## Seminar information archive

### 2012/09/04

#### Tuesday Seminar on Topology

17:00-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Piotr Nowak (the Institute of Mathematics, Polish Academy of Sciences)
Poincare inequalities, rigid groups and applications (ENGLISH)
[ Abstract ]
Kazhdan’s property (T) for a group G can be expressed as a
fixed point property for affine isometric actions of G on a Hilbert
space. This definition generalizes naturally to other normed spaces. In
this talk we will focus on the spectral (aka geometric) method for
proving property (T), based on the work of Garland and studied earlier
by Pansu, Zuk, Ballmann-Swiatkowski, Dymara-Januszkiewicz
(“lambda_1>1/2” conditions) and we generalize it to to the setting of
all reflexive Banach spaces.
As applications we will show estimates of the conformal dimension of the
boundary of random hyperbolic groups in the Gromov density model and
present progress on Shalom’s conjecture on vanishing of 1-cohomology
with coefficients in uniformly bounded representations on Hilbert spaces.

### 2012/08/29

#### thesis presentations

10:30-11:45   Room #123 (Graduate School of Math. Sci. Bldg.)
Shinichi MATSUMURA (Graduate School of Mathematical Sciences the University of Tokyo)
Studies on the asymptotic invariants of cohomology groups and the positivity in complex geometry (JAPANESE)

### 2012/08/20

#### thesis presentations

11:00-12:15   Room #128 (Graduate School of Math. Sci. Bldg.)
Yoshifumi MIMURA (Graduate School of Mathematical Sciences the University of Tokyo)
The variational formulation of the fully parabolic Keller-Segel system with degenerate diffusion (JAPANESE)

### 2012/07/30

#### Algebraic Geometry Seminar

15:30-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Gianluca Pacienza (Université de Strasbourg)
Log Bend-and-Break on Deligne-Mumford stacks (ENGLISH)
[ Abstract ]
We prove a logarithmic Bend-and-Break lemma on a LCI Deligne-Mumford stacks with projective moduli space and integral boundary divisor. As a by-product we obtain a logarithmic version of the Miyaoka-Mori numerical criterion of uniruledness for DM stacks (under additional conditions on the boundary and on the non-schematic locus) and a Cone Theorem for Deligne-Mumford stacks with boundary. These results hold on an algebraically closed field of any characteristic. This is joint work with Michael McQuillan.

### 2012/07/27

#### Seminar on Probability and Statistics

14:00-17:00   Room #006 (Graduate School of Math. Sci. Bldg.)
UENO, Tsuyoshi (Minato Discrete Structure Manipulation System Project, Japan Science and Technology Agency)
General approach to reinforcement learning based on statistical inference (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/06.html

### 2012/07/25

#### GCOE lecture series

16:30-18:00   Room #118 (Graduate School of Math. Sci. Bldg.)
George Elliott (University of Toronto)
A survey of recent results on the classification of C*-algebras (ENGLISH)

### 2012/07/24

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Greg McShane (Institut Fourier, Grenoble)
Orthospectra and identities (ENGLISH)
[ Abstract ]
The orthospectra of a hyperbolic manifold with geodesic
boundary consists of the lengths of all geodesics perpendicular to the
boundary.
We discuss the properties of the orthospectra, asymptotics, multiplicity
and identities due to Basmajian, Bridgeman and Calegari. We will give
a proof that the identities of Bridgeman and Calegari are the same.

#### Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Toshihisa Kubo (the University of Tokyo)
The Dynkin index and conformally invariant systems of Heisenberg parabolic type (ENGLISH)
[ Abstract ]
Recently, Barchini-Kable-Zierau systematically constructed conformally invariant systems of differential operators using Heisenberg parabolic subalgebras. When they built such systems, two constants, which are defined as the constant of proportionality between two expressions,played an important role. In this talk we give concrete and uniform expressions for these constants. To do so the Dynkin index of a finite dimensional representation of a complex simple Lie algebra plays a key role.

### 2012/07/23

#### Algebraic Geometry Seminar

15:30-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Shinnosuke Okawa (University of Tokyo)
Derived category of smooth proper Deligne-Mumford stack with p_g>0 (JAPANESE)
[ Abstract ]
Semiorthogonal decomposition (SOD) of the derived category of coherent sheaves reflects interesting geometry of varieties (more generally stacks), such as minimal model program. We show that the global sections of the canonical line bundle (if exists) give restrictions on the possible form of SODs. As a special case, we see that the global generation of the canonical line bundle implies the non-existence of SODs. (joint work with Kotaro Kawatani)

#### Lectures

16:30-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)
Thomas W. Roby (University of Connecticut)
Combinatorial Ergodicity (ENGLISH)
[ Abstract ]
Many cyclic actions $\\tau$ on a finite set $S$ of
combinatorial objects, along with many natural
statistics $\\phi$ on $S$, exhibitcombinatorial ergodicity'':
the average of $\\phi$ over each $\\tau$-orbit in $S$ is
the same as the average of $\\phi$ over the whole set $S$.
One example is the case where $S$ is the set of
length $n$ binary strings $a_{1}\\dots a_{n}$
with exactly $k$ 1's,
$\\tau$ is the map that cyclically rotates them,
and $\\phi$ is the number of \\textit{inversions}
(i.e, pairs $(a_{i},a_{j})=(1,0)$ for $iJ$ less than $j$).

This phenomenon was first noticed by Panyushev
in 2007 in the context of antichains in root posets;
Armstrong, Stump, and Thomas proved his
conjecture in 2011.
We describe a theoretical framework for results of this kind,
and discuss old and new results for products of two chains.

This is joint work with Jim Propp.

### 2012/07/21

#### Monthly Seminar on Arithmetic of Automorphic Forms

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)
S. Takemori (Kyoto Univ., School of Science) 13:30-14:30
On Fourier coefficients of Siegel-Eisenstein series of degree n. (JAPANESE)
[ Abstract ]
We define an Siegel-Eisenstein series G_{k,\\chi} of degree n and talk about an explicit formula of the Fourier coefficients. This Eisenstein series is different from ordinarily defined Eisenstein series E_{k,\\chi}, but if \\chi satisfies a certain condition, we can obtain an explicit formula of Fourier coefficients of E_{k,\\chi}.

Noriko HIRATA-Kohno (Nihon University) 15:00-16:00
Polylogarithms revisited from the viewpoint of the irrationality (JAPANESE)
[ Abstract ]
In this report, we consider a polylogarithmic function to give a lower bound for the dimension of the linear space over the rationals spanned by $1$ and values of the function. Our proof uses Pad\\'e approximation and a criterion due to Yu. V. Nesterenko. We also describe what happens in the $p$-adic case and in the elliptic one.

### 2012/07/19

#### GCOE Seminars

17:00-18:00   Room #370 (Graduate School of Math. Sci. Bldg.)
Inverse boundary value problem for Schroedinger equation in two dimensions (ENGLISH)
[ Abstract ]
We consider the Dirichlet-to-Neumann map for determining potential in two-dimensional Schroedinger equation. We relax the regularity condition on potentials and establish the uniqueness within L^p class with p > 2.

### 2012/07/18

#### Number Theory Seminar

16:40-17:40   Room #056 (Graduate School of Math. Sci. Bldg.)
Shane Kelly (Australian National University)
Voevodsky motives and a theorem of Gabber (ENGLISH)
[ Abstract ]
The assumption that the base field satisfies resolution of singularities litters Voevodsky's work on motives. While we don't have resolution of singularities in positive characteristic p, there is a theorem of Gabber on alterations which may be used as a substitute if we are willing to work with Z[1/p] coefficients. We will discuss how this theorem of Gabber may be applied in the context of Voevodsky's work and mention some consequences.

#### Classical Analysis

16:00-17:30   Room #128 (Graduate School of Math. Sci. Bldg.)
Jiro Sekiguchi (Tokyo University of Agriculture and Technology)
Free divisors, holonomic systems and algebraic Painlev\\'{e} sixth solutions (ENGLISH)
[ Abstract ]
In this talk, I will report an attempt to treat algebraic solutions of Painlev\\'{e} VI equation in a unified manner.
A classification of algebraic solutions of Painlev\\'{e} VI equation was accomplished by O. Lisovyy and Y. Tykhyy after efforts on the construction of such solutions by many authors, K. Iwasaki N. J. Hitchin, P. Boalch, B. Dubrovin, M. Mazzocco, A. V. Kitaev, R. Vidunas and others.
The outline of my approach is as follows.
Let $t$ be a variable and let $w$ be its algebraic function such that $w$ is a solution of Painlev\\'{e} sixth equation. Suppose that both $t$ and $w$ are rational functions of a parameter. Namely $(t,w)$ defines a rational curve.
(1) Find a polynomial $P(u)$ such that $t=\\frac{P(-u)}{P(u)}$.
(2) From $P(u)$, define a weighted homogeneous polynomial $f(x_1,x_2,x_3)=x_3f_1(x_1,x_2,x_3)$ of three variables $x_1,x_2,x_3$, where $(1,2,n)$ is the weight system of $(x_1,x_2,x_3)$ with $n=\\deg P(u)$. The hypersurface $D:f(x)=0$ is a free divisor in ${\\bf C}^3$. Note that $\\deg_{x_3}f_1=2$.
(3) Construct a holonomic system ${\\sl M}$ on ${\\bf C}^3$ of rank two with singularities along $D$.
(4) Construct an ordinary differential equation from the holonomic system ${\\sl M}$ with respect to $x_3$. This differential equation has three singular points $z_0,z_1,a_s$ in $x_3$-line.
(5) Putting $t=\\frac{z_1}{z_0},\\lambda=\\frac{a_s}{z_0}$, we conclude that $(t,\\lambda)$ is equivalent to the pair $(t,w)$.
Our study starts with showing the existence of $P(u)$ in (1). From the classification by Losovyy and Tykhyy, I find that the existence of $P(u)$ is guaranteed for Solutions III, IV, Solutions $k$ ($1\\le k\\le 21$, $k\\not= 4,13,14,20$) and Solution 30. We checked whether (1)-(5) are true or not in these cases separately and as a consequence (1)-(5) hold for the all these cases except Solutions 19, 21.

### 2012/07/17

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Mutsuo Oka (Tokyo University of Science)
Contact structure of mixed links (JAPANESE)
[ Abstract ]
A strongly non-degenerate mixed function has a Milnor open book
structures on a sufficiently small sphere. We introduce the notion of
{\\em a holomorphic-like} mixed function
and we will show that a link defined by such a mixed function has a
canonical contact structure.
Then we will show that this contact structure for a certain
holomorphic-like mixed function
is carried by the Milnor open book.

#### GCOE lecture series

16:30-18:00   Room #118 (Graduate School of Math. Sci. Bldg.)
George Elliott (University of Toronto)
An introduction to C*-algebra classification theory (ENGLISH)

#### Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Toru Kan (Mathematical institute, Tohoku University)
On non-radially symmetric solutions of the Liouville-Gel'fand equation on a two-dimensional annular domain (JAPANESE)
[ Abstract ]

#### Lie Groups and Representation Theory

17:00-18:30   Room #126 (Graduate School of Math. Sci. Bldg.)
Eric Opdam (Universiteit van Amsterdam)
Dirac induction for graded affine Hecke algebras (ENGLISH)
[ Abstract ]
In recent joint work with Dan Ciubotaru and Peter Trapa we
constructed a model for the discrete series representations of graded affine Hecke algebras as the index of a Dirac operator.
We discuss the K-theoretic meaning of this result, and the remarkable relation between elliptic character theory of a Weyl group and the ordinary character theory of its Pin cover.

### 2012/07/14

#### Harmonic Analysis Komaba Seminar

13:30-17:00   Room #128 (Graduate School of Math. Sci. Bldg.)
On various inequalities characterizing critical Sobolev-Lorentz spaces (JAPANESE)
Yoshihiro Sawano (Tokyo Metropolitan University) 15:30-17:00
Boundedness of operators on Hardy spaces with variable exponents
(JAPANESE)
[ Abstract ]
In this talk, as an off-spring, we will discuss the boundedness of various operators. Our plan of the talk is as follows:
First we recall the definition of Hardy spaces with variable exponents and then we describe the atomic decomposition.
Based upon the atomic decomposition, I define linear operators such as singular integral operators and commutators.
After the definition, I will state the boundedness results and outline the proof of the boundedness of these operators.

### 2012/07/12

#### Lectures

16:30-17:30   Room #370 (Graduate School of Math. Sci. Bldg.)
M. Lavrentiev (Sobolev Institute of Mathematics)
Real time tsunami parameters evaluation (ENGLISH)
[ Abstract ]
We would like to propose several improvements to the existing software tools for tsunami modeling. Combination of optimaly located system of sensors with advantages of modern hardware architectures will make it possible to deliver calculated parameters of tsunami wave in 12-15 minutes after seismic event.

### 2012/07/11

#### Classical Analysis

14:00-17:30   Room #128 (Graduate School of Math. Sci. Bldg.)
Seiji Nishioka (Yamagata University) 14:00-15:30
On a q-analog of Painlevé III (D_7^{(1)}) and its algebraic function solutions (Joint work with N. Nakazono) (JAPANESE)
Kazuki Hiroe (Kyoto University) 16:00-17:30
First order systems of linear ordinary differential equations and
representations of quivers (ENGLISH)

### 2012/07/10

#### Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Erika Ushikoshi (Mathematical Institute, Tohoku University)
Hadamard variational formula for the Green function
of the Stokes equations with the boundary condition (JAPANESE)

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Marcus Werner (Kavli IPMU)
Topology in Gravitational Lensing (ENGLISH)
[ Abstract ]
General relativity implies that light is deflected by masses
due to the curvature of spacetime. The ensuing gravitational
lensing effect is an important tool in modern astronomy, and
topology plays a significant role in its properties. In this
talk, I will review topological aspects of gravitational lensing
theory: the connection of image numbers with Morse theory; the
interpretation of certain invariant sums of the signed image
magnification in terms of Lefschetz fixed point theory; and,
finally, a new partially topological perspective on gravitational
light deflection that emerges from the concept of optical geometry
and applications of the Gauss-Bonnet theorem.

### 2012/07/09

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Tomoyuki Hisamoto (Univ. of Tokyo)
Volume of graded linear series and the existence problem of constant scalar curvature Kaehler metric (JAPANESE)
[ Abstract ]
We describe the volume of a graded linear series by the Monge-Ampere mass of the associated equilibrium metric. We relate this formula to the question whether the weak geodesic ray associated to a test configuration of given polarized manifold recovers the Donaldson-Futaki invariant.

### 2012/07/06

#### Colloquium

16:30-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
S.R.Srinivasa Varadhan (Courant Institute of Mathematical Sciences, New York University)
Large Deviations of Random Graphs and Random Matrices (ENGLISH)
[ Abstract ]
A random graph with $n$ vertices is a random symmetric matrix of $0$'s and $1$'s and they share some common aspects in their large deviation behavior. For random matrices it is the question of having large eigenvalues. For random graphs it is having too many or too few subgraph counts, like the number of triangles etc. The question that we will try to answer is what would a random matrix or a random graph conditioned to exhibit such a large deviation look like. Since the randomness is of size $n^2$ large deviation rates of order $n^2$ are possible.