## Seminar information archive

Seminar information archive ～08/09｜Today's seminar 08/10 | Future seminars 08/11～

#### Tokyo Probability Seminar

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

On the Chapman-Kolmogorov equation for LPP (JAPANESE)

**新井裕太**(千葉商科大学)On the Chapman-Kolmogorov equation for LPP (JAPANESE)

[ Abstract ]

KPZ普遍クラスに属するいくつかのモデルにおいて，その推移確率等が複素積分形の関数で書き表せることが知られている．しかしながら，複素積分を用いた計算は複雑となることも多く，KPZ普遍クラスに属するモデルにとって重要な確率論的性質を証明するのが困難となっていた．近年，この問題を解決するものとして対称多項式等を用いた組合せ論的手法に注目が集まってきている．本講演では，最先端の組合せ論的アプローチを用いることで，KPZ普遍クラスの基礎的なモデルであるLast Passage Percolation（LPP）において， Chapman-Kolmogorov equationが容易に得られることを紹介する.

KPZ普遍クラスに属するいくつかのモデルにおいて，その推移確率等が複素積分形の関数で書き表せることが知られている．しかしながら，複素積分を用いた計算は複雑となることも多く，KPZ普遍クラスに属するモデルにとって重要な確率論的性質を証明するのが困難となっていた．近年，この問題を解決するものとして対称多項式等を用いた組合せ論的手法に注目が集まってきている．本講演では，最先端の組合せ論的アプローチを用いることで，KPZ普遍クラスの基礎的なモデルであるLast Passage Percolation（LPP）において， Chapman-Kolmogorov equationが容易に得られることを紹介する.

### 2023/05/02

#### Operator Algebra Seminars

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

KK-theory, localization algebras, and approximation

[ Reference URL ]

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

**Ayoub Hafid**(Univ. Tokyo)KK-theory, localization algebras, and approximation

[ Reference URL ]

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

#### Operator Algebra Seminars

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

KK-theory, localization algebras, and approximation

[ Reference URL ]

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

**Ayoub Hafid**(Univ. Tokyo)KK-theory, localization algebras, and approximation

[ Reference URL ]

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

### 2023/04/28

#### Colloquium

15:30-16:30 Hybrid

If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please take part online [Reference URL]

On quantum topology (日本語)

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZIkc-Cvrz4oHNXj_kafJqhU6ZFWCABqgojM

If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please take part online [Reference URL]

**Kazuo Habiro**(Graduate School of Mathematical Sciences, the University of Tokyo)On quantum topology (日本語)

[ Abstract ]

I started my research from surgery theory of knots and 3-manifolds. This is related to finite type invariants, which was studied intensively at that time. I obtained a result which characterises the information that is carried by finite type invariants in terms of clasper surgery. After that, I have studied quantum invariants of integral homology spheres, Kirby calculus of framed links, quantum invariants of bottom tangles, functorialization of Le-Murakami-Ohtsuki invariants, quantum fundamental groups and quantum representation variety of 3-manifolds, traces of categorified quantum groups, etc. I would like to reflect on these studies and also discuss future prospects.

[ Reference URL ]I started my research from surgery theory of knots and 3-manifolds. This is related to finite type invariants, which was studied intensively at that time. I obtained a result which characterises the information that is carried by finite type invariants in terms of clasper surgery. After that, I have studied quantum invariants of integral homology spheres, Kirby calculus of framed links, quantum invariants of bottom tangles, functorialization of Le-Murakami-Ohtsuki invariants, quantum fundamental groups and quantum representation variety of 3-manifolds, traces of categorified quantum groups, etc. I would like to reflect on these studies and also discuss future prospects.

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZIkc-Cvrz4oHNXj_kafJqhU6ZFWCABqgojM

#### Tokyo-Nagoya Algebra Seminar

13:00-14:30 Online

Please see the reference URL for details on the online seminar.

Full exceptional collections associated with Bridgeland stability conditions (Japanese)

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

Please see the reference URL for details on the online seminar.

**Takumi Otani**(Osaka Univeristy)Full exceptional collections associated with Bridgeland stability conditions (Japanese)

[ Abstract ]

The space of Bridgeland stability conditions on a triangulated category is important in mirror symmetry and many people develop various techniques to study it. In order to study the homotopy type of the space of stability conditions, Macri studied stability conditions associated with full exceptional collections. Based on his work, Dimitrov-Katzarkov introduced the notion of a full σ-exceptional collection for a stability condition σ.

In this talk, I will explain the relationship between full exceptional collections and stability conditions and some properties. I will also talk about the existence of full σ-exceptional collections for the derived category of an acyclic quiver.

[ Reference URL ]The space of Bridgeland stability conditions on a triangulated category is important in mirror symmetry and many people develop various techniques to study it. In order to study the homotopy type of the space of stability conditions, Macri studied stability conditions associated with full exceptional collections. Based on his work, Dimitrov-Katzarkov introduced the notion of a full σ-exceptional collection for a stability condition σ.

In this talk, I will explain the relationship between full exceptional collections and stability conditions and some properties. I will also talk about the existence of full σ-exceptional collections for the derived category of an acyclic quiver.

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

#### Algebraic Geometry Seminar

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

On the degree of irrationality of complete intersections (Japanese )

**Taro Yoshino**(Tokyo)On the degree of irrationality of complete intersections (Japanese )

[ Abstract ]

The degree of irrationality of a variety X is the minimum degree of a dominant, generically finite rational map from X to a rational variety. This invariant gives a measure of how far X is from being rational. There were some varieties whose degree of irrationality was computed. For example, in 2017, Bastianelli, De Poi, Ein, Lazarsfeld, and Ullery computed the degree of irrationality of very general hypersurfaces of general type by using the positivity of the canonical line bundle. On the other hand, in 2020, Chen and Stapleton obtained the lower bound of the degree of irrationality of very general Fano hypersurfaces by using the reduction of modulo p.

In this talk, we will show that we can obtain the lower bound of the degree of irrationality of very general Fano complete intersections. For obtaining the bound, we make a minor adjustment to Chen--Stapleton's method using the trace map of differential modules.

This talk is based on joint work with Lucas Braune.

The degree of irrationality of a variety X is the minimum degree of a dominant, generically finite rational map from X to a rational variety. This invariant gives a measure of how far X is from being rational. There were some varieties whose degree of irrationality was computed. For example, in 2017, Bastianelli, De Poi, Ein, Lazarsfeld, and Ullery computed the degree of irrationality of very general hypersurfaces of general type by using the positivity of the canonical line bundle. On the other hand, in 2020, Chen and Stapleton obtained the lower bound of the degree of irrationality of very general Fano hypersurfaces by using the reduction of modulo p.

In this talk, we will show that we can obtain the lower bound of the degree of irrationality of very general Fano complete intersections. For obtaining the bound, we make a minor adjustment to Chen--Stapleton's method using the trace map of differential modules.

This talk is based on joint work with Lucas Braune.

### 2023/04/27

#### Information Mathematics Seminar

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

The basics of cryptography II (Japanese)

**Tatsuaki Okamoto**(NTT)The basics of cryptography II (Japanese)

[ Abstract ]

Explanation of the basics of cryptography

Explanation of the basics of cryptography

### 2023/04/26

#### Number Theory Seminar

18:00-19:30 Room #117 (Graduate School of Math. Sci. Bldg.)

Live transmission from IHES, Warning: Start time is one hour later than usual.

A Conjectural Reciprocity Law for Realizations of Motives

https://indico.math.cnrs.fr/event/9634/

Live transmission from IHES, Warning: Start time is one hour later than usual.

**Dustin Clausen**(Institut des Hautes Études Scientifiques)A Conjectural Reciprocity Law for Realizations of Motives

[ Abstract ]

A motive over a scheme S is a bit of linear algebra which is supposed to "universally" capture the cohomology of smooth proper S-schemes. Motives can be studied via various "realizations", which are objects of more concrete linear algebraic categories attached to S. It is known that over certain S, these different realizations are related to one another via comparison isomorphisms, as in Hodge theory. In this talk, I will try to explain that for completely general S, there is a much more subtle kind of relationship between these realizations, which takes a similar form to classical reciprocity laws in number theory.

[ Reference URL ]A motive over a scheme S is a bit of linear algebra which is supposed to "universally" capture the cohomology of smooth proper S-schemes. Motives can be studied via various "realizations", which are objects of more concrete linear algebraic categories attached to S. It is known that over certain S, these different realizations are related to one another via comparison isomorphisms, as in Hodge theory. In this talk, I will try to explain that for completely general S, there is a much more subtle kind of relationship between these realizations, which takes a similar form to classical reciprocity laws in number theory.

https://indico.math.cnrs.fr/event/9634/

### 2023/04/25

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Harmonic measures and rigidity of surface group actions on the circle (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Hiraku Nozawa**(Ritsumeikan University)Harmonic measures and rigidity of surface group actions on the circle (JAPANESE)

[ Abstract ]

We study rigidity properties of surface group actions on the circle via harmonic measures on the suspension bundles, which are measures invariant under the heat diffusion along leaves. We will explain a curvature estimate and a Gauss-Bonnet formula for an S^1-connection obtained by taking the average of the flat connection on the suspension bundle with respect to a harmonic measure. As consequences, we give a precise description of the harmonic measure on suspension foliations with maximal Euler number and an alternative proof of semiconjugacy rigidity theorems of Matsumoto and Burger-Iozzi-Wienhard for actions with maximal Euler number. This is joint work with Masanori Adachi and Yoshifumi Matsuda.

[ Reference URL ]We study rigidity properties of surface group actions on the circle via harmonic measures on the suspension bundles, which are measures invariant under the heat diffusion along leaves. We will explain a curvature estimate and a Gauss-Bonnet formula for an S^1-connection obtained by taking the average of the flat connection on the suspension bundle with respect to a harmonic measure. As consequences, we give a precise description of the harmonic measure on suspension foliations with maximal Euler number and an alternative proof of semiconjugacy rigidity theorems of Matsumoto and Burger-Iozzi-Wienhard for actions with maximal Euler number. This is joint work with Masanori Adachi and Yoshifumi Matsuda.

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

#### Numerical Analysis Seminar

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

Combinatorial preprocessing methods for differential-algebraic equations (Japanese)

[ Reference URL ]

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

**Taihei Oki**(The University of Tokyo)Combinatorial preprocessing methods for differential-algebraic equations (Japanese)

[ Reference URL ]

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

### 2023/04/24

#### Seminar on Geometric Complex Analysis

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

On site+Zoom

Guan's theorems on optimal strong openness and concavity of minimal $L^2$ integrals (日本語)

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

On site+Zoom

**Takeo Ohsawa**(Nogoya Universiry)Guan's theorems on optimal strong openness and concavity of minimal $L^2$ integrals (日本語)

[ Abstract ]

Motivated by a question of approximating plurisubharmonic (=psh) functions by those with tame singularities, Demailly and Kollar asked several basic questions on the singularities of psh functions. Guan solved two of them effectively in a paper published in 2019. One of their corollaries says the following.

THEOREM. Let $\Omega$ be a pseudoconvex domain in $\mathbb{C}^n$ and let $\varphi$ be a negative psh function on $\Omega$ such that $\int_\Omega{e^{-\varphi}}<\infty$. Then, $e^{-p\varphi}\in L^1_{\text{loc}}$ around $x$ for any $x\in\Omega$ and $p>1$ satisfying the inequality $$

\frac{p}{p-1}>\frac{\int_\Omega{e^{-\varphi}}}{K_\Omega(x)},

$$ where $K_\Omega$ denotes the diagonalized Bergman kernel of $\Omega$.

This remarkable result is a consequence of a basic property of the minimal $L^2$ integrals (=MLI). The main purpose of the talk is to give an outline of the proof of Theorem by explaining the relation between several notions including the MLI which measure the singularities of psh functions. It will also be mentioned that the proof of Theorem is essentially based on the optimal Ohsawa-Takegoshi type extension theorem, which leads to a concavity property of MLI. Recent papers by Guan and his students will be reviewed, too.

[ Reference URL ]Motivated by a question of approximating plurisubharmonic (=psh) functions by those with tame singularities, Demailly and Kollar asked several basic questions on the singularities of psh functions. Guan solved two of them effectively in a paper published in 2019. One of their corollaries says the following.

THEOREM. Let $\Omega$ be a pseudoconvex domain in $\mathbb{C}^n$ and let $\varphi$ be a negative psh function on $\Omega$ such that $\int_\Omega{e^{-\varphi}}<\infty$. Then, $e^{-p\varphi}\in L^1_{\text{loc}}$ around $x$ for any $x\in\Omega$ and $p>1$ satisfying the inequality $$

\frac{p}{p-1}>\frac{\int_\Omega{e^{-\varphi}}}{K_\Omega(x)},

$$ where $K_\Omega$ denotes the diagonalized Bergman kernel of $\Omega$.

This remarkable result is a consequence of a basic property of the minimal $L^2$ integrals (=MLI). The main purpose of the talk is to give an outline of the proof of Theorem by explaining the relation between several notions including the MLI which measure the singularities of psh functions. It will also be mentioned that the proof of Theorem is essentially based on the optimal Ohsawa-Takegoshi type extension theorem, which leads to a concavity property of MLI. Recent papers by Guan and his students will be reviewed, too.

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

#### Tokyo Probability Seminar

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

Mobility edge, the Poisson Infinite weighted tree of Aldous and Lévy Matrices (English)

**Charles Bordenave**(Institut de Mathématiques de Marseille)Mobility edge, the Poisson Infinite weighted tree of Aldous and Lévy Matrices (English)

[ Abstract ]

Anderson's 1958 paper on wave scattering in disordered media is still of central importance in contemporary mathematical physics. In this talk, we will present recent progress in understanding the phenomena of localization / delocalization of eigenwaves for some random operators. These operators are built on random trees introduced by Aldous and these are the scaling limits of heavy-tailed random matrices, the Lévy matrices. The focus will be put on the existence of a mobility edge, that is to say of かn abrupt transition between localization and delocalization of eigenwaves. It is a work in collaboration with Amol Aggarwal (Columbia) and Patrick Lopatto (NYU).

Anderson's 1958 paper on wave scattering in disordered media is still of central importance in contemporary mathematical physics. In this talk, we will present recent progress in understanding the phenomena of localization / delocalization of eigenwaves for some random operators. These operators are built on random trees introduced by Aldous and these are the scaling limits of heavy-tailed random matrices, the Lévy matrices. The focus will be put on the existence of a mobility edge, that is to say of かn abrupt transition between localization and delocalization of eigenwaves. It is a work in collaboration with Amol Aggarwal (Columbia) and Patrick Lopatto (NYU).

#### Infinite Analysis Seminar Tokyo

16:00-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Euler type integral formulas and hypergeometric solutions for

variants of the $q$ hypergeometric equations.

(Japanese)

**Takahiko Nobukawa**(Kobe University )Euler type integral formulas and hypergeometric solutions for

variants of the $q$ hypergeometric equations.

(Japanese)

[ Abstract ]

We know that Papperitz's differential equation is essentially obtained from

Gauss' hypergeometric equation by applying a Moebius transformation,

implying that we have Euler type integral formulas or hypergeometric solutions.

The variants of the $q$ hypergeometric equations, introduced by

Hatano-Matsunawa-Sato-Takemura (Funkcial. Ekvac.,2022), are second order

$q$-difference systems which can be regarded as $q$ analoges of Papperitz's equation.

This motivates us for deriving Euler type integral formulas and hypergeometric solutions

for the pertinent $q$-difference systems. If time admits, I explain

the relation with $q$-analogues of Kummer's 24 solutions,

or the variants of multivariate $q$-hypergeometric functions.

This talk is based on the collaboration with Taikei Fujii.

We know that Papperitz's differential equation is essentially obtained from

Gauss' hypergeometric equation by applying a Moebius transformation,

implying that we have Euler type integral formulas or hypergeometric solutions.

The variants of the $q$ hypergeometric equations, introduced by

Hatano-Matsunawa-Sato-Takemura (Funkcial. Ekvac.,2022), are second order

$q$-difference systems which can be regarded as $q$ analoges of Papperitz's equation.

This motivates us for deriving Euler type integral formulas and hypergeometric solutions

for the pertinent $q$-difference systems. If time admits, I explain

the relation with $q$-analogues of Kummer's 24 solutions,

or the variants of multivariate $q$-hypergeometric functions.

This talk is based on the collaboration with Taikei Fujii.

### 2023/04/21

#### Tokyo-Nagoya Algebra Seminar

13:00-14:30 Online

Please see the reference URL for details on the online seminar.

Categorifications of deformed Cartan matrices (Japanese)

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

Please see the reference URL for details on the online seminar.

**Kota Murakami**(University of Tokyo)Categorifications of deformed Cartan matrices (Japanese)

[ Abstract ]

In a series of works of Gei\ss-Leclerc-Schr\″oer, they introduced a version of preprojective algebra associated with a symmetrizable generalized Cartan matrix and its symmetrizer. For finite type, it can be regarded as an un-graded analogue of Jacobian algebra of certain quiver with potential appeared in the theory of (monoidal) categorification of cluster algebras.

In this talk, we will present an interpretation of graded structures of the preprojective algebra of general type, in terms of a multi-parameter deformation of generalized Cartan matrix and relevant combinatorics motivated from several contexts in the theory of quantum loop algebras or quiver $\mathcal{W}$-algebras. From the vantage point of the representation theory of preprojective algebra, we will prove several purely combinatorial properties of these concepts. This talk is based on a joint work with Ryo Fujita (RIMS).

[ Reference URL ]In a series of works of Gei\ss-Leclerc-Schr\″oer, they introduced a version of preprojective algebra associated with a symmetrizable generalized Cartan matrix and its symmetrizer. For finite type, it can be regarded as an un-graded analogue of Jacobian algebra of certain quiver with potential appeared in the theory of (monoidal) categorification of cluster algebras.

In this talk, we will present an interpretation of graded structures of the preprojective algebra of general type, in terms of a multi-parameter deformation of generalized Cartan matrix and relevant combinatorics motivated from several contexts in the theory of quantum loop algebras or quiver $\mathcal{W}$-algebras. From the vantage point of the representation theory of preprojective algebra, we will prove several purely combinatorial properties of these concepts. This talk is based on a joint work with Ryo Fujita (RIMS).

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

#### Algebraic Geometry Seminar

14:00-15:30 Room #117 (Graduate School of Math. Sci. Bldg.)

Endomorphisms of varieties and Bott vanishing (Japanese)

**Tatsuro Kawakami**(Kyoto University)Endomorphisms of varieties and Bott vanishing (Japanese)

[ Abstract ]

In this talk, we show that a projective variety with an int-amplified endomorphism of degree invertible in the base field satisfies Bott vanishing. This is a new way to analyze which varieties have nontrivial endomorphisms. In particular, we extend some classification results on varieties admitting endomorphisms (for Fano threefolds of Picard number one and several other cases) to any characteristic. This talk is based on joint work with Burt Totaro.

In this talk, we show that a projective variety with an int-amplified endomorphism of degree invertible in the base field satisfies Bott vanishing. This is a new way to analyze which varieties have nontrivial endomorphisms. In particular, we extend some classification results on varieties admitting endomorphisms (for Fano threefolds of Picard number one and several other cases) to any characteristic. This talk is based on joint work with Burt Totaro.

#### Algebraic Geometry Seminar

12:45-13:45 Room #ハイブリッド開催/117 (Graduate School of Math. Sci. Bldg.)

ACC of plc thresholds (English)

**Sung Rak Choi**(Yonsei University )ACC of plc thresholds (English)

[ Abstract ]

The notion of potential pairs was developed as a means to bound the singularities while running the anti-MMP. They behave similarly with the usual klt, lc pairs.

We introduce potential log canonical threshold and prove that the set of these thresholds also satisfies the ascending chain condition (ACC). We also study the relation with the complements. This is a joint work with Sungwook Jang.

The notion of potential pairs was developed as a means to bound the singularities while running the anti-MMP. They behave similarly with the usual klt, lc pairs.

We introduce potential log canonical threshold and prove that the set of these thresholds also satisfies the ascending chain condition (ACC). We also study the relation with the complements. This is a joint work with Sungwook Jang.

### 2023/04/20

#### Information Mathematics Seminar

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

The basics of cryptography (Japanese)

**Tatsuaki Okamoto**(NTT)The basics of cryptography (Japanese)

[ Abstract ]

Explanation of the basics of cryptography

Explanation of the basics of cryptography

### 2023/04/19

#### Number Theory Seminar

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

The conjugate uniformization in the semistable case (English)

https://sites.google.com/site/nclmzzr/

**Nicola Mazzari**(University of Padua)The conjugate uniformization in the semistable case (English)

[ Abstract ]

We will review some recent results by Iovita-Morrow-Zaharescu about p-adic uniformization of abelian varieties with good reduction. Most of it relies on the theory developed by Fontaine especially about almost Cp-representations. These results were recently generalised by Howe-Morrow-Wear, via p-divisible groups.

We will explain how to treat the semistable case with focus on some really basic example, like the Tate elliptic curve.

[ Reference URL ]We will review some recent results by Iovita-Morrow-Zaharescu about p-adic uniformization of abelian varieties with good reduction. Most of it relies on the theory developed by Fontaine especially about almost Cp-representations. These results were recently generalised by Howe-Morrow-Wear, via p-divisible groups.

We will explain how to treat the semistable case with focus on some really basic example, like the Tate elliptic curve.

https://sites.google.com/site/nclmzzr/

### 2023/04/18

#### Operator Algebra Seminars

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

Representation theory of subregular W-algebras and principal W-superalgebras (English)

[ Reference URL ]

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

**Naoki Genra**(Univ. Tokyo)Representation theory of subregular W-algebras and principal W-superalgebras (English)

[ Reference URL ]

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

#### Operator Algebra Seminars

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

Representation theory of subregular W-algebras and principal W-superalgebras

[ Reference URL ]

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

**Naoki Genra**(Univ. Tokyo)Representation theory of subregular W-algebras and principal W-superalgebras

[ 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.

A crossed homomorphism on a big mapping class group (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Shuhei Maruyama**(Chuo University)A crossed homomorphism on a big mapping class group (JAPANESE)

[ Abstract ]

Big mapping class groups are mapping class groups of surfaces of infinite type. Calegari and Chen determined the second (co)homology group of the mapping class group of the sphere minus a Cantor set. They also raised related questions: one of the questions asks an explicit form of certain crossed homomorphisms on the big mapping class group. In this talk, we provide a construction of crossed homomorphisms via group actions on the circle, which answers the question of Calegari and Chen.

[ Reference URL ]Big mapping class groups are mapping class groups of surfaces of infinite type. Calegari and Chen determined the second (co)homology group of the mapping class group of the sphere minus a Cantor set. They also raised related questions: one of the questions asks an explicit form of certain crossed homomorphisms on the big mapping class group. In this talk, we provide a construction of crossed homomorphisms via group actions on the circle, which answers the question of Calegari and Chen.

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

### 2023/04/17

#### Tokyo Probability Seminar

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

Construction of Sobolev spaces and energies on the Sierpinski carpet (Japanese)

**清水良輔**(早稲田大学)Construction of Sobolev spaces and energies on the Sierpinski carpet (Japanese)

### 2023/04/13

#### Information Mathematics Seminar

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

Certification and signature

------Foundation of cryptography (Japanese)

**Tatsuaki Okamoto**(NTT)Certification and signature

------Foundation of cryptography (Japanese)

[ Abstract ]

Explanation on certification and signature.

Explanation on certification and signature.

### 2023/04/11

#### 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 stable cohomology of the (IA-)automorphism groups of free groups (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Kazuo Habiro**(The Univesity of Tokyo)On the stable cohomology of the (IA-)automorphism groups of free groups (JAPANESE)

[ Abstract ]

By combining Borel's stability and vanishing theorem for the stable cohomology of GL(n,Z) with coefficients in algebraic GL(n,Z)-representations and the Hochschild-Serre spectral sequence, we compute the twisted first cohomology of the automorphism group Aut(F_n) of the free group F_n of rank n. This method is used also in the study of the stable rational cohomology of the IA-automorphism group IA_n of F_n. We propose a conjectural algebraic structure of the stable rational cohomology of IA_n, and consider some relations to known results and conjectures. We also consider a conjectural structure of the stable rational cohomology of the Torelli groups of surfaces. This is a joint work with Mai Katada.

[ Reference URL ]By combining Borel's stability and vanishing theorem for the stable cohomology of GL(n,Z) with coefficients in algebraic GL(n,Z)-representations and the Hochschild-Serre spectral sequence, we compute the twisted first cohomology of the automorphism group Aut(F_n) of the free group F_n of rank n. This method is used also in the study of the stable rational cohomology of the IA-automorphism group IA_n of F_n. We propose a conjectural algebraic structure of the stable rational cohomology of IA_n, and consider some relations to known results and conjectures. We also consider a conjectural structure of the stable rational cohomology of the Torelli groups of surfaces. This is a joint work with Mai Katada.

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

### 2023/04/06

#### Applied Analysis

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

Blowup solutions to the Keller-Segel system (English)

https://forms.gle/7ogZKyh1oXKkPbN56

**Van Tien Nguyen**(National Taiwan University)Blowup solutions to the Keller-Segel system (English)

[ Abstract ]

I will present constructive examples of finite-time blowup solutions to the Keller-Segel system in $\mathbb{R}^d$. For $d = 2$ ($L^1$-critical), there are finite time blowup solutions that are of Type II with finite mass. Blowup rates are completely quantized according to a discrete spectrum of a linearized operator around the rescaled stationary solution in the self-similar setting. There is a stable blowup mechanism which is expected to be generic among others. For $d \geq 3$ ($L^1$-supercritical), we construct finite time blowup solutions that are completely unrelated to the self-similar scale, in particular, they are of Type II with finite mass. Interestingly, the radial blowup profile is linked to the traveling-wave of the 1D viscous Burgers equation. Our constructed solution actually has the form of collapsing-ring which consists of an imploding, smoothed-out shock wave moving towards the origin to form a Dirac mass at the singularity. I will also discuss other blowup patterns that possibly occur in the cases $d = 2,3,4$.

[ Reference URL ]I will present constructive examples of finite-time blowup solutions to the Keller-Segel system in $\mathbb{R}^d$. For $d = 2$ ($L^1$-critical), there are finite time blowup solutions that are of Type II with finite mass. Blowup rates are completely quantized according to a discrete spectrum of a linearized operator around the rescaled stationary solution in the self-similar setting. There is a stable blowup mechanism which is expected to be generic among others. For $d \geq 3$ ($L^1$-supercritical), we construct finite time blowup solutions that are completely unrelated to the self-similar scale, in particular, they are of Type II with finite mass. Interestingly, the radial blowup profile is linked to the traveling-wave of the 1D viscous Burgers equation. Our constructed solution actually has the form of collapsing-ring which consists of an imploding, smoothed-out shock wave moving towards the origin to form a Dirac mass at the singularity. I will also discuss other blowup patterns that possibly occur in the cases $d = 2,3,4$.

https://forms.gle/7ogZKyh1oXKkPbN56

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