## Seminar information archive

### 2014/09/22

#### Infinite Analysis Seminar Tokyo

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

### 2014/09/19

#### Colloquium

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

#### FMSP Lectures

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

### 2014/09/12

#### FMSP Lectures

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

#### FMSP Lectures

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

### 2014/09/08

#### FMSP Lectures

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

### 2014/08/06

#### Mathematical Biology Seminar

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

### 2014/07/29

#### Operator Algebra Seminars

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

#### 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)

### 2014/07/24

#### Applied Analysis

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

### 2014/07/19

#### Monthly Seminar on Arithmetic of Automorphic Forms

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Yoshihiro Onishi (Miejyo University) 13:30-14:30
Hurwitz integrality of the power series expansion of the sigma function at the origin (JAPANESE)
Yoshihiro Onishi (Meijyo University) 15:00-16:00

### 2014/07/17

#### Geometry Colloquium

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

### 2014/07/16

#### Infinite Analysis Seminar Tokyo

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

### 2014/07/15

#### Infinite Analysis Seminar Tokyo

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

### 2014/07/14

#### Seminar on Geometric Complex Analysis

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