## Colloquium

Seminar information archive ～06/17｜Next seminar｜Future seminars 06/18～

Organizer(s) | ASUKE Taro, TERADA Itaru, HASEGAWA Ryu, MIYAMOTO Yasuhito (chair) |
---|---|

URL | https://www.ms.u-tokyo.ac.jp/seminar/colloquium_e/index_e.html |

**Seminar information archive**

### 2015/06/26

16:50-17:50 Room #056 (Graduate School of Math. Sci. Bldg.)

Dimer models and mirror symmetry (JAPANESE)

**Kazushi Ueda**(Graduate School of Mathematical Sciences, University of Tokyo)Dimer models and mirror symmetry (JAPANESE)

### 2015/04/24

16:50-17:50 Room #123 (Graduate School of Math. Sci. Bldg.)

Rigidity of conformal functionals on spheres (ENGLISH)

**Bent Oersted**(Aarhus University and University of Tokyo)Rigidity of conformal functionals on spheres (ENGLISH)

[ Abstract ]

On a compact smooth manifold one may construct a Riemannian metric in many different ways. Each metric gives rise to natural elliptic operators such as the Laplace-Beltrami operator and corresponding spectral invariants, e.g. the eigenvalues, the trace of the heat semigroup, and the zeta function. In

this lecture we shall consider such functionals on the space of metrics on the sphere, combining conformal differential geometry and representation theory of semisimple Lie groups to obtain results about local extremal properties of special functionals. This is based on joint work with Niels Martin Moeller.

On a compact smooth manifold one may construct a Riemannian metric in many different ways. Each metric gives rise to natural elliptic operators such as the Laplace-Beltrami operator and corresponding spectral invariants, e.g. the eigenvalues, the trace of the heat semigroup, and the zeta function. In

this lecture we shall consider such functionals on the space of metrics on the sphere, combining conformal differential geometry and representation theory of semisimple Lie groups to obtain results about local extremal properties of special functionals. This is based on joint work with Niels Martin Moeller.

### 2015/03/13

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

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~takayuki/index-j.html

**Takayuki Oda**(Graduate School of Mathematical Sciences, University of Tokyo)[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~takayuki/index-j.html

### 2015/03/13

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

(JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/teacher/kusuoka.html

**Shigeo KUSUOKA**(Graduate School of Mathematical Sciences, University of Tokyo)(JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/teacher/kusuoka.html

### 2015/03/13

15:10-16:10 Room #大講義室 (Graduate School of Math. Sci. Bldg.)

(JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/teacher/miyaoka.html

**Yoichi Miyaoka**(Graduate School of Mathematical Sciences, University of Tokyo)(JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/teacher/miyaoka.html

### 2015/01/23

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

Grothendieck and algebraic geometry

**Luc Illusie**(Université de Paris-Sud)Grothendieck and algebraic geometry

[ Abstract ]

Between 1957 and 1970 Grothendieck deeply and durably transformed algebraic geometry. I will discuss some of his revolutionary contributions.

Between 1957 and 1970 Grothendieck deeply and durably transformed algebraic geometry. I will discuss some of his revolutionary contributions.

### 2014/11/28

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

Estimating the reproduction numbers of emerging infectious diseases: Case studies of Ebola and dengue

(JAPANESE)

http://www.ghp.m.u-tokyo.ac.jp/profile/staff/hnishiura/

**Hiroshi Nishiura**(Graduate School of Medicine, The University of Tokyo)Estimating the reproduction numbers of emerging infectious diseases: Case studies of Ebola and dengue

(JAPANESE)

[ Abstract ]

The basic and effective reproduction numbers offer epidemiological

insights into the growth of generations of infectious disease cases,

informing the required control effort. Recently, the renewal process

model has appeared to be a usefu tool for quantifying the reproduction

numbers in real-time using only case data. Here I present methods,

results and pitfalls of the use of renewal process model, presenting

recent case studies of Ebola virus disease epidemic in West Africa and a

massive epidemic of dengue fever in the summer of Japan 2014.

[ Reference URL ]The basic and effective reproduction numbers offer epidemiological

insights into the growth of generations of infectious disease cases,

informing the required control effort. Recently, the renewal process

model has appeared to be a usefu tool for quantifying the reproduction

numbers in real-time using only case data. Here I present methods,

results and pitfalls of the use of renewal process model, presenting

recent case studies of Ebola virus disease epidemic in West Africa and a

massive epidemic of dengue fever in the summer of Japan 2014.

http://www.ghp.m.u-tokyo.ac.jp/profile/staff/hnishiura/

### 2014/10/10

16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Etale cohomology of local Shimura varieties and the local Langlands correspondence (JAPANESE)

**Yoichi Mieda**(Graduate School of Mathematical Sciences, University of Tokyo)Etale cohomology of local Shimura varieties and the local Langlands correspondence (JAPANESE)

### 2014/09/19

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.

### 2014/07/25

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.

### 2014/07/11

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

Global Geometry and Analysis on Locally Symmetric Spaces with

Indefinite-metric (JAPANESE)

**Toshiyuki Kobayashi**(Graduate School of Mathematical Sciences, University of Tokyo)Global Geometry and Analysis on Locally Symmetric Spaces with

Indefinite-metric (JAPANESE)

[ Abstract ]

The local to global study of geometries was a major trend of 20th

century geometry,

with remarkable developments achieved particularly in Riemannian geometry.

In contrast, in areas such as pseudo-Riemannian geometry, familiar to us

as the space-time of relativity theory, and more generally in

pseudo-Riemannian geometry of general signature, surprising little is

known about global properties of the geometry even if we impose a

locally homogeneous structure.

I plan to explain two programs:

1. (global shape) Existence problem of compact locally homogeneous spaces,

and deformation theory.

2. (spectral analysis) Construction of the spectrum of the Laplacian,

and its stability under the deformation of the geometric structure.

by taking anti-de Sitter manifolds as a typical example.

The local to global study of geometries was a major trend of 20th

century geometry,

with remarkable developments achieved particularly in Riemannian geometry.

In contrast, in areas such as pseudo-Riemannian geometry, familiar to us

as the space-time of relativity theory, and more generally in

pseudo-Riemannian geometry of general signature, surprising little is

known about global properties of the geometry even if we impose a

locally homogeneous structure.

I plan to explain two programs:

1. (global shape) Existence problem of compact locally homogeneous spaces,

and deformation theory.

2. (spectral analysis) Construction of the spectrum of the Laplacian,

and its stability under the deformation of the geometric structure.

by taking anti-de Sitter manifolds as a typical example.

### 2014/06/06

16:30-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Lie algebras from secondary polytopes (ENGLISH)

**Mikhail Kapranov**(Kavli IPMU)Lie algebras from secondary polytopes (ENGLISH)

[ Abstract ]

The secondary polytope of a point configuration

in the Euclidean space was introduced by Gelfand, Zelevinsky

and the speaker long time ago in order to understand discriminants

of multi-variable polynomials. These polytopes have

a remarkable factorization (or operadic) property: each

face of any secondary polytope is isomorphic to the

product of several other secondary polytopes.

The talk, based on joint work in progress with M. Kontsevich

and Y. Soibelman, will explain how the factorization property

can be used to construct Lie algebra-type objects:

$L_¥infty$ and $A_¥infty$-algebras. These algebras

turn out to be related to the problem of deformation

of triangulated categories with semiorthogonal decompositions.

The secondary polytope of a point configuration

in the Euclidean space was introduced by Gelfand, Zelevinsky

and the speaker long time ago in order to understand discriminants

of multi-variable polynomials. These polytopes have

a remarkable factorization (or operadic) property: each

face of any secondary polytope is isomorphic to the

product of several other secondary polytopes.

The talk, based on joint work in progress with M. Kontsevich

and Y. Soibelman, will explain how the factorization property

can be used to construct Lie algebra-type objects:

$L_¥infty$ and $A_¥infty$-algebras. These algebras

turn out to be related to the problem of deformation

of triangulated categories with semiorthogonal decompositions.

### 2014/05/02

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

From hyperplane arrangements to Deligne-Mumford moduli spaces: Kohno-Drinfeld way (ENGLISH)

**A.P. Veselov**(Loughborough, UK and Tokyo, Japan)From hyperplane arrangements to Deligne-Mumford moduli spaces: Kohno-Drinfeld way (ENGLISH)

[ Abstract ]

Gaudin subalgebras are abelian Lie subalgebras of maximal

dimension spanned by generators of the Kohno-Drinfeld Lie algebra t_n,

associated to A-type hyperplane arrangement.

It turns out that Gaudin subalgebras form a smooth algebraic variety

isomorphic to the Deligne-Mumford moduli space \\bar M_{0,n+1} of

stable genus zero curves with n+1 marked points.

A real version of this result allows to describe the

moduli space of integrable n-dimensional tops and

separation coordinates on the unit sphere

in terms of the geometry of Stasheff polytope.

The talk is based on joint works with L. Aguirre and G. Felder and with K.

Schoebel.

Gaudin subalgebras are abelian Lie subalgebras of maximal

dimension spanned by generators of the Kohno-Drinfeld Lie algebra t_n,

associated to A-type hyperplane arrangement.

It turns out that Gaudin subalgebras form a smooth algebraic variety

isomorphic to the Deligne-Mumford moduli space \\bar M_{0,n+1} of

stable genus zero curves with n+1 marked points.

A real version of this result allows to describe the

moduli space of integrable n-dimensional tops and

separation coordinates on the unit sphere

in terms of the geometry of Stasheff polytope.

The talk is based on joint works with L. Aguirre and G. Felder and with K.

Schoebel.

### 2014/01/31

16:30-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Controllability of fluid flows (ENGLISH)

**Jean-Pierre Puel**(Université de Versailles Saint-Quentin-en-Yvelines)Controllability of fluid flows (ENGLISH)

[ Abstract ]

First of all we will describe in an abstract situation the various concepts

of controllability for evolution equations.

We will then present some problems and results concerning the

controllability of systems modeling fluid flows.

First of all we will consider the Euler equation describing the motion of an

incompressible inviscid fluid.

Then we will give some results concerning the Navier-Stokes equations,

modeling an incompressible viscous fluid, and some related systems.

Finally we will give a first result of controllability for the case of a

compressible fluid (in dimension 1) and some important open problems.

First of all we will describe in an abstract situation the various concepts

of controllability for evolution equations.

We will then present some problems and results concerning the

controllability of systems modeling fluid flows.

First of all we will consider the Euler equation describing the motion of an

incompressible inviscid fluid.

Then we will give some results concerning the Navier-Stokes equations,

modeling an incompressible viscous fluid, and some related systems.

Finally we will give a first result of controllability for the case of a

compressible fluid (in dimension 1) and some important open problems.

### 2014/01/24

16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Complex Brunn-Minkowski theory (ENGLISH)

**Bo Berndtsson**(Chalmers University of Technology)Complex Brunn-Minkowski theory (ENGLISH)

[ Abstract ]

The classical Brunn-Minkowski theory deals with the volume of convex sets.

It can be formulated as a statement about how the volume of slices of a convex set varies when the slice changes. Its complex counterpart deals with slices of pseudo convex sets, or more generally fibers of a complex fibration. It describes how $L^2$-norms of holomorphic functions, or sections of a line bundle, vary when the fibers change, and says essentially that a certain associated vector bundle has positive curvature. In the presence of enough symmetry this implies convexity properties of volumes; the real Brunn-Minkowski theorem corresponding to maximal symmetry. There are also applications and relations in other directions, like variations of Kahler metrics, variations of complex structures and the study of plurisubharmonic functions.

The classical Brunn-Minkowski theory deals with the volume of convex sets.

It can be formulated as a statement about how the volume of slices of a convex set varies when the slice changes. Its complex counterpart deals with slices of pseudo convex sets, or more generally fibers of a complex fibration. It describes how $L^2$-norms of holomorphic functions, or sections of a line bundle, vary when the fibers change, and says essentially that a certain associated vector bundle has positive curvature. In the presence of enough symmetry this implies convexity properties of volumes; the real Brunn-Minkowski theorem corresponding to maximal symmetry. There are also applications and relations in other directions, like variations of Kahler metrics, variations of complex structures and the study of plurisubharmonic functions.

### 2013/12/06

16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Local Langlands correspondence and Lubin-Tate perfectoid spaces (JAPANESE)

**Naoki Imai**(Graduate School of Mathematical Scinences, The University of Tokyo)Local Langlands correspondence and Lubin-Tate perfectoid spaces (JAPANESE)

### 2013/12/06

16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Local Langlands correspondence and Lubin-Tate perfectoid spaces (JAPANESE)

**Naoki Imai**(Graduate School of Mathematical Sciences, The University of Tokyo)Local Langlands correspondence and Lubin-Tate perfectoid spaces (JAPANESE)

### 2013/11/08

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

Ext Analogues of Branching laws (ENGLISH)

**Dipendra Prasad**(Tata Institute of Fundamental Research)Ext Analogues of Branching laws (ENGLISH)

[ Abstract ]

The decomposition of a representation of a group when restricted to a

subgroup is an important problem well-studied for finite and compact Lie

groups, and continues to be of much contemporary interest in the context

of real and $p$-adic groups. We will survey some of the questions that have

recently been considered, and look at a variation of these questions involving concepts in homological algebra which gives rise to interesting newer questions.

The decomposition of a representation of a group when restricted to a

subgroup is an important problem well-studied for finite and compact Lie

groups, and continues to be of much contemporary interest in the context

of real and $p$-adic groups. We will survey some of the questions that have

recently been considered, and look at a variation of these questions involving concepts in homological algebra which gives rise to interesting newer questions.

### 2013/07/26

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

Analysis of the Navier-Stokes and Complex Fluids Flow (ENGLISH)

**Matthias Hieber**(TU Darmstadt, Germany)Analysis of the Navier-Stokes and Complex Fluids Flow (ENGLISH)

[ Abstract ]

In this talk, we discuss the dynamics of fluid flow generated by the Navier-Stokes equations or, more generally, by models describing complex fluid flows. Besides classical questions concerning well-posedness of the underlying equations, we investigate analytically models arising in the theory of free boundary value problems, viscoelastic fluids and liquid crystals.

In this talk, we discuss the dynamics of fluid flow generated by the Navier-Stokes equations or, more generally, by models describing complex fluid flows. Besides classical questions concerning well-posedness of the underlying equations, we investigate analytically models arising in the theory of free boundary value problems, viscoelastic fluids and liquid crystals.

### 2013/06/28

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

The Geometry of protain modelling (JAPANESE)

**Hiroki Kodama**(Graduate School of Mathematical Sciences, The University of Tokyo)The Geometry of protain modelling (JAPANESE)

### 2013/05/31

16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Stable patterns and the nonlinear ``hot spots'' conjecture (JAPANESE)

**Yasuhito MIYAMOTO**(Graduate School of Mathematical Sciences, The University of Tokyo)Stable patterns and the nonlinear ``hot spots'' conjecture (JAPANESE)

### 2013/03/18

15:00-17:30 Room #050 (Graduate School of Math. Sci. Bldg.)

Value distribution theory and analytic function theory in several variables (JAPANESE)

My fifty years of differential equations (JAPANESE)

**NOGUCHI, Junjiro**(University of Tokyo) 15:00-16:00Value distribution theory and analytic function theory in several variables (JAPANESE)

**OSHIMA, Toshio**(University of Tokyo) 16:30-17:30My fifty years of differential equations (JAPANESE)

### 2013/01/25

16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

State of the art in numerical verification methods of solutions for partial differential equations (JAPANESE)

**Mitsuhiro T. Nakao**(Sasebo National College of Technology)State of the art in numerical verification methods of solutions for partial differential equations (JAPANESE)

### 2012/11/30

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

What do Siegel Eisenstein series know about all modular forms? (ENGLISH)

**Siegfried BOECHERER**(University of Tokyo)What do Siegel Eisenstein series know about all modular forms? (ENGLISH)

[ Abstract ]

Eisenstein series came up in C.L.Siegel's famous work on quadratic forms. The main properties of such Eisensetin series such as analytic continuation and explict form of Fourier expansion are well understood. Nowadays, we use Eisenstein series of higher rank symplectic groups and their restrictions to study properties of all modular forms. I will try to survey the use of “pullbacks of Eisenstein series”: Basis problem, L-functions, p-adic properties, rationality and integrality questions.

Eisenstein series came up in C.L.Siegel's famous work on quadratic forms. The main properties of such Eisensetin series such as analytic continuation and explict form of Fourier expansion are well understood. Nowadays, we use Eisenstein series of higher rank symplectic groups and their restrictions to study properties of all modular forms. I will try to survey the use of “pullbacks of Eisenstein series”: Basis problem, L-functions, p-adic properties, rationality and integrality questions.

### 2012/11/16

16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Integral invariants in complex differential geometry (JAPANESE)

**Akito FUTAKI**(University of Tokyo)Integral invariants in complex differential geometry (JAPANESE)