## Seminar information archive

Seminar information archive ～10/22｜Today's seminar 10/23 | Future seminars 10/24～

### 2014/09/22

#### Infinite Analysis Seminar Tokyo

13:30-16:00 Room #117 (Graduate School of Math. Sci. Bldg.)

Colored HOMFLY homology of knots and links (ENGLISH)

**Satoshi Nawata**(Theoretical Physics at NIKHEF)Colored HOMFLY homology of knots and links (ENGLISH)

[ Abstract ]

In this talk I will present structural properties of colored HOMFLY homology of knots and links. These rich properties of the categorification of the colored HOMFLY polynomial are obtained by using various methods: physics insights, representation theory of Lie super-algebras, double affine Hecke algebras, etc. This in turn enables computation of colored HOMFLY homology for various classes of knots and links and consequent computation of super-A-polynomial - the deformation of the classical A-polynomial. I will also explain recent results and special additional properties for colored Kauffman homology as well as the case of links. Although I will try to give a talk accessible to mathematicians, there is no proof and rigorousness in this talk.

In this talk I will present structural properties of colored HOMFLY homology of knots and links. These rich properties of the categorification of the colored HOMFLY polynomial are obtained by using various methods: physics insights, representation theory of Lie super-algebras, double affine Hecke algebras, etc. This in turn enables computation of colored HOMFLY homology for various classes of knots and links and consequent computation of super-A-polynomial - the deformation of the classical A-polynomial. I will also explain recent results and special additional properties for colored Kauffman homology as well as the case of links. Although I will try to give a talk accessible to mathematicians, there is no proof and rigorousness in this talk.

### 2014/09/19

#### Colloquium

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

William Thurston and foliation theory (ENGLISH)

**Etienne Ghys**(École normale supérieure de Lyon)William Thurston and foliation theory (ENGLISH)

[ Abstract ]

Between 1972 and 1976, William Thurston revolutionized foliation theory. Twenty years later, he described this period of his mathematical life in a remarkable paper « On proofs and progress in mathematics ». In this talk, I will begin by a general overview of some of Thurston's contribution to this theory. I will then describe some of the current development.

Between 1972 and 1976, William Thurston revolutionized foliation theory. Twenty years later, he described this period of his mathematical life in a remarkable paper « On proofs and progress in mathematics ». In this talk, I will begin by a general overview of some of Thurston's contribution to this theory. I will then describe some of the current development.

#### FMSP Lectures

14:30-16:00 Room #128 (Graduate School of Math. Sci. Bldg.)

A bridge between knotted graphs and axiomatizations of groups (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Lebed.pdf

**Victoria Lebed**(Osaka City University, JSPS)A bridge between knotted graphs and axiomatizations of groups (ENGLISH)

[ Abstract ]

This talk will be devoted to a new algebraic structure called qualgebra. From the topological viewpoint, our construction is motivated by a study of knotted 3-valent graphs via combinatorially defined coloring invariants. From the algebraic viewpoint, it gives a part of an alternative axiomatization of groups, describing the properties of the conjugation operation and its interactions with the group multiplication. Explicit examples of qualgebras and associated graph invariants will be given.

[ Reference URL ]This talk will be devoted to a new algebraic structure called qualgebra. From the topological viewpoint, our construction is motivated by a study of knotted 3-valent graphs via combinatorially defined coloring invariants. From the algebraic viewpoint, it gives a part of an alternative axiomatization of groups, describing the properties of the conjugation operation and its interactions with the group multiplication. Explicit examples of qualgebras and associated graph invariants will be given.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Lebed.pdf

### 2014/09/17

#### PDE Real Analysis Seminar

16:30-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)

On the abstract evolution equations of hyperbolic type (JAPANESE)

**Kentarou Yoshii**(Faculty of Science Division I, Tokyo University of Science)On the abstract evolution equations of hyperbolic type (JAPANESE)

[ Abstract ]

This talk deals with the abstract Cauchy problem for linear evolution equations of hyperbolic type in a Hilbert space. We will discuss the existence and uniqueness of its classical solution and apply the results to linear Schrödinger equations with time dependent potentials.

This talk deals with the abstract Cauchy problem for linear evolution equations of hyperbolic type in a Hilbert space. We will discuss the existence and uniqueness of its classical solution and apply the results to linear Schrödinger equations with time dependent potentials.

### 2014/09/12

#### FMSP Lectures

10:30-15:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Stochastic homogenization for first order Hamilton-Jacobi equations(III) (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/Tran2014_0908-0912.pdf

**Hung V. Tran**(The University of Chicago)Stochastic homogenization for first order Hamilton-Jacobi equations(III) (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/Tran2014_0908-0912.pdf

### 2014/09/10

#### FMSP Lectures

10:30-15:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Stochastic homogenization for first order Hamilton-Jacobi equations(II) (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/Tran2014_0908-0912.pdf

**Hung V. Tran**(The University of Chicago)Stochastic homogenization for first order Hamilton-Jacobi equations(II) (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/Tran2014_0908-0912.pdf

### 2014/09/09

#### Tuesday Seminar of Analysis

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Energy methods and blow-up rate for semilinear wave equations in the superconformal case (ENGLISH)

**Hatem Zaag**(CNRS / University of Paris Nord)Energy methods and blow-up rate for semilinear wave equations in the superconformal case (ENGLISH)

[ Abstract ]

In a series of papers with Mohamed Ali Hamza (University of Tunis-el Manar), we consider the semilinear wave equations with power nonlinearity.

In the subconformal and the conformal case, we consider perturbations with lower order terms and modify the Lyapunov functional Antonini and Merle designed for the unperturbed case. We also find a blow-up criterion for the equation. As a consequence, we bound the Lyapunov functional. Thanks to interpolations in Sobolev spaces and a Gagliardo-Nirenberg inequality, we bound the solution in the self-similar variable, which gives a sharp bound on the blow-up rate.

Surprisingly, our approach works in the superconformal case (still Sobolev subcritical), leading to a new bound on the blow-up rate, which improves the bound of Killip, Stoval and Visan.

In a series of papers with Mohamed Ali Hamza (University of Tunis-el Manar), we consider the semilinear wave equations with power nonlinearity.

In the subconformal and the conformal case, we consider perturbations with lower order terms and modify the Lyapunov functional Antonini and Merle designed for the unperturbed case. We also find a blow-up criterion for the equation. As a consequence, we bound the Lyapunov functional. Thanks to interpolations in Sobolev spaces and a Gagliardo-Nirenberg inequality, we bound the solution in the self-similar variable, which gives a sharp bound on the blow-up rate.

Surprisingly, our approach works in the superconformal case (still Sobolev subcritical), leading to a new bound on the blow-up rate, which improves the bound of Killip, Stoval and Visan.

#### FMSP Lectures

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Energy methods and blow-up rate for semilinear wave equations in the superconformal case (ENGLISH)

**Hatem Zaag**(CNRS/University of Paris Nord)Energy methods and blow-up rate for semilinear wave equations in the superconformal case (ENGLISH)

[ Abstract ]

In a series of papers with Mohamed Ali Hamza (University of Tunis-el Manar), we consider the semilinear wave equations with power nonlinearity.

In the subconformal and the conformal case, we consider perturbations with lower order terms and modify the Lyapunov functional Antonini and Merle designed for the unperturbed case. We also find a blow-up criterion for the equation. As a consequence, we bound the Lyapunov functional. Thanks to interpolations in Sobolev spaces and a Gagliardo-Nirenberg inequality, we bound the solution in the self-similar variable, which gives a sharp bound on the blow-up rate.

Surprisingly, our approach works in the superconformal case (still Sobolev subcritical), leading to a new bound on the blow-up rate, which improves the bound of Killip, Stoval and Visan.

In a series of papers with Mohamed Ali Hamza (University of Tunis-el Manar), we consider the semilinear wave equations with power nonlinearity.

In the subconformal and the conformal case, we consider perturbations with lower order terms and modify the Lyapunov functional Antonini and Merle designed for the unperturbed case. We also find a blow-up criterion for the equation. As a consequence, we bound the Lyapunov functional. Thanks to interpolations in Sobolev spaces and a Gagliardo-Nirenberg inequality, we bound the solution in the self-similar variable, which gives a sharp bound on the blow-up rate.

Surprisingly, our approach works in the superconformal case (still Sobolev subcritical), leading to a new bound on the blow-up rate, which improves the bound of Killip, Stoval and Visan.

### 2014/09/08

#### FMSP Lectures

10:30-15:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Stochastic homogenization for first order Hamilton-Jacobi equations(I) (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/Tran2014_0908-0912.pdf

**Hung V. Tran**(The University of Chicago)Stochastic homogenization for first order Hamilton-Jacobi equations(I) (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/Tran2014_0908-0912.pdf

### 2014/09/04

#### Lectures

12:10-13:00 Room #470 (Graduate School of Math. Sci. Bldg.)

"X-ray imaging of moving objects" (ENGLISH)

**Samuli Siltanen**(University of Helsinki, Finland)"X-ray imaging of moving objects" (ENGLISH)

### 2014/08/28

#### thesis presentations

10:00-11:15 Room #128 (Graduate School of Math. Sci. Bldg.)

On the C1 stabilization of homoclinic tangencies for diffeomorphisms in dimension three(3次元の微分同相写像に対するホモクリニック接触のC1安定化について) (JAPANESE)

**李 曉龍**(東京大学大学院数理科学研究科)On the C1 stabilization of homoclinic tangencies for diffeomorphisms in dimension three(3次元の微分同相写像に対するホモクリニック接触のC1安定化について) (JAPANESE)

### 2014/08/06

#### Mathematical Biology Seminar

14:50-16:20 Room #128 (Graduate School of Math. Sci. Bldg.)

The stochastic SIS epidemic model in a periodic environment (ENGLISH)

**Nicolas Bacaer**(Insitut de Recherche pour le Developpement (IRD))The stochastic SIS epidemic model in a periodic environment (ENGLISH)

[ Abstract ]

In the stochastic SIS epidemic model with a contact rate a,

a recovery rate bT is such that (log T)/N converges to c=b/a-1-log(b/a) as N grows to

infinity. We consider the more realistic case where the contact rate

a(t) is a periodic function whose average is bigger than b. Then (log

T)/N converges to a new limit C, which is linked to a time-periodic

Hamilton-Jacobi equation. When a(t) is a cosine function with small

amplitude or high (resp. low) frequency, approximate formulas for C

can be obtained analytically following the method used in [Assaf et

al. (2008) Population extinction in a time-modulated environment. Phys

Rev E 78, 041123]. These results are illustrated by numerical

simulations.

In the stochastic SIS epidemic model with a contact rate a,

a recovery rate bT is such that (log T)/N converges to c=b/a-1-log(b/a) as N grows to

infinity. We consider the more realistic case where the contact rate

a(t) is a periodic function whose average is bigger than b. Then (log

T)/N converges to a new limit C, which is linked to a time-periodic

Hamilton-Jacobi equation. When a(t) is a cosine function with small

amplitude or high (resp. low) frequency, approximate formulas for C

can be obtained analytically following the method used in [Assaf et

al. (2008) Population extinction in a time-modulated environment. Phys

Rev E 78, 041123]. These results are illustrated by numerical

simulations.

### 2014/07/29

#### Operator Algebra Seminars

16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Asymptotic structure of free Araki-Woods factors (ENGLISH)

**Cyril Houdayer**(ENS Lyon)Asymptotic structure of free Araki-Woods factors (ENGLISH)

### 2014/07/28

#### Numerical Analysis Seminar

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Computer assisted analysis of Craik’s and Pehlivan’s 3D dynamical systems (JAPANESE)

[ Reference URL ]

http://www.infsup.jp/utnas/

**Tomoyuki Miyaji**(RIMS, Kyoto University)Computer assisted analysis of Craik’s and Pehlivan’s 3D dynamical systems (JAPANESE)

[ Reference URL ]

http://www.infsup.jp/utnas/

### 2014/07/25

#### Colloquium

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

Mathematical modelling of Tumor Immune System Interaction (JAPANESE)

**Yasuhiro Takeuchi**(Aoyama Gakuin University)Mathematical modelling of Tumor Immune System Interaction (JAPANESE)

[ Abstract ]

We study the dynamical behavior of a tumor-immune system (T-IS) interaction model with two discrete delays,

namely the immune activation delay for effector cells (ECs) and activation delay for Helper T cells (HTCs).

By analyzing the characteristic equations, we establish the stability of two equilibria (tumor-free equilibrium and immune-control equilibrium) and the existence of Hopf bifurcations when two delays are used as the bifurcation parameter.

Our results exhibit that both delays do not affect the stability of tumor-free equilibrium.

However, they are able to destabilize the immune-control equilibrium and cause periodic solutions.

We numerically illustrate how these two delays can change the stability region of the immune-control equilibrium and display the different impacts to the control of tumors.

The numerical simulation results show that the immune activation delay for HTCs can induce heteroclinic cycles to connect the tumor-free equilibrium and immune-control equilibrium.

Furthermore, we observe that the immune activation delay for HTCs can even stabilize the unstable immune-control equilibrium.

We study the dynamical behavior of a tumor-immune system (T-IS) interaction model with two discrete delays,

namely the immune activation delay for effector cells (ECs) and activation delay for Helper T cells (HTCs).

By analyzing the characteristic equations, we establish the stability of two equilibria (tumor-free equilibrium and immune-control equilibrium) and the existence of Hopf bifurcations when two delays are used as the bifurcation parameter.

Our results exhibit that both delays do not affect the stability of tumor-free equilibrium.

However, they are able to destabilize the immune-control equilibrium and cause periodic solutions.

We numerically illustrate how these two delays can change the stability region of the immune-control equilibrium and display the different impacts to the control of tumors.

The numerical simulation results show that the immune activation delay for HTCs can induce heteroclinic cycles to connect the tumor-free equilibrium and immune-control equilibrium.

Furthermore, we observe that the immune activation delay for HTCs can even stabilize the unstable immune-control equilibrium.

#### thesis presentations

10:30-11:45 Room #128 (Graduate School of Math. Sci. Bldg.)

On the study of front propagation in nonlinear free boundary problems(非線形自由境界問題における波面の伝播の研究) (JAPANESE)

**周 茂林**(東京大学大学院数理科学研究科)On the study of front propagation in nonlinear free boundary problems(非線形自由境界問題における波面の伝播の研究) (JAPANESE)

### 2014/07/24

#### Applied Analysis

16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Decomposition of the Mobius energy (JAPANESE)

**Nagasawa Takeyuki**(Saitama University)Decomposition of the Mobius energy (JAPANESE)

### 2014/07/23

#### Operator Algebra Seminars

16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)

The Cuntz semigroup---a critical component for classification? (ENGLISH)

**George Elliott**(Univ. Toronto)The Cuntz semigroup---a critical component for classification? (ENGLISH)

#### Mathematical Biology Seminar

14:50-16:20 Room #128 (Graduate School of Math. Sci. Bldg.)

Resting-state brain networks, their energy landscapes, and sleep (JAPANESE)

**Naoki Masuda**(University of Bristol, Department of Engineering Mathematics)Resting-state brain networks, their energy landscapes, and sleep (JAPANESE)

### 2014/07/22

#### Tuesday Seminar on Topology

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

The Index Map and Reciprocity Laws for Contou-Carrere Symbols (ENGLISH)

**Jesse Wolfson**(Northwestern University)The Index Map and Reciprocity Laws for Contou-Carrere Symbols (ENGLISH)

[ Abstract ]

In the 1960s, Atiyah and Janich constructed the families index as a natural map from the space of Fredholm operators to the classifying space of topological K-theory, and showed it to be an equivalence. In joint work with Oliver Braunling and Michael Groechenig, we construct an analogous index map in algebraic K-theory. Building on recent work of Sho Saito, we show this provides an analogue of Atiyah and Janich's equivalence. More significantly, the index map allows us to relate the Contou-Carrere symbol, a local analytic invariant of schemes, to algebraic K-theory. Using this, we provide new proofs of reciprocity laws for Contou-Carrere symbols in dimension 1 (first established by Anderson--Pablos Romo) and 2 (established recently by Osipov--Zhu). We extend these reciprocity laws to all dimensions.

In the 1960s, Atiyah and Janich constructed the families index as a natural map from the space of Fredholm operators to the classifying space of topological K-theory, and showed it to be an equivalence. In joint work with Oliver Braunling and Michael Groechenig, we construct an analogous index map in algebraic K-theory. Building on recent work of Sho Saito, we show this provides an analogue of Atiyah and Janich's equivalence. More significantly, the index map allows us to relate the Contou-Carrere symbol, a local analytic invariant of schemes, to algebraic K-theory. Using this, we provide new proofs of reciprocity laws for Contou-Carrere symbols in dimension 1 (first established by Anderson--Pablos Romo) and 2 (established recently by Osipov--Zhu). We extend these reciprocity laws to all dimensions.

### 2014/07/19

#### Monthly Seminar on Arithmetic of Automorphic Forms

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Hurwitz integrality of the power series expansion of the sigma function at the origin (JAPANESE)

種数 3 の trigonal curve から来る Kummer 多様体の定義方程式と Coble の超平面 (JAPANESE)

**Yoshihiro Onishi**(Miejyo University) 13:30-14:30Hurwitz integrality of the power series expansion of the sigma function at the origin (JAPANESE)

**Yoshihiro Onishi**(Meijyo University) 15:00-16:00種数 3 の trigonal curve から来る Kummer 多様体の定義方程式と Coble の超平面 (JAPANESE)

### 2014/07/17

#### Geometry Colloquium

10:00-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)

The space of compact shrinking solutions to Lagrangian mean curvature flow in $C^2$ (ENGLISH)

**Jingyi Chen**(University of British Columbia)The space of compact shrinking solutions to Lagrangian mean curvature flow in $C^2$ (ENGLISH)

[ Abstract ]

We will discuss compactness and rigidity of compact surfaces which are shrinking solutions to Lagrangian mean curvature flow. This is recent joint work with John Ma.

We will discuss compactness and rigidity of compact surfaces which are shrinking solutions to Lagrangian mean curvature flow. This is recent joint work with John Ma.

### 2014/07/16

#### Infinite Analysis Seminar Tokyo

10:30-12:00 Room #002 (Graduate School of Math. Sci. Bldg.)

From the Hilbert scheme to m/n Pieri rules (ENGLISH)

**Andrei Negut**(Columbia University, Department of Mathematics)From the Hilbert scheme to m/n Pieri rules (ENGLISH)

[ Abstract ]

In this series of talks, we will discuss several occurrences of shuffle

algebras: in representation theory, in geometry of moduli spaces, and in

the combinatorics of symmetric functions. All the connections will be

explained in detail.

In this series of talks, we will discuss several occurrences of shuffle

algebras: in representation theory, in geometry of moduli spaces, and in

the combinatorics of symmetric functions. All the connections will be

explained in detail.

### 2014/07/15

#### Infinite Analysis Seminar Tokyo

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

From the shuffle algebra to the Hilbert scheme (ENGLISH)

**Andrei Negut**(Columbia University, Department of Mathematics)From the shuffle algebra to the Hilbert scheme (ENGLISH)

[ Abstract ]

In this series of talks, we will discuss several occurrences of shuffle

algebras: in representation theory, in geometry of moduli spaces, and in

the combinatorics of symmetric functions. All the connections will be

explained in detail.

In this series of talks, we will discuss several occurrences of shuffle

algebras: in representation theory, in geometry of moduli spaces, and in

the combinatorics of symmetric functions. All the connections will be

explained in detail.

### 2014/07/14

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Higher dimensional analogues of fake projective planes (ENGLISH)

**Gopal Prasad**(University of Michigan)Higher dimensional analogues of fake projective planes (ENGLISH)

[ Abstract ]

A fake projective plane is a smooth projective complex algebraic surface which is not isomorphic to the complex projective plane but whose Betti numbers are that of the complex projective plane. The fake projective planes are algebraic surfaces of general type and have smallest possible Euler-Poincare characteristic among them. The first fake projective plane was constructed by D. Mumford using p-adic uniformization, and it was known that there can only be finitely many of them. A complete classification of the fake projective planes was obtained by Sai-Kee Yeung and myself. We showed that there are 28 classes of them, and constructed at least one explicit example in each class. Later, using long computer assisted computations, D. Cartwright and Tim Steger found that the 28 families altogether contain precisely 100 fake projective planes. Using our work, they also found a very interesting smooth projective complex algebraic surface whose Euler-Poincare characteristic is 3 but whose first Betti

number is 2. We have a natural notion of higher dimensional analogues of fake projective planes and to a large extent determined them. My talk will be devoted to an exposition of this work.

A fake projective plane is a smooth projective complex algebraic surface which is not isomorphic to the complex projective plane but whose Betti numbers are that of the complex projective plane. The fake projective planes are algebraic surfaces of general type and have smallest possible Euler-Poincare characteristic among them. The first fake projective plane was constructed by D. Mumford using p-adic uniformization, and it was known that there can only be finitely many of them. A complete classification of the fake projective planes was obtained by Sai-Kee Yeung and myself. We showed that there are 28 classes of them, and constructed at least one explicit example in each class. Later, using long computer assisted computations, D. Cartwright and Tim Steger found that the 28 families altogether contain precisely 100 fake projective planes. Using our work, they also found a very interesting smooth projective complex algebraic surface whose Euler-Poincare characteristic is 3 but whose first Betti

number is 2. We have a natural notion of higher dimensional analogues of fake projective planes and to a large extent determined them. My talk will be devoted to an exposition of this work.

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