## Seminar information archive

### 2009/12/02

#### PDE Real Analysis Seminar

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Juergen Saal (University of Konstanz)
A hyperbolic fluid model based on Cattaneo's law
[ Abstract ]
In various applications a delay of the propagation speed of a fluid (temperature, ...) has been observed. Such phenomena cannot be described by standard parabolic models, whose derivation relies on Fourier's law (Paradoxon of infinite propagation speed).
One way to give account to these observations and which was successfully applied to several models, is to replace Fourier's law by the law of Cattaneo. In the case of a fluid, this leads to a hyperbolicly perturbed quasilinear Navier-Stokes system for which existence and uniqueness results will be presented.

### 2009/12/01

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Andrei Pajitnov (Univ. de Nantes)
Non-Abelian Novikov homology
[ Abstract ]
Classical construction of S.P. Novikov
associates to each circle-valued Morse map
a chain complex defined over a ring
of Laurent power series in one variable.

In this survey talk we shall explain several
results related to the construction and
properties of non-Abelian generalizations of the
Novikov complex.

### 2009/11/30

#### Seminar on Geometric Complex Analysis

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

Equidistribution and Nevanlinna theory

#### Kavli IPMU Komaba Seminar

16:30-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Junya Yagi (Rutgers University)
Chiral Algebras of (0,2) Models: Beyond Perturbation Theory
[ Abstract ]
The chiral algebras of two-dimensional sigma models with (0,2)
supersymmetry are infinite-dimensional generalizations of the chiral
rings of (2,2) models. Perturbatively, they enjoy rich mathematical
structures described by sheaves of chiral differential operators.
Nonperturbatively, however, they vanish completely for certain (0,2)
models with no left-moving fermions. In this talk, I will explain how
this vanishing phenomenon takes places. The vanishing of the chiral
algebra of a (0, 2) model implies that supersymmetry is spontaneously
broken in the model, which in turn suggests that no harmonic spinors
exist on the loop space of the target space. In particular, the
elliptic genus of the model vanishes, thereby providing a physics
proof of a special case of the Hoelhn-Stolz conjecture.

### 2009/11/27

#### Lecture Series on Mathematical Sciences in Soceity

16:20-17:50   Room #117 (Graduate School of Math. Sci. Bldg.)

#### Seminar on Probability and Statistics

13:40-14:50   Room #128 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]
In this talk, we consider the problem of estimating the innovation density in nonlinear autoregressive models. Specifically, we establish the convergence rate of the supremum distance between the residual-based kernel density estimator and the kernel density estimator using the unobservable actual innovation variables. The proof of the main theorem relies on empirical process theory instead of the conventional Taylor expansion approach. As applications, we obtain the exact rate of weak uniform consistency on the whole line, pointwise asymptotic normality of the residual-based kernel density estimator and the asymptotic distribution of a Bickel-Rosenblatt type global measure statistic related to it. We also examine the conditions of the main theorem for some specic time series model.
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/09.html

### 2009/11/26

#### Applied Analysis

16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)

L^p 粘性解の弱ハルナック不等式の最近の進展
[ Abstract ]
Caffarelli による粘性解の regularity 研究 (1989 年) を基に, 1996 年に Caffarelli- Crandall-Kocan-Swiech によって L^p 粘性解の概念が導入された. L^p 粘性解とは, 通 常の粘性解理論では扱えなかった, 非有界非斉次項を持つ (非発散型) 偏微分方程 式にも適用可能な弱解である.
しかしながら, 係数に関しては有界係数しか研究されていなかった. その後, Swiech との共同研究により, 係数が非有界だが適当なべき乗可積分性を仮定して Aleksandrov-Bakelman-Pucci 型の最大値原理を導くことが可能になった.

### 2009/11/25

#### PDE Real Analysis Seminar

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Hermann Sohr (University Paderborn)
Recent results on weak and strong solutions of the Navier-Stokes equations
[ Abstract ]
Our purpose is to develop the optimal initial value condition for the existence of a unique local strong solution of the Navier-Stokes equations in a smooth bounded domain.

This condition is not only sufficient
- there are several well-known sufficient conditions in this context
- but also necessary, and yields therefore the largest possible class of such strong solutions.

As an application we obtain several extensions of Serrin's regularity condition. A restricted result also holds for completely general domains. Furthermore we extend the well-known class of Leray-Hopf weak solutions with zero boundary conditions and zero divergence to a larger class with corresponding nonzero conditions.

### 2009/11/24

#### Tuesday Seminar of Analysis

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

Analytic Properties of Eigen Values of Daubechies Localization Operator
[ Abstract ]
1)ドーベシー局在化作用素の固有値の解析的性質、積分表示式、
(2)ドーベシー局在化作用素のシンボルの再現公式、
(3)ドーベシー局在化作用素のバーグマンーフォック空間での表示

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Adam Clay (University of British Columbia)
A topological approach to left orderable groups
[ Abstract ]
A group G is said to be left orderable if there is a strict
total ordering of its elements such that gin G. Left orderable groups have been useful in solving many problems in topology, and now we find that topology is returning the favour: the set of all left orderings of a group is denoted by LO(G), and it admits a natural topology, under which LO(G) becomes a compact topological
space. In general, the structure of the space LO(G) is not well understood, although there are surprising results in a few special cases.
For example, the space of left orderings of the braid group B_n for n>2
contains isolated points (yet it is uncountable), while the space of left
orderings of the fundamental group of the Klein bottle is finite.

Twice in recent years, the space of left orderings has been used very
successfully to solve difficult open problems from the field of left
orderable groups, even though the connection between the topology of LO(G) and the algebraic properties of G was still unclear. I will explain the
newest understanding of this connection, and highlight some potential
applications of further advances.

### 2009/11/20

#### Lecture Series on Mathematical Sciences in Soceity

16:20-17:50   Room #117 (Graduate School of Math. Sci. Bldg.)

#### Colloquium

16:30-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Louis Nirenberg
(New York University)
On solving fully nonlinear elliptic Partial Differential Equations

[ Abstract ]
The talk will present some results in recent work by R.Harvey and B. Lawson: Dirichlet duality and the nonlinear Dirichlet problem, Comm. Pure Appl. Math. 62 (2009), 396-443. It concerns solving boundary value problems for elliptic equations of the form F(D'2u) = 0. They find generalized solutions which are merely continuous . The talk will be expository. No knowledge of Partial Differential Equations will be necessary.

### 2009/11/19

#### Lectures

15:00-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)

### 2009/11/18

#### Lectures

15:30-17:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Herbert Spohn (ミュンヘン工科大学・九州大学)
The stochastic Burgers equation and its discretization

#### Number Theory Seminar

16:30-18:45   Room #056 (Graduate School of Math. Sci. Bldg.)

Elementary computation of ramified component of the Jacobi sum
[ Abstract ]
R. Coleman and W. McCallum calculated the Jacobi sum Hecke characters using their computation of the stable reduction of the Fermat curve in 1988. In my talk, we give an elementary proof of the main result of them without using rigid geometry or the stable model of the Fermat curve.
Christopher Deninger (Universität Münster) 17:45-18:45
P-divisible groups and the p-adic Corona problem

### 2009/11/17

#### Tuesday Seminar on Topology

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

On the $SO(N)$ and $Sp(N)$ free energy of a closed oriented 3-manifold
[ Abstract ]
We give an explicit formula of the $SO(N)$ and $Sp(N)$ free energy
of a lens space and show that the genus $g$ terms of it are analytic
in a neighborhood at zero, where we can choose the neighborhood
independently of $g$.
Moreover, it is proved that for any closed oriented 3-manifold $M$
and any $g$, the genus $g$ terms of $SO(N)$ and $Sp(N)$ free energy
of $M$ coincide up to sign.

### 2009/11/16

#### Seminar on Geometric Complex Analysis

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

Weighted Green functions of polynomial skew products on C^2

#### Algebraic Geometry Seminar

16:40-18:10   Room #126 (Graduate School of Math. Sci. Bldg.)
Colin Ingalls (University of New Brunswick and RIMS)
Rationality of the Brauer-Severi Varieties of Skylanin algebras
[ Abstract ]
Iskovskih's conjecture states that a conic bundle over
a surface is rational if and only if the surface has a pencil of
rational curves which meet the discriminant in 3 or fewer points,
(with one exceptional case). We generalize Iskovskih's proof that
such conic bundles are rational, to the case of projective space
bundles of higher dimension. The proof involves maximal orders
and toric geometry. As a corollary we show that the Brauer-Severi
variety of a Sklyanin algebra is rational.

### 2009/11/14

#### Monthly Seminar on Arithmetic of Automorphic Forms

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

On weak endoscopic lift (117号室)
[ Abstract ]
rank 2のsymplectic 群の保型表現$\\pi$の spinor L-関数(4次)が殆どの素点で楕円保型形式のL-関数の積になっているものをweak ndoscopic liftと呼びます. $\\pi$がtemperedならば, 全てのweak endoscopic liftはrank 4のtheta関数(theta lift)でかける事がBrooks Roberts氏により知られています.

Derivations and Automorphisms on the noncommutative algebra of power series.

[ Abstract ]
We discuss a relationship between a class of derivations and a class of automorphisms on the noncommutative algebra of formal power series in two variables. Each class relates bijectively by exponential and logarithm maps. In this talk we define a specific class of derivations, which generates a noncommutaive Lie algebra whose defining relations are related to a classical Witt algebra. The main claim is the explicit description of the
automorphisms which are corresponding to the derivations via exponential map.

### 2009/11/12

#### Lectures

10:40-12:10   Room #128 (Graduate School of Math. Sci. Bldg.)

#### Operator Algebra Seminars

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

Recent results for amalgamated free products of type II$_1$ factors

### 2009/11/11

#### Lectures

14:40-16:10   Room #128 (Graduate School of Math. Sci. Bldg.)

### 2009/11/10

#### Lectures

14:40-16:10   Room #128 (Graduate School of Math. Sci. Bldg.)

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Alexander Getmanenko (IPMU)
Resurgent analysis of the Witten Laplacian in one dimension
[ Abstract ]
I will recall Witten's approach to the Morse theory through properties of a certain differential operator. Then I will introduce resurgent analysis -- an asymptotic method used, in particular, for studying quantum-mechanical tunneling. In conclusion I will discuss how the methods of resurgent analysis can help us "see" pseudoholomorphic discs in the eigenfunctions of the Witten Laplacian.

### 2009/11/09

#### Kavli IPMU Komaba Seminar

16:30-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Makoto Sakurai (東京大学大学院数理科学研究科)
Differential Graded Categories and heterotic string theory
[ Abstract ]
The saying "category theory is an abstract nonsense" is even physically not true.
The schematic language of triangulated category presents a new stage of string theory.

To illuminate this idea, I will draw your attention to the blow-up minimal model
of complex algebraic surfaces. This is done under the hypothetical assumptions
of "generalized complex structure" of cotangent bundle due to Hitchin school.
The coordinate transformation Jacobian matrices of the measure of sigma model
with spin structures cause one part of the gravitational "anomaly cancellation"
of smooth Kahler manifold $X$ and Weyl anomaly of compact Riemann surface $\\Sigma$.

$Anom = c_1 (X) c_1 (\\Sigma) \\oplus ch_2 (X)$,

in terms of 1st and 2nd Chern characters. Note that when $\\Sigma$ is a puctured disk
with flat metric, the chiral algebra is nothing but the ordinary vertex algebra.

Note that I do not explain the complex differential geometry,
but essentially more recent works with the category of DGA (Diffenreial Graded Algebra),
which is behind the super conformal field theory of chiral algebras.

My result of "vanishing tachyon" (nil-radical part of vertex algebras)
and "causality resortation" in compactified non-critical heterotic sigma model
is physically a promising idea of new solution to unitary representation of operator algebras.
This idea is realized in the formalism of BRST cohomology and its generalization
in $\\mathcal{N} = (0,2)$ supersymmetry, that is, non-commutative geometry
with non-linear constraint condition of pure spinors for covariant quantization.