## Seminar information archive

Seminar information archive ～05/25｜Today's seminar 05/26 | Future seminars 05/27～

### 2024/01/23

#### Tuesday Seminar on Topology

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

Pre-registration required. See our seminar webpage.

On the rational cohomology of spin hyperelliptic mapping class groups (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Gefei Wang**(The University of Tokyo)On the rational cohomology of spin hyperelliptic mapping class groups (JAPANESE)

[ Abstract ]

Let $G$ be the subgroup $S_{n−q} \times S_q$ of the $n$-th symmetric group $S_n$ for $n-q \ge q$. In this talk, we study the $G$-invariant part of the rational cohomology group of the pure braid group $P_n$. The invariant part $H^*(P_n)^G$ includes the rational cohomology of a spin hyperelliptic mapping class group of genus $g$ as a subalgebra when $n=2g+2$. Based on the study of Lehrer-Solomon, we prove that they are independent of n and q in degree $* \le q-1$. We also give a formula to calculate the dimension of $H^* (P_n)^G$ and calculate it in all degree for $q \le 3$.

[ Reference URL ]Let $G$ be the subgroup $S_{n−q} \times S_q$ of the $n$-th symmetric group $S_n$ for $n-q \ge q$. In this talk, we study the $G$-invariant part of the rational cohomology group of the pure braid group $P_n$. The invariant part $H^*(P_n)^G$ includes the rational cohomology of a spin hyperelliptic mapping class group of genus $g$ as a subalgebra when $n=2g+2$. Based on the study of Lehrer-Solomon, we prove that they are independent of n and q in degree $* \le q-1$. We also give a formula to calculate the dimension of $H^* (P_n)^G$ and calculate it in all degree for $q \le 3$.

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

#### FJ-LMI Seminar

13:30-14:40 Room #118 (Graduate School of Math. Sci. Bldg.)

Particle systems with geometrical constraints and applications (英語)

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

**Antoine DIEZ**(京都大学, Kyoto University, ASHBi)Particle systems with geometrical constraints and applications (英語)

[ Abstract ]

Since the pioneering work of Boltzmann, statistical physics has moti-vated the mathematical study or large systems of interacting particles, especially at the interface between stochastic analysis and PDE. More recently, there has been a surge of interest to consider applications to life sciences, where particles can be seen as convenient modeling entities to represent e.g. cell aggregates, bacterial swarms or animal societies. An important question in this context is the link between the microscopic agent-based description and the macroscopic continuum PDE description. Unlike physical systems which generally obey conservation laws, biological systems are rather subjects to constraints which are more geometrical in nature: volume constraints, shape or internal structure for instance. This poses a number of challenges on the modeling, analytical and numerical aspects. In this talk, I will first review earlier works on the study of particle systems with geometrical constraints. Then I will introduce a new framework, based on optimal transport theory, to model particles with arbitrary shapes and deformability properties. I will discuss potential applications in biology and compare this novel approach to other more classical methods.

[ Reference URL ]Since the pioneering work of Boltzmann, statistical physics has moti-vated the mathematical study or large systems of interacting particles, especially at the interface between stochastic analysis and PDE. More recently, there has been a surge of interest to consider applications to life sciences, where particles can be seen as convenient modeling entities to represent e.g. cell aggregates, bacterial swarms or animal societies. An important question in this context is the link between the microscopic agent-based description and the macroscopic continuum PDE description. Unlike physical systems which generally obey conservation laws, biological systems are rather subjects to constraints which are more geometrical in nature: volume constraints, shape or internal structure for instance. This poses a number of challenges on the modeling, analytical and numerical aspects. In this talk, I will first review earlier works on the study of particle systems with geometrical constraints. Then I will introduce a new framework, based on optimal transport theory, to model particles with arbitrary shapes and deformability properties. I will discuss potential applications in biology and compare this novel approach to other more classical methods.

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

### 2024/01/19

#### 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].

Lagrangian correspondence and Floer theory (JAPANESE)

https://forms.gle/7T6ewXWtrVEKM9dY7

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

**Kenji Fukaya**(Simons Center for Geometry and Physics)Lagrangian correspondence and Floer theory (JAPANESE)

[ Abstract ]

It was proposed by Weinstein that the morphism of the `category’ of symplectic manifold should be a Lagrangian correspondence (a Lagrangian submanifold of the direct product).

Gromov-Witten invariant is not functorial for this functor.

However Lagrangian Floer theory is functorial.

I will explain present status of the study of this functoriality and a few of its applications.

[ Reference URL ]It was proposed by Weinstein that the morphism of the `category’ of symplectic manifold should be a Lagrangian correspondence (a Lagrangian submanifold of the direct product).

Gromov-Witten invariant is not functorial for this functor.

However Lagrangian Floer theory is functorial.

I will explain present status of the study of this functoriality and a few of its applications.

https://forms.gle/7T6ewXWtrVEKM9dY7

### 2024/01/16

#### Operator Algebra Seminars

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

Inclusions of simple C$^*$-algebras arising from isometrically shift absorbing actions

[ Reference URL ]

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

**Miho Mukohara**(Univ. Tokyo)Inclusions of simple C$^*$-algebras arising from isometrically shift absorbing actions

[ Reference URL ]

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

#### Tuesday Seminar on Topology

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

Pre-registration required. See our seminar webpage.

A gauge theoretic invariant of embedded surfaces in 4-manifolds and exotic P

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

Pre-registration required. See our seminar webpage.

**Jin Miyazawa**(The University of Tokyo)A gauge theoretic invariant of embedded surfaces in 4-manifolds and exotic P

^{2}-knots (JAPANESE)
[ Abstract ]

When two embeddings of surfaces on a 4-dimensional manifold are given, if they are topologically isotopic but not smoothly isotopic, we call them a pair of exotic surfaces. While there is a great deal of study of exotic surfaces in 4-manifolds, studies of closed exotic surfaces in S

[ Reference URL ]When two embeddings of surfaces on a 4-dimensional manifold are given, if they are topologically isotopic but not smoothly isotopic, we call them a pair of exotic surfaces. While there is a great deal of study of exotic surfaces in 4-manifolds, studies of closed exotic surfaces in S

^{4}are limited. In particular, the existence of orientable exotic surfaces in S^{4}remains unknown to date. There are some examples of non-orientable exotic surfaces in S^{4}, including the initial example given by Finashin-Kreck-Viro in 1988, but all such cases have genus greater than or equal to 5. The difficulty in detecting exotic surfaces in S^{4}is to prove that two embeddings of surfaces are not smoothly isotopic. All examples of exotic non-orientable surfaces in S^{4}have been detected by proving the 4-manifolds obtained by the double branched covers are exotic. If we attempt to apply this technique to low-genus non-orientable surfaces in S^{4}, we have to discover exotic small 4-manifolds, which is known to be difficult. In this seminar, we construct an invariant for embedded surfaces in 4-manifolds using Real Seiberg-Witten theory. As an application, we give an infinite family of exotic embeddings into S^{4}for the real projective plane.https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

### 2024/01/11

#### Information Mathematics Seminar

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

Introduction to quantum computation and quantum error correction (Japanese)

**Yasunari Suzuki**(MTT)Introduction to quantum computation and quantum error correction (Japanese)

[ Abstract ]

To demonstrate quantum computational advantage, we need quantum error-correction technology to reduce effective error rates to a small value. In this talk, we introduce the basic theory of quantum computation and quantum error-correcting codes.

To demonstrate quantum computational advantage, we need quantum error-correction technology to reduce effective error rates to a small value. In this talk, we introduce the basic theory of quantum computation and quantum error-correcting codes.

#### Tokyo-Nagoya Algebra Seminar

10:30-12:00 Online

量子Grothendieck環とその量子団代数構造について (Japanese)

[ Reference URL ]

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

**Ryo Fujita**(RIMS)量子Grothendieck環とその量子団代数構造について (Japanese)

[ Reference URL ]

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

### 2024/01/10

#### Number Theory Seminar

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

Characteristic cycle and partially logarithmic characteristic cycle of a rank 1 sheaf (Japanese)

**Yuri Yatagawa**(Tokyo Institute of Technology)Characteristic cycle and partially logarithmic characteristic cycle of a rank 1 sheaf (Japanese)

### 2024/01/09

#### Numerical Analysis Seminar

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

Deep learning that learns from, becomes part of, or replaces numerical methods for differential equations (Japanese)

[ Reference URL ]

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

**Takashi Matsubara**(Osaka University)Deep learning that learns from, becomes part of, or replaces numerical methods for differential equations (Japanese)

[ Reference URL ]

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

#### Tuesday Seminar on Topology

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

Pre-registration required. See our seminar webpage.

Stabilizer subgroups of Thompson's group F in Thompson knot theory (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Akihiro Takano**(The University of Tokyo)Stabilizer subgroups of Thompson's group F in Thompson knot theory (JAPANESE)

[ Abstract ]

Thompson knot theory, introduced by Vaughan Jones, is a study of knot theory using Thompson's group F.

More specifically, he defined a method of constructing a knot from an element of F, and proved that any knot can be realized in his way. This fact is called Alexander’s theorem, which is an analogy of the braid group. In this talk, we consider Thompson knot theory in terms of a relation between subgroups of F and knots obtained from their elements. In particular, we focus on stabilizer subgroups of F with respect to the natural action on the unit interval. This talk is based on joint work with Yuya Kodama (Tokyo Metropolitan University).

[ Reference URL ]Thompson knot theory, introduced by Vaughan Jones, is a study of knot theory using Thompson's group F.

More specifically, he defined a method of constructing a knot from an element of F, and proved that any knot can be realized in his way. This fact is called Alexander’s theorem, which is an analogy of the braid group. In this talk, we consider Thompson knot theory in terms of a relation between subgroups of F and knots obtained from their elements. In particular, we focus on stabilizer subgroups of F with respect to the natural action on the unit interval. This talk is based on joint work with Yuya Kodama (Tokyo Metropolitan University).

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

### 2023/12/26

#### Tokyo-Nagoya Algebra Seminar

15:00-16:30 Room #ハイブリッド・002 (Graduate School of Math. Sci. Bldg.)

t-structures on the equivariant derived category of the Steinberg scheme (English)

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

**Ivan Losev**(Yale University)t-structures on the equivariant derived category of the Steinberg scheme (English)

[ Abstract ]

The Steinberg scheme and the equivariant coherent sheaves on it play a very important role in Geometric Representation theory. In this talk we will discuss various t-structures on the equivariant derived category of the Steinberg of importance for Representation theory in positive characteristics. Based on arXiv:2302.05782.

[ Reference URL ]The Steinberg scheme and the equivariant coherent sheaves on it play a very important role in Geometric Representation theory. In this talk we will discuss various t-structures on the equivariant derived category of the Steinberg of importance for Representation theory in positive characteristics. Based on arXiv:2302.05782.

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

### 2023/12/21

#### Information Mathematics Seminar

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

Quantum Computing and Cryptography (Japanese)

**Takashi Yamakawa**(NTT)Quantum Computing and Cryptography (Japanese)

[ Abstract ]

I explain several topics on quantum computing and cryptography including quantum money and verification of quantum computation based on cryptography.

I explain several topics on quantum computing and cryptography including quantum money and verification of quantum computation based on cryptography.

### 2023/12/20

#### Number Theory Seminar

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

Accessing the big de Rham-Witt complex via algebraic cycles with a vanishing condition (English)

**Jinhyun Park**(KAIST)Accessing the big de Rham-Witt complex via algebraic cycles with a vanishing condition (English)

[ Abstract ]

The big de Rham-Witt complexes of certain good rings over a field are known to admit certain motivic descriptions, namely via cycles with a modulus condition, e.g. additive higher Chow groups. This allowed us to define the trace maps on the de Rham-Witt forms in geometric terms, for instance.

Inspired by a lemma of Kato-Saito on the class field theory and Milnor K-groups, in this talk I would introduce a recent attempt in progress, where a version of “vanishing algebraic cycles” is defined over the formal power series k[[t]]. Using these cycles, I would sketch an alternative cycle-theoretic description of the big de Rham-Witt forms.

The big de Rham-Witt complexes of certain good rings over a field are known to admit certain motivic descriptions, namely via cycles with a modulus condition, e.g. additive higher Chow groups. This allowed us to define the trace maps on the de Rham-Witt forms in geometric terms, for instance.

Inspired by a lemma of Kato-Saito on the class field theory and Milnor K-groups, in this talk I would introduce a recent attempt in progress, where a version of “vanishing algebraic cycles” is defined over the formal power series k[[t]]. Using these cycles, I would sketch an alternative cycle-theoretic description of the big de Rham-Witt forms.

### 2023/12/19

#### 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.

Topological quantum computing, tensor networks and operator algebras (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Yasuyuki Kawahigashi**(The University of Tokyo)Topological quantum computing, tensor networks and operator algebras (JAPANESE)

[ Abstract ]

Modular tensor categories have caught much attention in connection to topological quantum computing based on anyons recently. Condensed matter physicists recently try to understand structures of modular tensor categories appearing in two-dimensional topological order using tensor networks. We present understanding of their tools in terms of operator algebras. For example, 4-tensors they use are exactly bi-unitary connections in the Jones theory of subfactors and their sequence of finite dimensional Hilbert spaces on which their gapped Hamiltonians act is given by the so-called higher relative commutants of a subfactor. No knowledge on operator algebras are assumed.

[ Reference URL ]Modular tensor categories have caught much attention in connection to topological quantum computing based on anyons recently. Condensed matter physicists recently try to understand structures of modular tensor categories appearing in two-dimensional topological order using tensor networks. We present understanding of their tools in terms of operator algebras. For example, 4-tensors they use are exactly bi-unitary connections in the Jones theory of subfactors and their sequence of finite dimensional Hilbert spaces on which their gapped Hamiltonians act is given by the so-called higher relative commutants of a subfactor. No knowledge on operator algebras are assumed.

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

### 2023/12/15

#### Algebraic Geometry Seminar

13:30-15:00 Room #118 (Graduate School of Math. Sci. Bldg.)

On a pair of a smooth variety and a multi-ideal with a real exponent in positive characteristic (日本語)

**Shihoko Ishii**(University of Tokyo)On a pair of a smooth variety and a multi-ideal with a real exponent in positive characteristic (日本語)

[ Abstract ]

In birational geometry, the behaviors of the invariants, mld (minimal log discrepancy) and lct (log canonical threshold), play important roles. These invariants are studied well in case the base field is characteristic zero, but not so in positive characteristic case. In this talk, I work on a pair consisting of smooth variety and a multi-ideal with a real exponent over an algebraically closed field of positive characteristic. We reduce some behaviors of the invariants for such pairs in positive characteristic case into characteristic zero.

In birational geometry, the behaviors of the invariants, mld (minimal log discrepancy) and lct (log canonical threshold), play important roles. These invariants are studied well in case the base field is characteristic zero, but not so in positive characteristic case. In this talk, I work on a pair consisting of smooth variety and a multi-ideal with a real exponent over an algebraically closed field of positive characteristic. We reduce some behaviors of the invariants for such pairs in positive characteristic case into characteristic zero.

#### 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].

Hessenberg varieties and Stanley-Stembridge conjecture in graph theory (JAPANESE)

https://forms.gle/42wEF5c2pqsqrHqR7

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

**Mikiya Masuda**(Osaka Central Advanced Mathematical Institute, Osaka Metropolitan University)Hessenberg varieties and Stanley-Stembridge conjecture in graph theory (JAPANESE)

[ Abstract ]

Hessenberg varieties, a family of subvarieties of flag varieties, includes Springer fibers in geometric representation theory, Peterson varieties related to the quantum cohomology of flag varieties, and permutohedral varieties which are nonsingular toric varieties. Hessenberg varieties are also related to the QR algorithm for matrix eigenvalues and to hyperplane arrangements. Recently, Hessenberg varieties have attracted attention because of their connection to the Stanley-Stembridge conjecture on symmetric functions in graph theory. In this talk, I will explain how Hessenberg varieties are related to this conjecture.

[ Reference URL ]Hessenberg varieties, a family of subvarieties of flag varieties, includes Springer fibers in geometric representation theory, Peterson varieties related to the quantum cohomology of flag varieties, and permutohedral varieties which are nonsingular toric varieties. Hessenberg varieties are also related to the QR algorithm for matrix eigenvalues and to hyperplane arrangements. Recently, Hessenberg varieties have attracted attention because of their connection to the Stanley-Stembridge conjecture on symmetric functions in graph theory. In this talk, I will explain how Hessenberg varieties are related to this conjecture.

https://forms.gle/42wEF5c2pqsqrHqR7

#### Infinite Analysis Seminar Tokyo

13:00-14:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Bi-Hamiltonian structures of integrable many-body models from Poisson reduction (ENGLISH)

**Laszlo Feher**(University of Szeged, Hungary)Bi-Hamiltonian structures of integrable many-body models from Poisson reduction (ENGLISH)

[ Abstract ]

We review our results on bi-Hamiltonian structures of trigonometric spin Sutherland models

built on collective spin variables.

Our basic observation was that the cotangent bundle $T^*\mathrm{U}(n)$ and its holomorphic analogue $T^* \mathrm{GL}(n,{\mathbb C})$,

as well as $T^*\mathrm{GL}(n,{\mathbb C})_{\mathbb R}$, carry a natural quadratic Poisson bracket,

which is compatible with the canonical linear one. The quadratic bracket arises by change of variables and analytic continuation

from an associated Heisenberg double.

Then, the reductions of $T^*{\mathrm{U}}(n)$ and $T^*{\mathrm{GL}}(n,{\mathbb C})$ by the conjugation actions of the

corresponding groups lead to the real and holomorphic spin Sutherland models, respectively, equipped

with a bi-Hamiltonian structure. The reduction of $T^*{\mathrm{GL}}(n,{\mathbb C})_{\mathbb R}$ by the group $\mathrm{U}(n) \times \mathrm{U}(n)$ gives

a generalized Sutherland model coupled to two ${\mathfrak u}(n)^*$-valued spins.

We also show that

a bi-Hamiltonian structure on the associative algebra ${\mathfrak{gl}}(n,{\mathbb R})$ that appeared in the context

of Toda models can be interpreted as the quotient of compatible Poisson brackets on $T^*{\mathrm{GL}}(n,{\mathbb R})$.

Before our work, all these reductions were studied using the canonical Poisson structures of the cotangent bundles,

without realizing the bi-Hamiltonian aspect.

Finally, if time permits, the degenerate integrability of some of the reduced systems

will be explained as well.

[1] L. Feher, Reduction of a bi-Hamiltonian hierarchy on $T^*\mathrm{U}(n)$

to spin Ruijsenaars--Sutherland models, Lett. Math. Phys. 110, 1057-1079 (2020).

[2] L. Feher, Bi-Hamiltonian structure of spin Sutherland models: the holomorphic case, Ann. Henri Poincar\'e 22, 4063-4085 (2021).

[3] L. Feher, Bi-Hamiltonian structure of Sutherland models coupled to two $\mathfrak{u}(n)^*$-valued spins from Poisson reduction,

Nonlinearity 35, 2971-3003 (2022).

[4] L. Feher and B. Juhasz,

A note on quadratic Poisson brackets on $\mathfrak{gl}(n,\mathbb{R})$ related to Toda lattices,

Lett. Math. Phys. 112:45 (2022).

[5] L. Feher,

Notes on the degenerate integrability of reduced systems obtained from the master systems of free motion on cotangent bundles of

compact Lie groups, arXiv:2309.16245

We review our results on bi-Hamiltonian structures of trigonometric spin Sutherland models

built on collective spin variables.

Our basic observation was that the cotangent bundle $T^*\mathrm{U}(n)$ and its holomorphic analogue $T^* \mathrm{GL}(n,{\mathbb C})$,

as well as $T^*\mathrm{GL}(n,{\mathbb C})_{\mathbb R}$, carry a natural quadratic Poisson bracket,

which is compatible with the canonical linear one. The quadratic bracket arises by change of variables and analytic continuation

from an associated Heisenberg double.

Then, the reductions of $T^*{\mathrm{U}}(n)$ and $T^*{\mathrm{GL}}(n,{\mathbb C})$ by the conjugation actions of the

corresponding groups lead to the real and holomorphic spin Sutherland models, respectively, equipped

with a bi-Hamiltonian structure. The reduction of $T^*{\mathrm{GL}}(n,{\mathbb C})_{\mathbb R}$ by the group $\mathrm{U}(n) \times \mathrm{U}(n)$ gives

a generalized Sutherland model coupled to two ${\mathfrak u}(n)^*$-valued spins.

We also show that

a bi-Hamiltonian structure on the associative algebra ${\mathfrak{gl}}(n,{\mathbb R})$ that appeared in the context

of Toda models can be interpreted as the quotient of compatible Poisson brackets on $T^*{\mathrm{GL}}(n,{\mathbb R})$.

Before our work, all these reductions were studied using the canonical Poisson structures of the cotangent bundles,

without realizing the bi-Hamiltonian aspect.

Finally, if time permits, the degenerate integrability of some of the reduced systems

will be explained as well.

[1] L. Feher, Reduction of a bi-Hamiltonian hierarchy on $T^*\mathrm{U}(n)$

to spin Ruijsenaars--Sutherland models, Lett. Math. Phys. 110, 1057-1079 (2020).

[2] L. Feher, Bi-Hamiltonian structure of spin Sutherland models: the holomorphic case, Ann. Henri Poincar\'e 22, 4063-4085 (2021).

[3] L. Feher, Bi-Hamiltonian structure of Sutherland models coupled to two $\mathfrak{u}(n)^*$-valued spins from Poisson reduction,

Nonlinearity 35, 2971-3003 (2022).

[4] L. Feher and B. Juhasz,

A note on quadratic Poisson brackets on $\mathfrak{gl}(n,\mathbb{R})$ related to Toda lattices,

Lett. Math. Phys. 112:45 (2022).

[5] L. Feher,

Notes on the degenerate integrability of reduced systems obtained from the master systems of free motion on cotangent bundles of

compact Lie groups, arXiv:2309.16245

### 2023/12/14

#### 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.

Torus orbit closures in the flag variety (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Mikiya Masuda**(Osaka City University)Torus orbit closures in the flag variety (JAPANESE)

[ Abstract ]

The study of torus orbit closures in the flag variety was initiated by Gelfand-Serganova and Klyachko in 1980’s but has not been studied much since then. Recently, I have studied its geometry and topology jointly with Eunjeong Lee, Seonjeong Park, Jongbaek Song in connection with combinatorics of polytopes, Coxeter matroids, and polygonal triangulations. In this talk I will report on the development of this subject.

[ Reference URL ]The study of torus orbit closures in the flag variety was initiated by Gelfand-Serganova and Klyachko in 1980’s but has not been studied much since then. Recently, I have studied its geometry and topology jointly with Eunjeong Lee, Seonjeong Park, Jongbaek Song in connection with combinatorics of polytopes, Coxeter matroids, and polygonal triangulations. In this talk I will report on the development of this subject.

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

#### Information Mathematics Seminar

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

Functional encryption and attribute-based encryption (Japanese)

**Junichi Tomida**(NTT)Functional encryption and attribute-based encryption (Japanese)

[ Abstract ]

I will explain the basics and the recent progress of functional encryption and attribute-based encryption.

I will explain the basics and the recent progress of functional encryption and attribute-based encryption.

#### Tokyo-Nagoya Algebra Seminar

10:30-12:00 Online

On exact dg categories (English)

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

**Xiaofa Chen**(University of Science and Technology of China)On exact dg categories (English)

[ Abstract ]

In this talk, I will give an introduction to exact dg categories and then explore their application to various correspondences in representation theory. We will generalize the Auslander–Iyama correspondence, the Iyama–Solberg correspondence, and a correspondence considered in a paper by Iyama in 2005 to the setting of exact dg categories. The slogan is that solving correspondence-type problems becomes easier using dg categories, and interesting phenomena emerge when the dg category is concentrated in degree zero or is abelian.

[ Reference URL ]In this talk, I will give an introduction to exact dg categories and then explore their application to various correspondences in representation theory. We will generalize the Auslander–Iyama correspondence, the Iyama–Solberg correspondence, and a correspondence considered in a paper by Iyama in 2005 to the setting of exact dg categories. The slogan is that solving correspondence-type problems becomes easier using dg categories, and interesting phenomena emerge when the dg category is concentrated in degree zero or is abelian.

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

### 2023/12/12

#### 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.

Multivariable knot polynomials from braided Hopf algebras with automorphisms (ENGLISH)

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

Pre-registration required. See our seminar webpage.

**Stavros Garoufalidis**(Southern University of Science and Technology)Multivariable knot polynomials from braided Hopf algebras with automorphisms (ENGLISH)

[ Abstract ]

We will discuss a unified approach to define multivariable polynomial invariants of knots that include the colored Jones polynomials, the ADO polynomials and the invariants defined using the theory of quantum groups. Our construction uses braided Hopf algebras with automorphisms. We will give examples of 2-variable invariants, and discuss their structural properties. Joint work with Rinat Kashaev.

[ Reference URL ]We will discuss a unified approach to define multivariable polynomial invariants of knots that include the colored Jones polynomials, the ADO polynomials and the invariants defined using the theory of quantum groups. Our construction uses braided Hopf algebras with automorphisms. We will give examples of 2-variable invariants, and discuss their structural properties. Joint work with Rinat Kashaev.

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

### 2023/12/11

#### Seminar on Geometric Complex Analysis

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

On Partial deformations and Bers embedding (Japanese)

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

**Ryo Matsuda**(Kyoto Univeristy)On Partial deformations and Bers embedding (Japanese)

[ Abstract ]

The Teichmüller space of the Riemann surface S is the space of deformations of the complex structure of S. For complex analysis on Teich(S), it is biholomorphic embedded into a bounded set of the space of complex Banach spaces, denoted as B(S). This embedding is known as the Bers embedding. Additionally, when S is of infinite type, considering partial deformations can reveal properties of Teich(S). Earle-Gardiner-Lakic prove that asymptotically conformal deformations correspond to subspaces where the norm of the embedding decays at infinity. In this talk, we generalize this result, showing that deformations that become asymptotically conformal at some end correspond to spaces where the norm decays at that end. Finally, using this result and the David map, a generalization of quasiconformal maps, I’ll give that in the Bers boundary of infinite-type Riemann surface satisfying the Shiga condition, Maximal cusps are not dense.

[ Reference URL ]The Teichmüller space of the Riemann surface S is the space of deformations of the complex structure of S. For complex analysis on Teich(S), it is biholomorphic embedded into a bounded set of the space of complex Banach spaces, denoted as B(S). This embedding is known as the Bers embedding. Additionally, when S is of infinite type, considering partial deformations can reveal properties of Teich(S). Earle-Gardiner-Lakic prove that asymptotically conformal deformations correspond to subspaces where the norm of the embedding decays at infinity. In this talk, we generalize this result, showing that deformations that become asymptotically conformal at some end correspond to spaces where the norm decays at that end. Finally, using this result and the David map, a generalization of quasiconformal maps, I’ll give that in the Bers boundary of infinite-type Riemann surface satisfying the Shiga condition, Maximal cusps are not dense.

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

### 2023/12/07

#### Information Mathematics Seminar

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

Cryptographic Program Obfuscation and Its Applications (Japanese)

**Ryo Nishimaki**(NTT)Cryptographic Program Obfuscation and Its Applications (Japanese)

[ Abstract ]

I will explain what cryptographically secure program obfuscation is, how to achieve it, and its applications in this talk.

I will explain what cryptographically secure program obfuscation is, how to achieve it, and its applications in this talk.

### 2023/12/06

#### Infinite Analysis Seminar Tokyo

13:00-14:30 Room #056 (Graduate School of Math. Sci. Bldg.)

This seminar has been cancelled.

Flat coordinates of algebraic Frobenius manifolds (ENGLISH)

**Misha Feigin**(University of Glasgow)This seminar has been cancelled.

Flat coordinates of algebraic Frobenius manifolds (ENGLISH)

[ Abstract ]

This seminar has been cancelled.

Orbit spaces of the reflection representation of finite irreducible Coxeter groups provide Frobenius manifolds with polynomial prepotentials. Flat coordinates of the corresponding flat metric, known as Saito metric, are distinguished basic invariants of the Coxeter group. They have applications in representations of Cherednik algebras. Frobenius manifolds with algebraic prepotentials remain not classified and they are typically related to quasi-Coxeter conjugacy classes in finite Coxeter groups. We obtain flat coordinates for the majority of known examples of algebraic Frobenius manifolds in dimensions up to 4. In all the cases, flat coordinates appear to be some algebraic functions on the orbit space of the Coxeter group. This is a joint work with Daniele Valeri and Johan Wright.

This seminar has been cancelled.

Orbit spaces of the reflection representation of finite irreducible Coxeter groups provide Frobenius manifolds with polynomial prepotentials. Flat coordinates of the corresponding flat metric, known as Saito metric, are distinguished basic invariants of the Coxeter group. They have applications in representations of Cherednik algebras. Frobenius manifolds with algebraic prepotentials remain not classified and they are typically related to quasi-Coxeter conjugacy classes in finite Coxeter groups. We obtain flat coordinates for the majority of known examples of algebraic Frobenius manifolds in dimensions up to 4. In all the cases, flat coordinates appear to be some algebraic functions on the orbit space of the Coxeter group. This is a joint work with Daniele Valeri and Johan Wright.

### 2023/12/05

#### 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.

On the Euler class for flat S

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

Pre-registration required. See our seminar webpage.

**Teruaki Kitano**(Soka University)On the Euler class for flat S

^{1}-bundles, C^{∞}vs C^{ω}(JAPANESE)
[ Abstract ]

We describe low dimensional homology groups of the real analytic, orientation preserving diffeomorphism group of S

[ Reference URL ]We describe low dimensional homology groups of the real analytic, orientation preserving diffeomorphism group of S

^{1}in terms of BΓ_{1}by applying a theorem of Thurston. It is an open problem whether some power of the rational Euler class vanishes for real analytic flat S^{1}bundles. In this talk we discuss that if it does, then the homology group should contain many torsion classes that vanish in the smooth case. Along this line we can give a new proof for the non-triviality of any power of the rational Euler class in the smooth case. If time permits, we will mention some attempts to study a Mather-Thurston map in the analytic case. This talk is based on a joint work with Shigeyuki Morita and Yoshihiko Mitsumatsu.https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

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