## Seminar information archive

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Atsushi Hayashimoto (Nagano National College of Technology)
CR equivalence problem of CR manifolds with slice structure (JAPANESE)

### 2012/06/20

#### Number Theory Seminar

16:40-17:40   Room #056 (Graduate School of Math. Sci. Bldg.)
Kazuki Tokimoto (University of Tokyo)
On the reduction modulo p of representations of a quaternion
division algebra over a p-adic field (JAPANESE)
[ Abstract ]
The p-adic Langlands correspondence and the mod p Langlands correspondence for GL_2(Q_p) are known to be compatible with the reduction modulo p in many cases.
In this talk, we examine whether a similar compatibility exists for the composition of the local Langlands correspondence and the local Jacquet-Langlands correspondence.
The simplest case has already been treated by Vign¥'eras. We deal with more cases.

#### PDE Real Analysis Seminar

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Paolo Maremonti (Seconda Università degli Studi di Napoli)
On the Navier-Stokes Cauchy problem with nondecaying data (ENGLISH)
[ Abstract ]
We prove the well posedeness of the Navier-Stokes Cauchy problem for nondecaying initial data u_0 \\in C (R^n) \\cap L^\\infty (R^n), n >= 3. This problem is studied by Giga, Inui and Matsui for n >= 3, and Giga, Matsui and Sawada in the two dimensional case. The aims of our paper are slight different since we also find pointwise estimates for the pressure field. Via a uniqueness theorem, we give a sort of structure theorem to GIM solutions.

### 2012/06/19

#### Tuesday Seminar on Topology

17:10-18:10   Room #056 (Graduate School of Math. Sci. Bldg.)
Yukio Matsumoto (Gakushuin University)
On the universal degenerating family of Riemann surfaces
over the D-M compactification of moduli space (JAPANESE)
[ Abstract ]
It is usually understood that over the Deligne-
Mumford compactification of moduli space of Riemann surfaces of
genus > 1, there is a family of stable curves. However, if one tries to
construct this family precisely, he/she must first take a disjoint union
of various types of smooth families of stable curves, and then divide
them by their automorphisms to paste them together. In this talk we will
show that once the smooth families are divided, the resulting quotient
family contains not only stable curves but virtually all types of
degeneration of Riemann surfaces, becoming a kind of universal
degenerating family of Riemann surfaces.

#### Numerical Analysis Seminar

16:30-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Hidenori Ogata (The University of Electro-Communications)
Advances in the charge simulation method (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/

### 2012/06/18

#### Algebraic Geometry Seminar

15:30-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Katsutoshi Yamanoi (Tokyo Institute of Technology)
アルバネーゼ次元最大の複素射影多様体の特殊集合について (JAPANESE)
[ Abstract ]
アルバネーゼ次元が最大の複素射影多様体の中に含まれる代数的あるいは超越的な複

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
CR Q-curvature flow and CR Paneitz operator on 3-dimensional CR manifolds (JAPANESE)

#### Lectures

09:45-12:30   Room #002 (Graduate School of Math. Sci. Bldg.)
James Nolen (Duke University) 09:45-10:45
Fluctuation of solutions to PDEs with random coefficients (Part 2) (ENGLISH)
[ Abstract ]
This is continuation of the previous day's lecture.
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~matano/SDE2012/
Leonid Ryzhik (Stanford University) 11:00-12:30
Weak coupling limits for particles and PDEs (Part 2) (ENGLISH)
[ Abstract ]
This is continuation of the previous day's lecture.
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~matano/SDE2012/

### 2012/06/17

#### Lectures

09:45-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
James Nolen (Duke University) 09:45-17:30
Fluctuation of solutions to PDEs with random coefficients (Part 1) (JAPANESE)
[ Abstract ]
For PDEs with random coefficients, it is interesting to understand whether the solutions exhibit some universal statistical behavior that is independent of the details of the coefficients. In particular, how do solutions fluctuate around the mean behavior? We will discuss this issue in the context of three examples:

(1) Traveling fronts in random media in one dimension.
(2) Elliptic homogenization problems.
(3) Random Hamilton-Jacobi equations.

The relation between PDE tools and probabilistic ideas will be
explained.
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~matano/SDE2012/

Leonid Ryzhik (Stanford Univeristy) 13:00-14:45
Weak coupling limits for particles and PDEs (Part 1) (JAPANESE)
[ Abstract ]
Weak random fluctuations in medium parameters may lead to a non-trivial effect after large times and propagation over long distances. We will consider several examples when the large time limit can be treated:

(1) a particle in a weakly random velocity field.
(2) weak random fluctuations of Hamilton equations, and
(3) the linear Scrhoedinger equation with a weak random potential.

The role of long range correlation of the random fluctuations will also be discussed.
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~matano/SDE2012/
Gregoire Nadin (CNRS / Paris 6) 15:15-17:15
Asymptotic spreading for heterogeneous Fisher-KPP reaction-diffusion equations (JAPANESE)
[ Abstract ]
The solutions of the heterogeneous Fisher-KPP equation associated with compactly supported initial data are known to take off from the unstable steady state 0 and to converge to the steady state 1 for large times. The aim of this lecture is to estimate the speed at which the interface between 0 and 1 spreads.

Using the new notion of generalized principal eigenvalues for non-compact elliptic operators, we will derive such estimates which will be proved to be optimal for several classes of heterogeneity such as periodic, almost periodic or random stationary ergodic ones.
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~matano/SDE2012/

### 2012/06/16

#### Lectures

13:15-17:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Tadahisa Funaki (University of Tokyo) 13:15-14:45
A viewpoint of the stochastic analysis in differential equations (JAPANESE)
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~matano/SDE2012/
Yoshiki Otobe (Shinshu University) 15:00-17:00
Stochastic (partial) differential equations from a functional analytic point of view (JAPANESE)
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~matano/SDE2012/

### 2012/06/14

#### Algebraic Geometry Seminar

13:30-15:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Christian Schnell (IPMU)
Vanishing theorems for perverse sheaves on abelian varieties (ENGLISH)
[ Abstract ]
I will describe a few results, due to Kraemer-Weissauer and myself, about perverse sheaves on complex abelian varieties; they are natural generalizations of the generic vanishing theorem of Green-Lazarsfeld.

### 2012/06/13

#### Number Theory Seminar

16:40-17:40   Room #056 (Graduate School of Math. Sci. Bldg.)
Tomoki Mihara (University of Tokyo)
Singular homologies of non-Archimedean analytic spaces and integrals along cycles (JAPANESE)

#### Lectures

17:00-18:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Sunder Sethuraman (University of Arizona)
A KPZ equation for zero-range interactions (ENGLISH)
[ Abstract ]
We derive a type of KPZ equation, in terms of a martingale problem, as a scaling limit of fluctuation fields in weakly asymmetric zero-range processes. Joint work (in progress) with Milton Jara and Patricia Goncalves.

#### Lectures

11:00-15:30   Room #128 (Graduate School of Math. Sci. Bldg.)
S. Harase, et. al. (Tokyo Institute of Technology/JSPS)
Workshop for Quasi-Monte Carlo and Pseudo Random Number Generation (ENGLISH)
[ Reference URL ]

### 2012/06/12

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Takefumi Nosaka (RIMS, Kyoto University, JSPS)
Topological interpretation of the quandle cocycle invariants of links (JAPANESE)
[ Abstract ]
Carter et al. introduced many quandle cocycle invariants
combinatorially constructed from link-diagrams. For connected quandles of
finite order, we give a topological meaning of the invariants, without
some torsion parts. Precisely, this invariant equals a sum of "knot
colouring polynomial" and of a Z-equivariant part of the Dijkgraaf-Witten
invariant. Moreover, our approach involves applications to compute "good"
torsion subgroups of the 3-rd quandle homologies and the 2-nd homotopy
groups of rack spaces.

#### Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Toshihisa Kubo (the University of Tokyo)
Conformally invariant systems of differential operators of non-Heisenberg parabolic type (ENGLISH)
[ Abstract ]
The wave operator in Minkowski space is a classical example of a conformally invariant differential operator.
Recently, the notion of conformality of one operator has been
generalized by Barchini-Kable-Zierau to systems of differential operators.
Such systems yield homomrophisms between generalized Verma modules. In this talk we build such systems of second-order differential operators in the maximal non-Heisenberg parabolic setting.
If time permits then we will discuss the corresponding homomorphisms between generalized Verma modules.

#### Lectures

09:50-17:10   Room #118 (Graduate School of Math. Sci. Bldg.)
Josef Dick, et. al. (Univ. New South Wales)
Workshop for Quasi-Monte Carlo and Pseudo Random Number Generation (ENGLISH)
[ Reference URL ]

### 2012/06/11

#### Kavli IPMU Komaba Seminar

16:30-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Changzheng Li (Kavli IPMU)
Quantum cohomology of flag varieties (ENGLISH)
[ Abstract ]
In this talk, I will give a brief introduction to the quantum cohomology of flag varieties first. Then I will introduce a Z^2-filtration on the quantum cohomology of complete flag varieties. In the end, we will study the quantum Pieri rules for complex/symplectic Grassmannians, as applications of the Z^2-filtration.

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Damian BROTBEK (University of Tokyo)
Differential forms on complete intersections (ENGLISH)
[ Abstract ]
Brückmann and Rackwitz proved a vanishing result for particular types of differential forms on complete intersection varieties. We will be interested in the cases not covered by their result. In some cases, we will show how the space $H^0(X,S^{m_1}\Omega_X\otimes \cdots \otimes S^{m_k}\Omega_X)$ depends on the equations defining $X$, and in particular we will prove that the theorem of Brückmann and Rackwitz is optimal. The proofs are based on simple, combinatorial, cohomology computations.

### 2012/06/09

#### Harmonic Analysis Komaba Seminar

13:30-17:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Yasuo Furuya (Tokai University) 13:30-15:00
Resent topics on the Cauchy integrals (the works of Muscalu and others) (JAPANESE)
Tsukasa Iwabuchi (Chuo University) 15:30-17:00
Ill-posedness for the nonlinear Schr\\"odinger equations in one
space dimension
(JAPANESE)
[ Abstract ]
In this talk, we consider the Cauchy problems for the nonlinear Schr\\"odinger equations. In particular, we study the ill-posedness by showing that the continuous dependence on initial data does not hold. In the known results, Bejenaru-Tao (2006) considered the problem in the Sobolev spaces $H^s (\\mathbb R)$ and showed the ill-posedness when $s < -1$. In this talk, we study the ill-posedness in the Besov space for one space dimension and in the Sobolev spaces for two space dimensions.

### 2012/06/08

#### GCOE lecture series

14:00-15:30   Room #118 (Graduate School of Math. Sci. Bldg.)
Mihnea Popa (University of Illinois at Chicago)
Derived categories and cohomological invariants II (ENGLISH)
[ Abstract ]
(Abstract for both Parts I and II)
I will discuss results on the derived invariance of various cohomological quantities, like the Hodge numbers, a twisted version of Hochschild cohomology, the Picard variety, and cohomological support loci. I will include a small discussion of current work on orbifolds if time permits.

#### Kavli IPMU Komaba Seminar

16:30-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Bong Lian (Brandeis University)
Period Integrals and Tautological Systems (ENGLISH)
[ Abstract ]
We develop a global Poincar\\'e residue formula to study
period integrals of families of complex manifolds. For any compact
complex manifold $X$ equipped with a linear system $V^*$ of
generically smooth CY hypersurfaces, the formula expresses period
integrals in terms of a canonical global meromorphic top form on $X$.
Two important ingredients of this construction are the notion of a CY
principal bundle, and a classification of such rank one bundles.
We also generalize the construction to CY and general type complete
intersections. When $X$ is an algebraic manifold having a sufficiently
large automorphism group $G$ and $V^*$ is a linear representation of
$G$, we construct a holonomic D-module that governs the period
integrals. The construction is based in part on the theory of
tautological systems we have developed earlier. The approach allows us
to explicitly describe a Picard-Fuchs type system for complete
intersection varieties of general types, as well as CY, in any Fano
variety, and in a homogeneous space in particular. In addition, the
approach provides a new perspective of old examples such as CY
complete intersections in a toric variety or partial flag variety. The
talk is based on recent joint work with R. Song and S.T. Yau.

### 2012/06/05

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Yusuke Kuno (Tsuda College)
A generalization of Dehn twists (JAPANESE)
[ Abstract ]
We introduce a generalization
of Dehn twists for loops which are not
necessarily simple loops on an oriented surface.
Our generalization is an element of a certain
enlargement of the mapping class group of the surface.
A natural question is whether a generalized Dehn twist is
in the mapping class group. We show some results related to this question.
This talk is partially based on a joint work
with Nariya Kawazumi (Univ. Tokyo).

#### GCOE lecture series

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Yves Benoist (CNRS, Orsay)
Random walk on reductive groups II (ENGLISH)
[ Abstract ]
The asymptotic behavior of the sum of real numbers chosen independantly with same probability law is controled by many classical theorems: Law of Large Numbers, Central Limit Theorem, Law of Iterated Logarithm, Local Limit Theorem, Large deviation Principle, 0-1 Law,... In these introductory talks I will recall these classical results and explain their analogs for products of matrices chosen independantly with same probability law, when the action of the support of the law is semisimple. We will see that the dynamics of the corresponding action on the flag variety is a crucial tool for studying these non-commutative random walks.

#### Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Yves Benoist (CNRS and Orsay)
Random walk on reductive groups (ENGLISH)
[ Abstract ]
The asymptotic behavior of the sum of real numbers chosen independantly with same probability law is controled by many classical theorems: Law of Large Numbers, Central Limit Theorem, Law of Iterated Logarithm, Local Limit Theorem, Large deviation Principle, 0-1 Law,... In these introductory talks I will recall these classical results and explain their analogs for products of matrices chosen independantly with same probability law, when the action of the support of the law is semisimple. We will see that the dynamics of the corresponding action on the flag variety is a crucial tool for studying these non-commutative random walks.