## Seminar information archive

Seminar information archive ～02/15｜Today's seminar 02/16 | Future seminars 02/17～

#### Mathematical Biology Seminar

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

Qualitative analysis of disease transmission dynamics for renewal equations (JAPANESE)

**Yoichi Enatsu**(Graduate School of Math. Sci. Bldg.)Qualitative analysis of disease transmission dynamics for renewal equations (JAPANESE)

### 2014/10/07

#### Tuesday Seminar on Topology

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

Transversality problems in string topology and de Rham chains (JAPANESE)

**Kei Irie**(RIMS, Kyoto University)Transversality problems in string topology and de Rham chains (JAPANESE)

[ Abstract ]

The starting point of string topology is the work of Chas-Sullivan, which uncovered the Batalin-Vilkovisky(BV) structure on homology of the free loop space of a manifold.

It is important to define chain level structures beneath the BV structure on homology, however this problem is yet to be settled.

One of difficulties is that, to define intersection products on chain level, we have to address the transversality issue.

In this talk, we introduce a notion of "de Rham chain" to bypass this trouble, and partially realize expected chain level structures.

The starting point of string topology is the work of Chas-Sullivan, which uncovered the Batalin-Vilkovisky(BV) structure on homology of the free loop space of a manifold.

It is important to define chain level structures beneath the BV structure on homology, however this problem is yet to be settled.

One of difficulties is that, to define intersection products on chain level, we have to address the transversality issue.

In this talk, we introduce a notion of "de Rham chain" to bypass this trouble, and partially realize expected chain level structures.

### 2014/10/03

#### Infinite Analysis Seminar Tokyo

13:30-17:00 Room #002 (Graduate School of Math. Sci. Bldg.)

KPZ equation and Macdonald process (JAPANESE)

Entanglement spectra in topological phases and coupled Tomonaga-Luttinger liquids (JAPANESE)

**Tomohiro SASAMOTO**(Department of Physics, Tokyo Institute of Technology) 13:30-15:00KPZ equation and Macdonald process (JAPANESE)

**Shunsuke FURUKAWA**(Department of Physics, the Tokyo University) 15:30-17:00Entanglement spectra in topological phases and coupled Tomonaga-Luttinger liquids (JAPANESE)

[ Abstract ]

The entanglement spectrum (ES) has been found to provide useful probes of topological phases of matter and other exotic strongly correlated states. For the system's ground state, the ES is defined as the full eigenvalue spectrum of the reduced density matrix obtained by tracing out the degrees of freedom in part of the system. A key result observed in various topological phases and other gapped systems has been the remarkable correspondence between the ES and the edge-state spectrum. While this correspondence has been analytically proven for some topological phases, it is interesting to ask what systems show this correspondence more generally and how the ES changes when the bulk energy gap closes.

We here study the ES in two coupled Tomonaga-Luttinger liquids (TLLs) on parallel periodic chains. In addition to having direct applications to ladder systems, this problem is closely related to the entanglement properties of two-dimensional topological phases. Based on the calculation for coupled chiral TLLs, we provide a simple physical proof for the correspondence between edge states and the ES in quantum Hall systems consistent with previous numerical and analytical studies. We also discuss violations of this correspondence in gapped and gapless phases of coupled non-chiral TLLs.

Reference: R. Lundgren, Y. Fuji, SF, and M. Oshikawa, Phys. Rev. B 88, 245137 (2013).

The entanglement spectrum (ES) has been found to provide useful probes of topological phases of matter and other exotic strongly correlated states. For the system's ground state, the ES is defined as the full eigenvalue spectrum of the reduced density matrix obtained by tracing out the degrees of freedom in part of the system. A key result observed in various topological phases and other gapped systems has been the remarkable correspondence between the ES and the edge-state spectrum. While this correspondence has been analytically proven for some topological phases, it is interesting to ask what systems show this correspondence more generally and how the ES changes when the bulk energy gap closes.

We here study the ES in two coupled Tomonaga-Luttinger liquids (TLLs) on parallel periodic chains. In addition to having direct applications to ladder systems, this problem is closely related to the entanglement properties of two-dimensional topological phases. Based on the calculation for coupled chiral TLLs, we provide a simple physical proof for the correspondence between edge states and the ES in quantum Hall systems consistent with previous numerical and analytical studies. We also discuss violations of this correspondence in gapped and gapless phases of coupled non-chiral TLLs.

Reference: R. Lundgren, Y. Fuji, SF, and M. Oshikawa, Phys. Rev. B 88, 245137 (2013).

### 2014/10/02

#### Operator Algebra Seminars

16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Entropy and $L^2$-torsion (ENGLISH)

**Hanfeng Li**(SUNY Buffalo)Entropy and $L^2$-torsion (ENGLISH)

### 2014/10/01

#### Operator Algebra Seminars

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

Back-and-forth between scattering theory and index theorems (ENGLISH)

**Serge Richard**(Nagoya Univ.)Back-and-forth between scattering theory and index theorems (ENGLISH)

### 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.

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