## Seminar information archive

Seminar information archive ～04/19｜Today's seminar 04/20 | Future seminars 04/21～

### 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

#### Lie Groups and Representation Theory

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

Examples of discrete branching laws of derived functor modules (Japanese)

**Yoshiki Oshima**(The University of Tokyo)Examples of 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 the last talk, by using the realization of representations as D-modules, a decomposition of Zuckerman's modules corresponding to an orbit decomposition of flag varieties was explained. In this talk, we would like to see that such a decomposition can be written as a direct sum of Zuckerman's modules of the subgroup in some concrete 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 the last talk, by using the realization of representations as D-modules, a decomposition of Zuckerman's modules corresponding to an orbit decomposition of flag varieties was explained. In this talk, we would like to see that such a decomposition can be written as a direct sum of Zuckerman's modules of the subgroup in some concrete examples.

### 2023/06/08

#### Information Mathematics Seminar

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

Security, construction and proof of digital signatures (Japanese)

**Tatsuaki Okamoto**(NTT)Security, construction and proof of digital signatures (Japanese)

[ Abstract ]

Explanation of security, construction and proof of digital signatures

Explanation of security, construction and proof of digital signatures

#### Discrete mathematical modelling seminar

18:15-19:15 Online

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

Deformations of Zamolodchikov periodicity, discrete integrability and the Laurent property (English)

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

**Andy Hone**(University of Kent)Deformations of Zamolodchikov periodicity, discrete integrability and the Laurent property (English)

[ Abstract ]

Zamolodchikov periodicity was a conjectured property of Y-systems observed in exactly solvable models of quantum field theory associated with simple Lie algebras. The advent of Fomin & Zelevinsky's theory of cluster algebras provided an ideal mathematical framework for proving and formulating extensions of this property. Recently we have found a family of birational maps which deforms the periodic dynamics observed by Zamolodchikov, and destroys the Laurent property that is an inherent feature of cluster dynamics, but still preserves integrability. In this talk we present a variety of examples of deformed integrable maps in types A, B & D, and show how to restore the Laurent property in higher dimensions. This is the combined result of joint work with Grabowski, Kouloukas, Kim and Mase.

Zamolodchikov periodicity was a conjectured property of Y-systems observed in exactly solvable models of quantum field theory associated with simple Lie algebras. The advent of Fomin & Zelevinsky's theory of cluster algebras provided an ideal mathematical framework for proving and formulating extensions of this property. Recently we have found a family of birational maps which deforms the periodic dynamics observed by Zamolodchikov, and destroys the Laurent property that is an inherent feature of cluster dynamics, but still preserves integrability. In this talk we present a variety of examples of deformed integrable maps in types A, B & D, and show how to restore the Laurent property in higher dimensions. This is the combined result of joint work with Grabowski, Kouloukas, Kim and Mase.

### 2023/06/07

#### Algebraic Geometry Seminar

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

Quasi-F-splitting and Hodge-Witt

**Fuetaro Yobuko**(Nagoya University)Quasi-F-splitting and Hodge-Witt

[ Abstract ]

Quasi-F-splitting is an extension of F-splitting, which is defined for schemes in positive characteristic. On the other hand, Hodge-Wittness is defined for smooth proper schemes over a perfect field using the de Rham-Witt complex and ordinarity implies Hodge-Wittness. In this talk, I will explain (unexpected) relations between F-split/quasi-F-split and ordinary/Hodge-Witt via examples and properties.

Quasi-F-splitting is an extension of F-splitting, which is defined for schemes in positive characteristic. On the other hand, Hodge-Wittness is defined for smooth proper schemes over a perfect field using the de Rham-Witt complex and ordinarity implies Hodge-Wittness. In this talk, I will explain (unexpected) relations between F-split/quasi-F-split and ordinary/Hodge-Witt via examples and properties.

#### Number Theory Seminar

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

On the dimension of spaces of p-ordinary half-integral weight Siegel modular forms

of degree 2 (日本語)

**Hirofumi Yamamoto**(The University of Tokyo)On the dimension of spaces of p-ordinary half-integral weight Siegel modular forms

of degree 2 (日本語)

[ Abstract ]

Hecke eigenforms whose eigenvalues at $p$ are $p$-adic units are called $p$-ordinary. The dimension of the spaces spanned by $p$-ordinary Siegel modular eigenforms is known to be bounded regardless of the power of $p$ of levels and weights. Furthermore, Hida showed that the degree is bounded in the case of half-integral weight modular forms, using the Shimura correspondence. In this talk, I will explain that a similar result holds for half-integral weight $p$-ordinary Siegel modular forms of degree 2. Let $F$ be a $p$-ordinary Hecke eigen cuspform, and $\pi_F$ be the corresponding cuspidal representation of $Mp_4(\mathbb{A}_\mathbb{Q})$. Then the weight of $F$ determines the Hecke eigenvalue of $\pi_F$ at $p$. Therefore, we can relate $F$ to $p$-ordinary integral weight Siegel modular forms or elliptic modular forms by using the local theta correspondence and the method of Ishimoto(Ibukiyama conjecture).

Hecke eigenforms whose eigenvalues at $p$ are $p$-adic units are called $p$-ordinary. The dimension of the spaces spanned by $p$-ordinary Siegel modular eigenforms is known to be bounded regardless of the power of $p$ of levels and weights. Furthermore, Hida showed that the degree is bounded in the case of half-integral weight modular forms, using the Shimura correspondence. In this talk, I will explain that a similar result holds for half-integral weight $p$-ordinary Siegel modular forms of degree 2. Let $F$ be a $p$-ordinary Hecke eigen cuspform, and $\pi_F$ be the corresponding cuspidal representation of $Mp_4(\mathbb{A}_\mathbb{Q})$. Then the weight of $F$ determines the Hecke eigenvalue of $\pi_F$ at $p$. Therefore, we can relate $F$ to $p$-ordinary integral weight Siegel modular forms or elliptic modular forms by using the local theta correspondence and the method of Ishimoto(Ibukiyama conjecture).

### 2023/06/06

#### Operator Algebra Seminars

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

Wightman fields and their construction for a class of 2D CFTs

[ Reference URL ]

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

**Maria Stella Adamo**(Univ. Tokyo)Wightman fields and their construction for a class of 2D CFTs

[ 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.)

Relation between regularity and numerical solutions of shape optimization problems

(Japanese)

[ Reference URL ]

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

**Hideyuki Azegami**(Nagoya Industrial Science Research Institute)Relation between regularity and numerical solutions of shape optimization problems

(Japanese)

[ Reference URL ]

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

#### Tuesday Seminar of Analysis

17:00-18:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Stationary completeness; the many-body short-range case (English)

https://forms.gle/kWHDfb6J6kcjfSah8

**Erik Skibsted**(Aarhus University)Stationary completeness; the many-body short-range case (English)

[ Abstract ]

For a general class of many-body Schr\"odinger operators with short-range pair-potentials the wave and scattering matrices as well as the restricted wave operators are all defined at any non-threshold energy. In fact this holds without imposing any a priori decay condition on channel eigenstates and even for models including long-range potentials of Derezi\'nski-Enss type. For short-range models we improve on the known \emph{weak continuity} statements in that we show that all non-threshold energies are \emph{stationary complete}, resolving in this case a recent conjecture. A consequence is that the above scattering quantities depend \emph{strongly continuously} on the energy parameter at all non-threshold energies (whence not only almost everywhere as previously demonstrated). Another consequence is that the scattering matrix is unitary at any such energy. Our procedure yields (as a side result) a new and purely stationary proof of asymptotic completeness for many-body short-range systems.

[ Reference URL ]For a general class of many-body Schr\"odinger operators with short-range pair-potentials the wave and scattering matrices as well as the restricted wave operators are all defined at any non-threshold energy. In fact this holds without imposing any a priori decay condition on channel eigenstates and even for models including long-range potentials of Derezi\'nski-Enss type. For short-range models we improve on the known \emph{weak continuity} statements in that we show that all non-threshold energies are \emph{stationary complete}, resolving in this case a recent conjecture. A consequence is that the above scattering quantities depend \emph{strongly continuously} on the energy parameter at all non-threshold energies (whence not only almost everywhere as previously demonstrated). Another consequence is that the scattering matrix is unitary at any such energy. Our procedure yields (as a side result) a new and purely stationary proof of asymptotic completeness for many-body short-range systems.

https://forms.gle/kWHDfb6J6kcjfSah8

#### Lie Groups and Representation Theory

17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Joint with Tuesday Seminar on Topology

Visible actions on reductive spherical homogeneous spaces and their invariant measures

(Japanese)

Joint with Tuesday Seminar on Topology

**Atsumu Sasaki**(Tokai University)Visible actions on reductive spherical homogeneous spaces and their invariant measures

(Japanese)

[ Abstract ]

Toshiyuki Kobayashi has established propagation theorem of multiplicity-freeness property.

This theorem enables us to give an unified explanation of multiplicity-freeness of multiplicity-free representations which have been found so far, and also to find new examples of multiplicity-free representations systematically. Kobayashi further has introduced the notion of visible actions on complex manifolds as a basic condition for propagation theorem of multiplicity-freeness property. This notion plays an important role to this theorem and also brings us to find various decomposition theorems of Lie groups and homogeneous spaces.

In this talk, we explain visible actions on reductive spherical homogeneous spaces. In particular, we see that for a visible action on reductive spherical homogeneous space our construction of a submanifold which meets every orbit (called a slice) is given by an explicit description of a Cartan decomposition for this space. As a corollary of this study, we characterize the invariant measure on a reductive spherical homogeneous space by giving an integral formula for a Cartan decomposition explicitly.

Toshiyuki Kobayashi has established propagation theorem of multiplicity-freeness property.

This theorem enables us to give an unified explanation of multiplicity-freeness of multiplicity-free representations which have been found so far, and also to find new examples of multiplicity-free representations systematically. Kobayashi further has introduced the notion of visible actions on complex manifolds as a basic condition for propagation theorem of multiplicity-freeness property. This notion plays an important role to this theorem and also brings us to find various decomposition theorems of Lie groups and homogeneous spaces.

In this talk, we explain visible actions on reductive spherical homogeneous spaces. In particular, we see that for a visible action on reductive spherical homogeneous space our construction of a submanifold which meets every orbit (called a slice) is given by an explicit description of a Cartan decomposition for this space. As a corollary of this study, we characterize the invariant measure on a reductive spherical homogeneous space by giving an integral formula for a Cartan decomposition explicitly.

#### Tuesday Seminar on Topology

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

Joint with Lie Groups and Representation Theory Seminar. See our seminar webpage.

Visible actions on reductive spherical homogeneous spaces and their invariant measures (JAPANESE)

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

Joint with Lie Groups and Representation Theory Seminar. See our seminar webpage.

**Atsumu Sasaki**(Tokai University)Visible actions on reductive spherical homogeneous spaces and their invariant measures (JAPANESE)

[ Abstract ]

Toshiyuki Kobayashi has established propagation theorem of multiplicity-freeness property. This theorem enables us to give an unified explanation of multiplicity-freeness of multiplicity-free representations which have been found so far, and also to find new examples of multiplicity-free representations systematically. Kobayashi further has introduced the notion of visible actions on complex manifolds as a basic condition for propagation theorem of multiplicity-freeness property. This notion plays an important role to this theorem and also brings us to find various decomposition theorems of Lie groups and homogeneous spaces.

In this talk, we explain visible actions on reductive spherical homogeneous spaces. In particular, we see that for a visible action on reductive spherical homogeneous space our construction of a submanifold which meets every orbit (called a slice) is given by an explicit description of a Cartan decomposition for this space. As a corollary of this study, we characterize the invariant measure on a reductive spherical homogeneous space by giving an integral formula for a Cartan decomposition explicitly.

[ Reference URL ]Toshiyuki Kobayashi has established propagation theorem of multiplicity-freeness property. This theorem enables us to give an unified explanation of multiplicity-freeness of multiplicity-free representations which have been found so far, and also to find new examples of multiplicity-free representations systematically. Kobayashi further has introduced the notion of visible actions on complex manifolds as a basic condition for propagation theorem of multiplicity-freeness property. This notion plays an important role to this theorem and also brings us to find various decomposition theorems of Lie groups and homogeneous spaces.

In this talk, we explain visible actions on reductive spherical homogeneous spaces. In particular, we see that for a visible action on reductive spherical homogeneous space our construction of a submanifold which meets every orbit (called a slice) is given by an explicit description of a Cartan decomposition for this space. As a corollary of this study, we characterize the invariant measure on a reductive spherical homogeneous space by giving an integral formula for a Cartan decomposition explicitly.

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

### 2023/06/05

#### Colloquium

15:30-16:30 Online

Billiards and Moduli Spaces (ENGLISH)

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZMkfu2grj4sE9ycW-1MmIQ-768hTpobQKAD

**Curtis T McMullen**(Harvard University)Billiards and Moduli Spaces (ENGLISH)

[ Abstract ]

The moduli space M_g of compact Riemann surface of genus g has been studied from diverse mathematical viewpoints for more than a century.

In this talk, intended for a general audience, we will discuss moduli space from a dynamical perspective. We will present general rigidity results, provide a glimpse of the remarkable curves and surfaces in M_g discovered during the last two decades, and explain how these algebraic varieties are related to the dynamics of billiards in regular polygons, L-shaped tables and quadrilaterals.

A variety of open problems will be mentioned along the way.

[ Reference URL ]The moduli space M_g of compact Riemann surface of genus g has been studied from diverse mathematical viewpoints for more than a century.

In this talk, intended for a general audience, we will discuss moduli space from a dynamical perspective. We will present general rigidity results, provide a glimpse of the remarkable curves and surfaces in M_g discovered during the last two decades, and explain how these algebraic varieties are related to the dynamics of billiards in regular polygons, L-shaped tables and quadrilaterals.

A variety of open problems will be mentioned along the way.

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZMkfu2grj4sE9ycW-1MmIQ-768hTpobQKAD

#### Tokyo Probability Seminar

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

大きな公比を持つ等比数列の差異量の重複対数の法則について (日本語)

**福山克司**(神戸大学)大きな公比を持つ等比数列の差異量の重複対数の法則について (日本語)

### 2023/05/31

#### Number Theory Seminar

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

Quadratic $\ell$-adic sheaf and its Heisenberg group (日本語)

**Daichi Takeuchi**(RIKEN)Quadratic $\ell$-adic sheaf and its Heisenberg group (日本語)

[ Abstract ]

Quadratic Gauss sums are usually defined only for finite fields of odd characteristic. However, it is known that there is a reformulation in which one can uniformly treat the case of even characteristic. In this talk, I will introduce a new class of $\ell$-adic sheaf, which I call quadratic sheaf. This is a sheaf-theoretic enhancement of the reformulation of quadratic Gauss sum, in the sense of the function-sheaf dictionary. After explaining its cohomological properties and consequences, such as a version of Hasse-Davenport relation, I will show that a certain finite Heisenberg group naturally acts on a quadratic sheaf. I will also report various results that can be deduced from this action.

Quadratic Gauss sums are usually defined only for finite fields of odd characteristic. However, it is known that there is a reformulation in which one can uniformly treat the case of even characteristic. In this talk, I will introduce a new class of $\ell$-adic sheaf, which I call quadratic sheaf. This is a sheaf-theoretic enhancement of the reformulation of quadratic Gauss sum, in the sense of the function-sheaf dictionary. After explaining its cohomological properties and consequences, such as a version of Hasse-Davenport relation, I will show that a certain finite Heisenberg group naturally acts on a quadratic sheaf. I will also report various results that can be deduced from this action.

### 2023/05/30

#### 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.

p-colorable subgroup of Thompson's group F (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Yuya Kodama**(Tokyo Metropolitan University)p-colorable subgroup of Thompson's group F (JAPANESE)

[ Abstract ]

Thompson's group F is a subgroup of Homeo([0, 1]). In 2017, Jones found a way to construct knots and links from elements in F. Moreover, any knot (or link) can be obtained in this way. So the next question is, which elements in F give the same knot (or link)? In this talk, I define a subgroup of F and show that every element (except the identity) gives a p-colorable knot (or link). When p=3, this gives a negative answer to a question by Aiello. This is a joint work with Akihiro Takano.

[ Reference URL ]Thompson's group F is a subgroup of Homeo([0, 1]). In 2017, Jones found a way to construct knots and links from elements in F. Moreover, any knot (or link) can be obtained in this way. So the next question is, which elements in F give the same knot (or link)? In this talk, I define a subgroup of F and show that every element (except the identity) gives a p-colorable knot (or link). When p=3, this gives a negative answer to a question by Aiello. This is a joint work with Akihiro Takano.

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

#### 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

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