Masao Oi in Kyoto. Let F be a p-adic field for some prime number p,

F^ac an algebraic closure of F, and G_F the Galois group of F^ac/F. A continuous finite dimensional

representation σ (on a complex vector space W) has a Swan exponent s(σ), a non-negative integer

which measures how "wildly ramified" σ is. Langlands functoriality makes it of interest

to compare s(σ) and s(r o σ) when r is an algebraic representation of Aut_C(W). The first cases

for r are the determinant, the adjoint representation, the symmetric square representation and

the alternating square representation. I shall give some relations (inequalities mostly, with

equality in interesting cases) between the Swan exponents of those representations r o σ. I shall

also indicate how such relations can be used to explicit the local Langlands correspondence of

Arthur for some simple cuspidal representations of split classical groups over F.

This is joint work with Masao Oi in Kyoto. Let F be a p-adic field for some prime number p,

F^ac an algebraic closure of F, and G_F the Galois group of F^ac/F. A continuous finite dimensional

representation σ (on a complex vector space W) has a Swan exponent s(σ), a non-negative integer

which measures how "wildly ramified" σ is. Langlands functoriality makes it of interest

to compare s(σ) and s(r o σ) when r is an algebraic representation of Aut_C(W). The first cases

for r are the determinant, the adjoint representation, the symmetric square representation and

the alternating square representation. I shall give some relations (inequalities mostly, with

equality in interesting cases) between the Swan exponents of those representations r o σ. I shall

also indicate how such relations can be used to explicit the local Langlands correspondence of

Arthur for some simple cuspidal representations of split classical groups over F.

#### Algebraic Geometry Seminar

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

Singularities in mixed characteristic via the Riemann-Hilbert correspondence (English)

**Jakub Witaszek**(Princeton University)Singularities in mixed characteristic via the Riemann-Hilbert correspondence (English)

[ Abstract ]

In my talk, I will start by reviewing how various properties of characteristic zero singularities can be understood topologically by ways of the Riemann-Hilbert correspondence. After that, I will explain how similar ideas can be applied in the study of mixed characteristic singularities. This is based on a joint work (in progress) with Bhargav Bhatt, Linquan Ma, Zsolt Patakfalvi, Karl Schwede, Kevin Tucker, and Joe Waldron.

In my talk, I will start by reviewing how various properties of characteristic zero singularities can be understood topologically by ways of the Riemann-Hilbert correspondence. After that, I will explain how similar ideas can be applied in the study of mixed characteristic singularities. This is based on a joint work (in progress) with Bhargav Bhatt, Linquan Ma, Zsolt Patakfalvi, Karl Schwede, Kevin Tucker, and Joe Waldron.

### 2023/05/09

#### Operator Algebra Seminars

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

Lattice Green functions (after Balaban/Dimock) (English)

[ Reference URL ]

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

**Yoh Tanimoto**(Univ Rome, Tor Vergata)Lattice Green functions (after Balaban/Dimock) (English)

[ 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.

Knots and frieze patterns (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Michihisa Wakui**(Kansai University)Knots and frieze patterns (JAPANESE)

[ Abstract ]

(joint work with Prof. Takeyoshi Kogiso (Josai University)) In the early 1970s, Conway and Coxeter introduced frieze patterns of positive integers arranged under the unimodular rule ad-bc=1, and showed that they are classified by triangulations of convex polygons. Currently, the frieze patterns by Conway and Coxeter are spotlighted in connection with cluster algebras which are introduced by Fomin and Zelevinsky in the early 2000s.

Working with Takeyoshi Kogiso in Josai University the speaker study on relationship between rational links and Conway-Coxeter friezes through ancestor triangles of rational numbers introduced by Shuji Yamada in Kyoto Sangyo University, and show that rational links are characterized by Conway-Coxeter friezes of zigzag type. At nearly the same time Morier-Genoud and Ovsienko also introduce the concept of q-deformation of rational numbers based on continued fraction expansions, and derive closely related results to our research. In this seminar we will talk about an outline of these results.

[ Reference URL ](joint work with Prof. Takeyoshi Kogiso (Josai University)) In the early 1970s, Conway and Coxeter introduced frieze patterns of positive integers arranged under the unimodular rule ad-bc=1, and showed that they are classified by triangulations of convex polygons. Currently, the frieze patterns by Conway and Coxeter are spotlighted in connection with cluster algebras which are introduced by Fomin and Zelevinsky in the early 2000s.

Working with Takeyoshi Kogiso in Josai University the speaker study on relationship between rational links and Conway-Coxeter friezes through ancestor triangles of rational numbers introduced by Shuji Yamada in Kyoto Sangyo University, and show that rational links are characterized by Conway-Coxeter friezes of zigzag type. At nearly the same time Morier-Genoud and Ovsienko also introduce the concept of q-deformation of rational numbers based on continued fraction expansions, and derive closely related results to our research. In this seminar we will talk about an outline of these results.

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

### 2023/05/08

#### Seminar on Geometric Complex Analysis

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

Non-Kähler Hodge theory and resolutions of cyclic orbifolds (日本語)

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

**Hisashi Kasuya**(Osaka Univeristy)Non-Kähler Hodge theory and resolutions of cyclic orbifolds (日本語)

[ Abstract ]

This talk is based on the joint works with Jonas Stelzig (LMU München). We discuss the Hodge theory of non-Kähler compact complex manifolds. In this term, we think several types of compact complex manifolds and compact Kähler manifolds are considered as the "simplest”. We give a way of constructing simply connected compact complex non-Kähler manifolds of certain types by using resolutions of cyclic orbifolds.

[ Reference URL ]This talk is based on the joint works with Jonas Stelzig (LMU München). We discuss the Hodge theory of non-Kähler compact complex manifolds. In this term, we think several types of compact complex manifolds and compact Kähler manifolds are considered as the "simplest”. We give a way of constructing simply connected compact complex non-Kähler manifolds of certain types by using resolutions of cyclic orbifolds.

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

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