## Seminar information archive

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

#### Seminar on Geometric Complex Analysis

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

The Nonvanishing problem for varieties with nef anticanonical bundle

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

**Shin-Ichi Matsumura**(Tohoku Univeristy)The Nonvanishing problem for varieties with nef anticanonical bundle

[ Abstract ]

In the framework of the minimal model program for generalized pairs, the abundance conjecture does not hold. However, interestingly, the generalized nonvanishing conjecture is expected to hold. This conjecture asks whether the canonical divisor of generalized pairs can be represented by an effective divisor in its numerical class. In this talk, we discuss the nonvanishing conjecture for generalized LC pairs in three dimensions and prove that the conjecture is true for the nef anti-canonical divisors.

This talk is based on joint work with V. Lazic, Th. Peternell, N. Tsakanikas, and Z. Xie.

[ Reference URL ]In the framework of the minimal model program for generalized pairs, the abundance conjecture does not hold. However, interestingly, the generalized nonvanishing conjecture is expected to hold. This conjecture asks whether the canonical divisor of generalized pairs can be represented by an effective divisor in its numerical class. In this talk, we discuss the nonvanishing conjecture for generalized LC pairs in three dimensions and prove that the conjecture is true for the nef anti-canonical divisors.

This talk is based on joint work with V. Lazic, Th. Peternell, N. Tsakanikas, and Z. Xie.

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

### 2023/10/27

#### 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].

Increasing stability and decreasing instability estimates for an inverse boundary value problem (English)

https://forms.gle/9xDcHfHXFFHPfsKW6

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

**Jenn-Nan Wang**(National Taiwan University)Increasing stability and decreasing instability estimates for an inverse boundary value problem (English)

[ Abstract ]

According to Hadamard’s definition, a well-posed problem satisfies three criteria: existence, uniqueness, and continuous dependence on the data. Most of forward problems (e.g., the boundary value problem or Calderón’s problem) can be proved to be well-posed. However, many inverse problems are known to be ill-posed, for example, the inverse boundary value problem in which one would like to determine unknown parameters from the boundary measurements. The failure of the continuous dependence on the data in Hadamard’s sense makes the feasible determination of unknown parameters rather difficult in practice. However, if one restricts the unknown parameters in a suitable subspace, one can restore the continuous dependence or stability. Nonetheless, the ill-posedness nature of the inverse problem may give rise a logarithmic type modulus of continuity. For Calderón’s problem, such logarithmic stability estimate was derived by Alessandrini and Mandache showed that this estimate is optimal by proving an instability estimate of exponential type. When we consider the time-harmonic equation, it was first proved by Isakov that the stability increases as the frequency increases. In this talk, I would like to discuss a refinement of Mandache’s idea aiming to derive explicitly the dependence of the instability estimate on the frequency. If time allows, I also want to discuss the increasing stability phenomenon from the statistical viewpoint based on the Bayes approach. The aim is to show that the posterior distribution contracts around the true parameter at a rate closely related to the decreasing instability estimate derived above.

[ Reference URL ]According to Hadamard’s definition, a well-posed problem satisfies three criteria: existence, uniqueness, and continuous dependence on the data. Most of forward problems (e.g., the boundary value problem or Calderón’s problem) can be proved to be well-posed. However, many inverse problems are known to be ill-posed, for example, the inverse boundary value problem in which one would like to determine unknown parameters from the boundary measurements. The failure of the continuous dependence on the data in Hadamard’s sense makes the feasible determination of unknown parameters rather difficult in practice. However, if one restricts the unknown parameters in a suitable subspace, one can restore the continuous dependence or stability. Nonetheless, the ill-posedness nature of the inverse problem may give rise a logarithmic type modulus of continuity. For Calderón’s problem, such logarithmic stability estimate was derived by Alessandrini and Mandache showed that this estimate is optimal by proving an instability estimate of exponential type. When we consider the time-harmonic equation, it was first proved by Isakov that the stability increases as the frequency increases. In this talk, I would like to discuss a refinement of Mandache’s idea aiming to derive explicitly the dependence of the instability estimate on the frequency. If time allows, I also want to discuss the increasing stability phenomenon from the statistical viewpoint based on the Bayes approach. The aim is to show that the posterior distribution contracts around the true parameter at a rate closely related to the decreasing instability estimate derived above.

https://forms.gle/9xDcHfHXFFHPfsKW6

### 2023/10/25

#### Number Theory Seminar

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

Geometric Eisenstein Series over the Fargues-Fontaine curve (English)

**Linus Hamann**(Stanford University)Geometric Eisenstein Series over the Fargues-Fontaine curve (English)

[ Abstract ]

Geometric Eisenstein series were first studied extensively by Braverman-Gaitsgory, Laumon, and Drinfeld, in the context of function field geometric Langlands. For a Levi subgroup M inside a connected reductive group G, they are functors which send Hecke eigensheaves on the moduli stack of M-bundles to Hecke eigensheaves on the moduli stack of G-bundles via certain relative compactifications of the moduli stack of P-bundles. We will discuss what this theory has to offer in the context of the recent Fargues-Scholze geometric Langlands program. Namely, motivated by the results in the function field setting, we will explicate what the analogous results tell us in this setting of the Fargues-Scholze program, as well as discuss various consequences for the cohmology of local and global Shimura varieties, via the relation between local Shimura varieties and the p-adic shtukas appearing in the Fargues-Scholze program.

Geometric Eisenstein series were first studied extensively by Braverman-Gaitsgory, Laumon, and Drinfeld, in the context of function field geometric Langlands. For a Levi subgroup M inside a connected reductive group G, they are functors which send Hecke eigensheaves on the moduli stack of M-bundles to Hecke eigensheaves on the moduli stack of G-bundles via certain relative compactifications of the moduli stack of P-bundles. We will discuss what this theory has to offer in the context of the recent Fargues-Scholze geometric Langlands program. Namely, motivated by the results in the function field setting, we will explicate what the analogous results tell us in this setting of the Fargues-Scholze program, as well as discuss various consequences for the cohmology of local and global Shimura varieties, via the relation between local Shimura varieties and the p-adic shtukas appearing in the Fargues-Scholze program.

### 2023/10/24

#### Numerical Analysis Seminar

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

Neural Network-based Enclosure of Solutions to Differential Equations and Reconsideration of the Sub- and Super-solution Method (Japanese)

[ Reference URL ]

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

**Kazuaki Tanaka**(Waseda University)Neural Network-based Enclosure of Solutions to Differential Equations and Reconsideration of the Sub- and Super-solution Method (Japanese)

[ Reference URL ]

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

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Index theory for quarter-plane Toeplitz operators via extended symbols (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Shin Hayashi**(Aoyama Gakuin University)Index theory for quarter-plane Toeplitz operators via extended symbols (JAPANESE)

[ Abstract ]

We consider index theory for some Toeplitz operators on a discrete quarter-plane. Index theory for such operators has been investigated by Simonenko, Douglas-Howe, Park and index formulas are obtained by Coburn-Douglas-Singer, Duducava. In this talk, we revisit Duducava’s idea and discuss an index formula for quarter-plane Toeplitz operators of two-variable rational matrix function symbols from a geometric viewpoint. By using Gohberg-Krein theory for matrix factorizations and analytic continuation, we see that the symbols of Fredholm quarter-plane Toeplitz operators defined originally on a two-dimensional torus can canonically be extended to some three-sphere, and show that their Fredholm indices coincides with the three-dimensional winding number of extended symbols. If time permits, we briefly mention a contact with a topic in condensed matter physics, called (higher-order) topological insulators.

[ Reference URL ]We consider index theory for some Toeplitz operators on a discrete quarter-plane. Index theory for such operators has been investigated by Simonenko, Douglas-Howe, Park and index formulas are obtained by Coburn-Douglas-Singer, Duducava. In this talk, we revisit Duducava’s idea and discuss an index formula for quarter-plane Toeplitz operators of two-variable rational matrix function symbols from a geometric viewpoint. By using Gohberg-Krein theory for matrix factorizations and analytic continuation, we see that the symbols of Fredholm quarter-plane Toeplitz operators defined originally on a two-dimensional torus can canonically be extended to some three-sphere, and show that their Fredholm indices coincides with the three-dimensional winding number of extended symbols. If time permits, we briefly mention a contact with a topic in condensed matter physics, called (higher-order) topological insulators.

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

### 2023/10/19

#### Information Mathematics Seminar

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

Mathematical Aspects of Lattice-Based Cryptography (Japanese)

**Katsuyuki Takashima**(Waseda Univ.)Mathematical Aspects of Lattice-Based Cryptography (Japanese)

[ Abstract ]

I will explain mathematical aspects of lattice-based cryptography.

I will explain mathematical aspects of lattice-based cryptography.

### 2023/10/18

#### Number Theory Seminar

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

On Igusa varieties (English)

**Wansu Kim**(KAIST/University of Tokyo)On Igusa varieties (English)

[ Abstract ]

In this talk, we construct Igusa varieties and study some basic properties in the setting of abelian-type Shimura varieties, as well as in the analogous setting for function fields (over shtuka spaces). The is joint work with Paul Hamacher.

In this talk, we construct Igusa varieties and study some basic properties in the setting of abelian-type Shimura varieties, as well as in the analogous setting for function fields (over shtuka spaces). The is joint work with Paul Hamacher.

### 2023/10/17

#### Numerical Analysis Seminar

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

Structure-preserving schemes for the Cahn-Hilliard equation with dynamic boundary conditions in two spatial dimensions (Japanese)

[ Reference URL ]

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

**Makoto Okumura**(Konan University)Structure-preserving schemes for the Cahn-Hilliard equation with dynamic boundary conditions in two spatial dimensions (Japanese)

[ Reference URL ]

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

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Train track combinatorics and cluster algebras (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Shunsuke Kano**(MathCCS, Tohoku University)Train track combinatorics and cluster algebras (JAPANESE)

[ Abstract ]

The concepts of train track was introduced by W. P. Thurston to study the measured foliations/laminations and the pseudo-Anosov mapping classes on a surface. In this talk, we translate some concepts of train tracks into the language of cluster algebras using the tropicalization of Goncharov--Shen's potential function. Using this, we translate a combinatorial property of a train track associated with a pseudo-Anosov mapping class into the combinatorial property in cluster algebras, called the sign stability which was introduced by Tsukasa Ishibashi and the speaker.

[ Reference URL ]The concepts of train track was introduced by W. P. Thurston to study the measured foliations/laminations and the pseudo-Anosov mapping classes on a surface. In this talk, we translate some concepts of train tracks into the language of cluster algebras using the tropicalization of Goncharov--Shen's potential function. Using this, we translate a combinatorial property of a train track associated with a pseudo-Anosov mapping class into the combinatorial property in cluster algebras, called the sign stability which was introduced by Tsukasa Ishibashi and the speaker.

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

#### Operator Algebra Seminars

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

$*$-homomorphisms between groupoid C$^*$-algebras

[ Reference URL ]

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

**Fuyuta Komura**(RIKEN)$*$-homomorphisms between groupoid C$^*$-algebras

[ Reference URL ]

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

### 2023/10/16

#### Algebraic Geometry Seminar

14:00-15:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Symmetries of Fano varieties

**Lena Ji**(University of Michigan)Symmetries of Fano varieties

[ Abstract ]

Prokhorov and Shramov proved that the BAB conjecture (which Birkar later proved) implies the uniform Jordan property for automorphism groups of complex Fano varieties of fixed dimension. This property in particular gives an upper bound on the size of semi-simple groups (meaning those with no non-trivial normal abelian subgroups) acting faithfully on n-dimensional complex Fano varieties, and this bound only depends on n. In this talk, we investigate the consequences of a large action by a particular semi-simple group: the symmetric group. This work is joint with Louis Esser and Joaquín Moraga.

Prokhorov and Shramov proved that the BAB conjecture (which Birkar later proved) implies the uniform Jordan property for automorphism groups of complex Fano varieties of fixed dimension. This property in particular gives an upper bound on the size of semi-simple groups (meaning those with no non-trivial normal abelian subgroups) acting faithfully on n-dimensional complex Fano varieties, and this bound only depends on n. In this talk, we investigate the consequences of a large action by a particular semi-simple group: the symmetric group. This work is joint with Louis Esser and Joaquín Moraga.

#### Seminar on Geometric Complex Analysis

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

The limit of Kähler-Ricci flows

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

**Hajime Tsuji**(Sophia University)The limit of Kähler-Ricci flows

[ Abstract ]

In this talk, I would like to present the (normalized) limit of Kähler-Ricci flows for compact Kähler manifolds with intermediate Kodaira dimesion under the condition that the canonical bundle is abundant.

[ Reference URL ]In this talk, I would like to present the (normalized) limit of Kähler-Ricci flows for compact Kähler manifolds with intermediate Kodaira dimesion under the condition that the canonical bundle is abundant.

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

### 2023/10/12

#### Tokyo-Nagoya Algebra Seminar

10:30-12:00 Online

q-deformed rational numbers, Farey sum and a 2-Calabi-Yau category of A_2 quiver (English)

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

**Xin Ren**(Kansai University)q-deformed rational numbers, Farey sum and a 2-Calabi-Yau category of A_2 quiver (English)

[ Abstract ]

Let q be a positive real number. The left and right q-deformed rational numbers were introduced by Bapat, Becker and Licata via regular continued fractions, and the right q-deformed rational number is exactly q-deformed rational number considered by Morier-Genoud and Ovsienko, when q is a formal parameter. They gave a homological interpretation for left and right q-deformed rational numbers by considering a special 2-Calabi–Yau category associated to the A_2 quiver.

In this talk, we begin by introducing the above definitions and related results. Then we give a formula for computing the q-deformed Farey sum of the left q-deformed rational numbers based on the negative continued fractions. We combine the homological interpretation of the left and right q-deformed rational numbers and the q-deformed Farey sum, and give a homological interpretation of the q-deformed Farey sum. We also apply the above results to real quadratic irrational numbers with periodic type.

[ Reference URL ]Let q be a positive real number. The left and right q-deformed rational numbers were introduced by Bapat, Becker and Licata via regular continued fractions, and the right q-deformed rational number is exactly q-deformed rational number considered by Morier-Genoud and Ovsienko, when q is a formal parameter. They gave a homological interpretation for left and right q-deformed rational numbers by considering a special 2-Calabi–Yau category associated to the A_2 quiver.

In this talk, we begin by introducing the above definitions and related results. Then we give a formula for computing the q-deformed Farey sum of the left q-deformed rational numbers based on the negative continued fractions. We combine the homological interpretation of the left and right q-deformed rational numbers and the q-deformed Farey sum, and give a homological interpretation of the q-deformed Farey sum. We also apply the above results to real quadratic irrational numbers with periodic type.

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

### 2023/10/10

#### Tuesday Seminar on Topology

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

Pre-registration required. See our seminar webpage.

Invariant quasimorphisms and coarse geometry of scl (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Masato Mimura**(Tohoku University)Invariant quasimorphisms and coarse geometry of scl (JAPANESE)

[ Abstract ]

The topic of this talk is completely independent from that of the intensive lecture (the Green--Tao theorem) from 9th to 13th, Oct. This talk is based on the series of the joint work with Morimichi Kawasaki, Mitsuaki Kimura, Takahiro Matsushita and Shuhei Maruyama. Quasimorphisms on a group are interesting objects, but for many naturally constructed groups the space of quasimorphisms tends to be either 'trivial' or infinite dimensional. We study the setting of a pair of a group and its normal subgroup, not of a single group, and invariant quasimorphisms. Then, we can obtain a non-zero finite dimensional vector space from this setting. The celebrated Bavard duality theorem is extended to this framework, and the resulting theorem yields some outcome on the coarse geometry of scl (stable commutator length). I will present an overview of the developments of this theory.

[ Reference URL ]The topic of this talk is completely independent from that of the intensive lecture (the Green--Tao theorem) from 9th to 13th, Oct. This talk is based on the series of the joint work with Morimichi Kawasaki, Mitsuaki Kimura, Takahiro Matsushita and Shuhei Maruyama. Quasimorphisms on a group are interesting objects, but for many naturally constructed groups the space of quasimorphisms tends to be either 'trivial' or infinite dimensional. We study the setting of a pair of a group and its normal subgroup, not of a single group, and invariant quasimorphisms. Then, we can obtain a non-zero finite dimensional vector space from this setting. The celebrated Bavard duality theorem is extended to this framework, and the resulting theorem yields some outcome on the coarse geometry of scl (stable commutator length). I will present an overview of the developments of this theory.

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

### 2023/10/05

#### Information Mathematics Seminar

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

Cryptography and Blockchain (Japanese)

**Tatsuaki Okamoto**(NTT)Cryptography and Blockchain (Japanese)

[ Abstract ]

Explanation of cryptography and blockchain

Explanation of cryptography and blockchain

### 2023/10/03

#### Operator Algebra Seminars

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

The VOA origins of Majorana theory

[ Reference URL ]

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

**Alexander Ivanov**(Imperial College London)The VOA origins of Majorana theory

[ Reference URL ]

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

### 2023/09/25

#### Tokyo Probability Seminar

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

Boundary current fluctuations for the half space ASEP (English)

**Jimmy He**(MIT)Boundary current fluctuations for the half space ASEP (English)

[ Abstract ]

The half space asymmetric simple exclusion process (ASEP) is an interacting particle system on the half line, with particles allowed to enter/exit at the boundary. I will discuss recent work on understanding fluctuations for the number of particles in the half space ASEP started with no particles, which exhibits the Baik-Rains phase transition between GSE, GOE, and Gaussian fluctuations as the boundary rates vary. As part of the proof, we find new distributional identities relating this system to two other models, the half space Hall-Littlewood process, and the free boundary Schur process, which allows exact formulas to be computed.

The half space asymmetric simple exclusion process (ASEP) is an interacting particle system on the half line, with particles allowed to enter/exit at the boundary. I will discuss recent work on understanding fluctuations for the number of particles in the half space ASEP started with no particles, which exhibits the Baik-Rains phase transition between GSE, GOE, and Gaussian fluctuations as the boundary rates vary. As part of the proof, we find new distributional identities relating this system to two other models, the half space Hall-Littlewood process, and the free boundary Schur process, which allows exact formulas to be computed.

### 2023/09/14

#### Applied Analysis

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

Bounds on the gradient of minimizers in variational denoising (English)

https://forms.gle/C39ZLdQNVHyVmJ4j8

**Michał Łasica**(The Polish Academy of Sciences)Bounds on the gradient of minimizers in variational denoising (English)

[ Abstract ]

We consider minimization problem for a class of convex integral functionals composed of two terms:

-- a regularizing term of linear growth in the gradient,

-- and a fidelity term penalizing the distance from a given function.

To ensure that such functionals attain their minima, one needs to extend their domain to the BV space. In particular minimizers may exhibit jump discontinuities. I will discuss estimates on the gradient of minimizers in terms of the data, focusing on singular part of the gradient measure.

The talk is based on joint works with P. Rybka, Z. Grochulska and A. Chambolle.

[ Reference URL ]We consider minimization problem for a class of convex integral functionals composed of two terms:

-- a regularizing term of linear growth in the gradient,

-- and a fidelity term penalizing the distance from a given function.

To ensure that such functionals attain their minima, one needs to extend their domain to the BV space. In particular minimizers may exhibit jump discontinuities. I will discuss estimates on the gradient of minimizers in terms of the data, focusing on singular part of the gradient measure.

The talk is based on joint works with P. Rybka, Z. Grochulska and A. Chambolle.

https://forms.gle/C39ZLdQNVHyVmJ4j8

### 2023/09/07

#### Applied Analysis

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

Uniform Convergence of Gradient Flows on a Stack of Banach Spaces (English)

https://forms.gle/T8yWr2gDTYzj8vkE7

**Samuel Mercer**(Delft University of Technology)Uniform Convergence of Gradient Flows on a Stack of Banach Spaces (English)

[ Abstract ]

Within this talk I will recall the classical result: Given a sequence of convex functionals on a Hilbert space, Gamma-convergence of this sequence implies uniform convergence on finite time-intervals for their gradient flows. I will then discuss a generalisation for this result. In particular our functionals are defined on a sequence of distinct Banach spaces that can be stacked together inside of a unifying space. We will study a kind of gradient flow for our functionals inside their respective Banach space and ask the following question. What structure is necessary within our unifying space to attain uniform convergence of gradient flows?

[ Reference URL ]Within this talk I will recall the classical result: Given a sequence of convex functionals on a Hilbert space, Gamma-convergence of this sequence implies uniform convergence on finite time-intervals for their gradient flows. I will then discuss a generalisation for this result. In particular our functionals are defined on a sequence of distinct Banach spaces that can be stacked together inside of a unifying space. We will study a kind of gradient flow for our functionals inside their respective Banach space and ask the following question. What structure is necessary within our unifying space to attain uniform convergence of gradient flows?

https://forms.gle/T8yWr2gDTYzj8vkE7

### 2023/08/30

#### Discrete mathematical modelling seminar

16:30-17:30 Room #370 (Graduate School of Math. Sci. Bldg.)

Classical structure theory for second-order semi-degenerate super-integrable systems (English)

**Joshua Capel**(University of New South Wales)Classical structure theory for second-order semi-degenerate super-integrable systems (English)

[ Abstract ]

Second-order superintegrable systems have long been a subject of interest in the study of integral systems, primarily due to their close connection with separation of variables. Among these, the 'non-degenerate' second-order systems on constant curvature spaces have been particularly well studies, and are mostly understood.

A non-degenerate system in n-dimensions comprises an (n+1)-dimensional vector space of potentials, along with 2n-1 second-order constants that commute with the Hamiltonian of the system.

In contrast, a semi-degenerate system is characterised by having fewer than n+1 parameters. In this talk, we will discuss the structure theory of truly n-dimensional potentials (meaning potentials that are not just restrictions of (n+1)-dimensional counterparts). We will see that the classical structure theory appears just as rich as the non-degenerate case.

This talk is joint work with Jeremy Nugent and Jonathan Kress.

Second-order superintegrable systems have long been a subject of interest in the study of integral systems, primarily due to their close connection with separation of variables. Among these, the 'non-degenerate' second-order systems on constant curvature spaces have been particularly well studies, and are mostly understood.

A non-degenerate system in n-dimensions comprises an (n+1)-dimensional vector space of potentials, along with 2n-1 second-order constants that commute with the Hamiltonian of the system.

In contrast, a semi-degenerate system is characterised by having fewer than n+1 parameters. In this talk, we will discuss the structure theory of truly n-dimensional potentials (meaning potentials that are not just restrictions of (n+1)-dimensional counterparts). We will see that the classical structure theory appears just as rich as the non-degenerate case.

This talk is joint work with Jeremy Nugent and Jonathan Kress.

### 2023/08/25

#### thesis presentations

13:00-14:15 Room #123 (Graduate School of Math. Sci. Bldg.)

Discrete quantum subgroups of quantum doubles

(量子ダブルの離散部分量子群について)

**KITAMURA Kan**(Graduate School of Mathematical Sciences University of Tokyo)Discrete quantum subgroups of quantum doubles

(量子ダブルの離散部分量子群について)

### 2023/08/24

#### Tokyo-Nagoya Algebra Seminar

10:30-12:00 Online

TF equivalence on the real Grothendieck group (Japanese)

[ Reference URL ]

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

**Sota Asai**(University of Tokyo)TF equivalence on the real Grothendieck group (Japanese)

[ Reference URL ]

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

### 2023/08/22

#### Tuesday Seminar of Analysis

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

Towards a Levinson's Theorem for Discrete Magnetic operators on tubes under finite rank perturbations (English)

https://forms.gle/VBp4nSnYYKVpXFhB9

**Daniel Parra**(Universidad de Santiago de Chile)Towards a Levinson's Theorem for Discrete Magnetic operators on tubes under finite rank perturbations (English)

[ Abstract ]

In this talk we study a family of magnetic Hamiltonians on discrete tubes under a finite rank perturbation supported on its border. We go into detail for the case of rank $2$ and show how the eigenvalues can be related to the scattering matrix to exhibit an index theorem in the tradition of Levison’s theorem. We then turn to the general case, discuss the different spectral scenarios that can occur and explain the C*-algebraic framework that could allow us to treat this case. This is an ongoing work with S. Richard (Nagoya), V. Austen (Nagoya) and A. Rennie (Wollongong).

[ Reference URL ]In this talk we study a family of magnetic Hamiltonians on discrete tubes under a finite rank perturbation supported on its border. We go into detail for the case of rank $2$ and show how the eigenvalues can be related to the scattering matrix to exhibit an index theorem in the tradition of Levison’s theorem. We then turn to the general case, discuss the different spectral scenarios that can occur and explain the C*-algebraic framework that could allow us to treat this case. This is an ongoing work with S. Richard (Nagoya), V. Austen (Nagoya) and A. Rennie (Wollongong).

https://forms.gle/VBp4nSnYYKVpXFhB9

### 2023/08/21

#### Classical Analysis

10:00-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Stokes matrices of confluent hypergeometric systems and the isomonodromy deformation equations (ENGLISH)

Stokes matrices of quantum confluent hypergeometric systems and the representation of quantum groups (ENGLISH)

The WKB approximation of (quantum) confluent hypergeometric systems, Cauchy interlacing inequality and crystal basis (ENGLISH)

**Xiaomeng Xu**(BICMR, China) 10:00-11:30Stokes matrices of confluent hypergeometric systems and the isomonodromy deformation equations (ENGLISH)

[ Abstract ]

This talk first gives an introduction to the Stokes matrices of a linear meromorphic system of Poncaré rank 1, and the associated nonlinear isomonodromy deformation equation. The nonlinear equation naturally arises from the theory of Frobenius manifolds, stability conditions, Poisson-Lie groups and so on, and can be seen as a higher rank generalizations of the sixth Painlevé equation. The talk then gives a parameterization of the asymptotics of the solutions of the isomonodromy equation at a critical point, the explicit formula of the monodromy/Stokes matrices of the linear problem via the parameterization, as well as a connection formula between two differential critical points. It can be seen as a generalization of Jimbo's work for the sixth Painlevé equation to a higher rank case. It is partially based on a joint work with Qian Tang.

This talk first gives an introduction to the Stokes matrices of a linear meromorphic system of Poncaré rank 1, and the associated nonlinear isomonodromy deformation equation. The nonlinear equation naturally arises from the theory of Frobenius manifolds, stability conditions, Poisson-Lie groups and so on, and can be seen as a higher rank generalizations of the sixth Painlevé equation. The talk then gives a parameterization of the asymptotics of the solutions of the isomonodromy equation at a critical point, the explicit formula of the monodromy/Stokes matrices of the linear problem via the parameterization, as well as a connection formula between two differential critical points. It can be seen as a generalization of Jimbo's work for the sixth Painlevé equation to a higher rank case. It is partially based on a joint work with Qian Tang.

**Xiaomeng Xu**(BICMR, China) 14:00-15:30Stokes matrices of quantum confluent hypergeometric systems and the representation of quantum groups (ENGLISH)

[ Abstract ]

This talk studies a quantum analog of Stokes matrices of confluent hypergeometric systems. It first gives an introduction to the Stokes phenomenon of an irregular Knizhnik–Zamolodchikov at a second order pole, associated to a regular semisimple element u and a representation $L(\lambda)$ of $gl_n$. It then shows that the Stokes matrices of the

irregular Knizhnik–Zamolodchikov equation define representation of $U_q(gl_n)$ on $L(\lambda)$. In then end, using the isomonodromy approach, it derives an explicit expression of the regularized limit of the Stokes matrices as the regular semisimple element u goes to the caterpillar point in the wonderful compactification.

This talk studies a quantum analog of Stokes matrices of confluent hypergeometric systems. It first gives an introduction to the Stokes phenomenon of an irregular Knizhnik–Zamolodchikov at a second order pole, associated to a regular semisimple element u and a representation $L(\lambda)$ of $gl_n$. It then shows that the Stokes matrices of the

irregular Knizhnik–Zamolodchikov equation define representation of $U_q(gl_n)$ on $L(\lambda)$. In then end, using the isomonodromy approach, it derives an explicit expression of the regularized limit of the Stokes matrices as the regular semisimple element u goes to the caterpillar point in the wonderful compactification.

**Xiaomeng Xu**(BICMR, China) 16:00-17:30The WKB approximation of (quantum) confluent hypergeometric systems, Cauchy interlacing inequality and crystal basis (ENGLISH)

[ Abstract ]

This talk studies the WKB approximation of the linear meromorphic systems of Poncaré rank 1 appearing in talk 1 and 2, via the isomonodromy approach. In the classical case, it unveils a relation between the WKB approximation, the Cauchy interlacing inequality and cluster algebras with the help of the spectral network; in the quantum case, motivated by the crystal limit of the quantum groups, it shows a relation between the WKB approximation and the gl_n-crystal structures. It is partially based on a joint work with

Anton Alekseev, Andrew Neitzke and Yan Zhou.

This talk studies the WKB approximation of the linear meromorphic systems of Poncaré rank 1 appearing in talk 1 and 2, via the isomonodromy approach. In the classical case, it unveils a relation between the WKB approximation, the Cauchy interlacing inequality and cluster algebras with the help of the spectral network; in the quantum case, motivated by the crystal limit of the quantum groups, it shows a relation between the WKB approximation and the gl_n-crystal structures. It is partially based on a joint work with

Anton Alekseev, Andrew Neitzke and Yan Zhou.

### 2023/08/08

#### Lectures

14:00-15:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Cars, Interchanges, Traffic Counters, and some Pretty Darned Good Knot Invariants (English)

http://www.math.toronto.edu/~drorbn/Talks/Tokyo-230808/

**Dror Bar-Natan**(University of Toronto)Cars, Interchanges, Traffic Counters, and some Pretty Darned Good Knot Invariants (English)

[ Abstract ]

Reporting on joint work with Roland van der Veen, I'll tell you some stories about ρ_1, an easy to define, strong, fast to compute, homomorphic, and well-connected knot invariant. ρ_1 was first studied by Rozansky and Overbay, it is dominated by the coloured Jones polynomial (but it isn't lesser!), it has far-reaching generalizations, and I wish I understood it.

[ Reference URL ]Reporting on joint work with Roland van der Veen, I'll tell you some stories about ρ_1, an easy to define, strong, fast to compute, homomorphic, and well-connected knot invariant. ρ_1 was first studied by Rozansky and Overbay, it is dominated by the coloured Jones polynomial (but it isn't lesser!), it has far-reaching generalizations, and I wish I understood it.

http://www.math.toronto.edu/~drorbn/Talks/Tokyo-230808/

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