## Seminar information archive

#### Applied Analysis

16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Joseph F. Grotowski (University of Queensland)
Two-dimensional harmonic map heat flow versus four-dimensional Yang-Mills heat flow
[ Abstract ]
Harmonic map heat flow and Yang-Mills heat flow are the gradient flows associated to particular energy functionals. In the considered dimension, (i.e. dimension two for the harmonic map heat flow, dimension four for the Yang-Mills heat flow), the associated energy functional is (locally) conformally invariant, that is, the dimension is critical. This leads to a number of interesting phenomena when considering both the functionals and the associated flows. In this talk we discuss qualitative similarities and differences between the flows.

#### GCOE lecture series

15:00-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Holomorphic extensions of unitary representations その3 Highest weight representations
[ Abstract ]
In this lecture we explain the extension results in a little more detail and explain how they lead to geometric realizations of singular highest weight representations on nilpotent coadjoint orbits.
[ Reference URL ]
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html

### 2008/10/15

#### PDE Real Analysis Seminar

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)

Asymptotic behavior of solutions for BCF model describing crystal surface growth
[ Abstract ]
This talk is concerned with the initial-boundary value problem for a nonlinear parabolic equation which was presented Johnson et al. for describing the process of growth of a crystal surface on the
basis of the BCF theory. We will investigate asymptotic behavior of solutions by construct exponential attractors and a Lyapunov function and by examining a structure of the $\\omega$ limit set.

#### Lectures

16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
George Sell (ミネソタ大学)

[ Abstract ]
In both lectures we will examine a new topic of the thin
3D Navier-Stokes equations with Navier boundary conditions.

In the first lecture we will treat the ultimate boundedness
of strong solutions and the related theory of global
attractors.

In the second lecture, which will include a brief summary
of the first lecture, we will examine the role played by the
2D Limit Problem. These issues are a special challenge for
analysis because the 2D Limit Problem is NOT imbedded the
3D problem.

These lectures are based on joint work with Genevieve Raugel,Dragos Iftimie, and Luan Hoang.

#### Lectures

15:00-16:00   Room #570 (Graduate School of Math. Sci. Bldg.)
GCOEレクチャー"Holomorphic extensions of unitary representations" その2 "Geometric Background"
[ Abstract ]
In this lecture we will explain the complex geometry needed to understand the phenomena described in the first lecture. The key words here are Olshanski semigroups, invariant cones in Lie algebras, Akhiezer-Gindikin domain, and coadjoint orbits of convex type.
[ Reference URL ]
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html

#### GCOE lecture series

15:00-16:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Holomorphic extensions of unitary representations その2 Geometric background
[ Abstract ]
In this lecture we will explain the complex geometry needed to understand the phenomena described in the first lecture. The key words here are Olshanski semigroups, invariant cones in Lie algebras, Akhiezer-Gindikin domain, and coadjoint orbits of convex type.
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2008.html#20081014hilgert

### 2008/10/14

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Jeffrey Herschel Giansiracusa (Oxford University)
Pontrjagin-Thom maps and the Deligne-Mumford compactification
[ Abstract ]
An embedding f: M -> N produces, via a construction of Pontrjagin-Thom, a map from N to the Thom space of the normal bundle over M. If f is an arbitrary map then one instead gets a map from N to the infinite loop space of the Thom spectrum of the normal bundle of f. We extend this Pontrjagin-Thom construction of wrong-way maps to differentiable stacks and use it to produce interesting maps from the Deligne-Mumford compactification of the moduli space of curves to certain infinite loop spaces. We show that these maps are surjective on mod p homology in a range of degrees. We thus produce large new families of torsion cohomology classes on the Deligne-Mumford compactification.

#### Lectures

16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
George Sell (ミネソタ大学)

Ultimate boundedness of solutions with large data and global attractors
[ Abstract ]
In both lectures we will examine a new topic of the thin 3D Navier-Stokes equations with Navier boundary conditions.

In the first lecture we will treat the ultimate boundedness of strong solutions and the related theory of global attractors.

In the second lecture, which will include a brief summary of the first lecture, we will examine the role played by the 2D Limit Problem. These issues are a special challenge for analysis because the 2D Limit Problem is NOT imbedded the 3D problem.

These lectures are based on joint work with Genevieve Raugel, Dragos Iftimie, and Luan Hoang.

#### Tuesday Seminar of Analysis

16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
George Sell (ミネソタ大学)
Thin 3D Navier-Stokes equations: Ultimate boundedness of solutions with large data and global attractors
[ Abstract ]
グローバルCOE連続講演会と共催です.詳細はそちらをご覧ください.

#### Lectures

15:00-16:00   Room #570 (Graduate School of Math. Sci. Bldg.)
GCOEレクチャー"Holomorphic extensions of unitary representations" その1 "Overview and Examples"
[ Abstract ]
In this lecture we present the Gelfand-Gindikin program of decomposing $L^2$-spaces into families of irreducible representations using complex geometry. We then briefly outline results due to Olshanski, Hilgert-Olafsson-Orsted, Hilgert-Neeb-Orsted, Krotz-Stanton and others in this direction. In particular, we will explain holomorphic extensions of holomorphic discrete series representations and their relation to Hardy and weighted Bergman spaces.
[ Reference URL ]
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html

#### Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
The Dirichlet-to-Neumann map as a pseudodifferential
operator
[ Abstract ]
Both Dirichlet and Neumann boundary conditions for the Laplace equation are of fundamental importance in Mathematics and Physics. Given a compact connected Riemannian manifold $M$ with boundary $\\partial M$ the Dirichlet-to-Neumann operator $\\Lambda_g$ maps Dirichlet boundary data $f$ to the corresponding Neumann boundary data $\\Lambda_g f =(\\partial_\\nu u)|_{\\partial M}$ where $u$ denotes the unique solution to the Dirichlet problem $\\laplace_g u=0$ in $M$, $u|_{\\partial M} = f$.
The main statement is that this operator is a first order elliptic pseudodifferential operator on the boundary $\\partial M$.

We will first give a brief overview of how to define the Dirichlet-to-Neumann operator as a map $\\Lambda_g:H^{1/2}(\\partial M)\\longrightarrow H^{-1/2}(\\partial M)$ between Sobolev spaces. In order to show that it is actually a pseudodifferential operator we introduce tangential pseudodifferential operators. This allows us to derive a
microlocal factorization of the Laplacian near boundary points. Together with a regularity statement for the heat equation this will finally give the main result.
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

#### GCOE lecture series

15:00-16:00   Room #118 (Graduate School of Math. Sci. Bldg.)
Holomorphic extensions of unitary representations" その1 "Overview and Examples"
[ Abstract ]
In this lecture we present the Gelfand-Gindikin program of decomposing $L^2$-spaces into families of irreducible representations using complex geometry. We then briefly outline results due to Olshanski, Hilgert-Olafsson-Orsted, Hilgert-Neeb-Orsted, Krotz-Stanton and others in this direction. In particular, we will explain holomorphic extensions of holomorphic discrete series representations and their relation to Hardy and weighted Bergman spaces.
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2008.html#20081014hilgert

### 2008/10/10

#### Lecture Series on Mathematical Sciences in Soceity

16:20-17:50   Room #128 (Graduate School of Math. Sci. Bldg.)

### 2008/10/06

#### Seminar on Geometric Complex Analysis

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

Lichtenbaum予想の幾何学的類似

### 2008/10/03

#### Lecture Series on Mathematical Sciences in Soceity

16:20-17:50   Room #128 (Graduate School of Math. Sci. Bldg.)

### 2008/09/29

#### Number Theory Seminar

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)
Christopher Deninger (Munster大学)
A determinant for p-adic group algebras
[ Abstract ]
For a discrete countable group G there is a classical determinant on the units of the L^1-convolution algebra of G. It is defined using functional analysis and can be used for example to calculate the entropy of certain G-actions. We will discuss a p-adic analogue of this theory. Instead of functional analysis the definition of the p-adic determinant uses algebraic K-theory. It has an application to the study of the p-adic distribution of periodic G-orbits in certain G-action.

### 2008/09/22

#### Lectures

14:45-15:45   Room #122 (Graduate School of Math. Sci. Bldg.)
Jean-Dominique Deuschel (TU Berlin)
Invariance principle for the random conductance model
with unbounded conductances (a joint work with Martin Barlow)

#### Lectures

16:00-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Sergio Albeverio (Bonn 大学)
Asymptotic expansions of infinite dimensional integrals with applications (quantum mechanics, mathematical finance, biology)

### 2008/09/17

#### Operator Algebra Seminars

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Cyril Houdayer (UCLA)
Free Araki-Woods Factors and Connes's Bicentralizer Problem

### 2008/09/09

#### Operator Algebra Seminars

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Yves de Cornulier (CNRS, Rennes)
The space of subgroups of an abelian group

### 2008/09/08

#### Lie Groups and Representation Theory

11:00-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Federico Incitti (ローマ第 1 大学)
Dyck partitions, quasi-minuscule quotients and Kazhdan-Lusztig polynomials
[ Abstract ]
Kazhdan-Lusztig polynomials were first defined by Kazhdan and Lusztig in [Invent. Math., 53 (1979), 165-184]. Since then, numerous applications have been found, especially to representation theory and to the geometry of Schubert varieties. In 1987 Deodhar introduced parabolic analogues of these polynomials. These are related to their ordinary counterparts in several ways, and also play a direct role in other areas, including geometry of partial flag manifolds and the theory of Macdonald polynomials.

In this talk I study the parabolic Kazhdan-Lusztig polynomials of the quasi-minuscule quotients of the symmetric group. More precisely, I will first show how these quotients are closely related to rooted partitions'' and then I will give explicit, closed combinatorial formulas for the polynomials. These are based on a special class of rooted partitions the rooted-Dyck'' partitions, and imply that they are always (either zero or) a power of $q$.

I will conclude with some enumerative results on Dyck and rooted-Dyck partitions, showing a connection with random walks on regular trees.

This is partly based on a joint work with Francesco Brenti and Mario Marietti.
[ Reference URL ]
http://akagi.ms.u-tokyo.ac.jp/seminar.html

### 2008/09/03

#### Lectures

16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Fred Weissler (University of Paris 13)
Finite time blowup of oscillating solutions to the nonlinear heat equation
[ Abstract ]
(This is joint work with T. Cazenave and F. Dickstein.)

We study finite time blowup properties of solutions of the nonlinear heat equation, both on $R^N$, and on a ball in $R^N$ with Dirichlet boundary conditions. We show, among other results, that the set of initial values producing global solutions is not always star-shaped around the 0 solution. This contrasts with the case where only non-negative solutions are considered.

### 2008/08/27

#### Number Theory Seminar

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)
Don Zagier (Max Planck研究所)
$q$-series and modularity

### 2008/08/25

#### Lectures

16:30-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Ronald C. King (Emeritus Professor, University of Southampton)
Affine Weyl groups, grids, coloured tableaux and characters of affine algebras
[ Abstract ]
It is shown that certain coloured Young diagrams serve to specify not
only all the elements of the affine Weyl groups of the classical
affine Lie algebras but also their action on an arbitrary weight
vector. Through a judicious choice of coset representatives with
respect to the finite Weyl groups of the corresponding maximal rank
simple Lie algebras, both denominator and numerator formulae are
derived and exemplified, along with the explicit calculation of
characters of irreducible representations of the affine Lie algebras.

### 2008/08/21

#### thesis presentations

15:00-15:40   Room #126 (Graduate School of Math. Sci. Bldg.)

On some asymptotic properties of the Expectation-Maximization Algorithm and the Metropolis-Hastings Algorithm (EMアルゴリズムとメトロポリス-ヘイスティングスアルゴリズムの漸近的性質)