## Seminar information archive

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Yu Kawakami (Yamaguchi University)
A ramification theorem for the ratio of canonical forms of flat surfaces in hyperbolic 3-space (JAPANESE)
[ Abstract ]
We provide an effective ramification theorem for the ratio of canonical forms of weakly complete flat fronts in the hyperbolic 3-space. As an application, we give a simple proof of the classification of complete nonsingular flat surfaces in the hyperbolic 3-space.

#### Operator Algebra Seminars

16:30-18:00   Room #117 (Graduate School of Math. Sci. Bldg.)
Narutaka Ozawa (RIMS, Kyoto University)
Is an irng singly generated as an ideal? (JAPANESE)

#### GCOE lecture series

15:30-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Mihai Paun (Institut Élie Cartan and KIAS)
TBA(中止になりました) (ENGLISH)

### 2012/01/12

#### Number Theory Seminar

18:15-19:15   Room #056 (Graduate School of Math. Sci. Bldg.)
Toby Gee (Imperial College London)
New perspectives on the Breuil-Mézard conjecture (joint with M. Emerton)
(ENGLISH)
[ Abstract ]
I will discuss joint work with Matthew Emerton on geometric approaches to the Breuil-Mézard conjecture, generalising a geometric approach of Breuil and Mézard. I will discuss a proof of the geometric version of the original conjecture, as well as work in progress on a geometric version of the conjecture which does not make use of a fixed residual representation.

(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)

### 2012/01/06

#### Operator Algebra Seminars

16:30-18:00   Room #118 (Graduate School of Math. Sci. Bldg.)
Yasuyuki Kawahigashi (Univ. Tokyo)
Diagrammatical methods in theory of subfactors (ENGLISH)

### 2012/01/05

#### Operator Algebra Seminars

16:30-18:00   Room #117 (Graduate School of Math. Sci. Bldg.)
Yasuyuki Kawahigashi (Univ. Tokyo)
Classification and amenability in theory of von Neumann algebras (ENGLISH)

### 2011/12/27

#### Operator Algebra Seminars

14:30-18:00   Room #117 (Graduate School of Math. Sci. Bldg.)
Makoto Yamashita (Universita di Roma "Tor Vergata") 14:30-16:00
Deformation of algebras associated to group cocycles (JAPANESE)
Yoh Tanimoto (Universitaet Goettingen) 16:30-18:00
Construction of wedge-local nets through
Longo-Witten endomorphisms (JAPANESE)

#### GCOE Seminars

13:30-14:30   Room #370 (Graduate School of Math. Sci. Bldg.)
Yichao Zhu (University of Oxford)
The Modelling of Dislocations in the Early Stage of the Metal Fatigue (ENGLISH)
[ Abstract ]
Understanding fatigue of metal under cyclic loads is crucial for some fields in mechanical engineering, such as the design of wheels of high speed trains and the aeroplane engine. Experimentally it has been found that this type of
fatigue is closely related to a ladder shape pattern of dislocations known as a persistent slip band (PSB) at a microscopic level. In this talk, a quantitative description for the formation of PSBs is proposed from two angles: 1. the motion of a single dislocation analysed by using asymptotic expansions and numerical simulations; 2. the collective behaviour of a large number of dislocations analysed by using a method of multiple scales.

#### GCOE Seminars

14:30-15:30   Room #370 (Graduate School of Math. Sci. Bldg.)
Manabu Machida (University of Michigan)
Wave Transport in Random Media and Inverse Problems (ENGLISH)
[ Abstract ]
Wave transport in random media is described by the radiative transport equation, which is a linear Boltzmann equation. Such transport phenomena are characterized by two optical parameters in the equation: the absorption and scattering coefficients. In this talk, inverse problems of determining optical parameters will be considered and the Lipschitz stability will be proved using a Carleman estimate. One application of this inverse problem is optical tomography, which detects tumors in a human body using (unlike X-ray CT scan) near-infrared light. I will also present tomographic images of lemon and lotus root slices which are obtained by numerically solving the radiative transport equation with the method of rotated reference frames.

### 2011/12/26

#### Algebraic Geometry Seminar

15:30-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Birational unboundedness of Q-Fano varieties and rationally connected strict Mori fiber spaces (JAPANESE)
[ Abstract ]
It has been known that suitably restricted classes of Q-Fano varieties are bounded. I will talk about the birational unboundedness of (log terminal) Q-Fano varieties with Picard number one and of rationally connected strict Mori fiber spaces in each dimension $¥geq 3$. I will explain the idea of the proof which will be done after passing to a positive characteristic.

### 2011/12/21

#### Number Theory Seminar

16:30-17:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Kazuya Kato (University of Chicago)
On Sharifi's conjecture (JAPANESE)

### 2011/12/20

#### Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Gueorgui Raykov (Catholic University of Chile)
A trace formula for the perturbed Landau Hamiltonian (ENGLISH)
[ Abstract ]
The talk will be based on a joint work with A. Pushnitski
and C. Villegas-Blas, the preprint is available here:
http://arxiv.org/abs/1110.3098 .

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Yoshihiko Mitsumatsu (Chuo University)
Leafwise symplectic structures on Lawson's Foliation on the 5-sphere (JAPANESE)
[ Abstract ]
We are going to show that Lawson's foliation on the 5-sphere
admits a smooth leafwise symplectic sturcture. Historically, Lawson's
foliation is the first one among foliations of codimension one which are
constructed on the 5-sphere. It is obtained by modifying the Milnor
fibration associated with the Fermat type cubic polynominal in three
variables.
Alberto Verjovsky proposed a question whether if the Lawson's
foliation or slighty modified ones admit a leafwise smooth symplectic
structure and/or a leafwise complex structure. As Lawson's one has a
Kodaira-Thurston nil 4-manifold as a compact leaf, the question can not
be solved simultaneously both for the symplectic and the complex cases.
The main part of the construction is to show that the Fermat type
cubic surface admits an `end-periodic' symplectic structure, while the
natural one as an affine surface is conic at the end. Even though for
the other two families of the simple elliptic hypersurface singularities
almost the same construction works, at present, it seems very limited
where a Stein manifold admits an end-periodic symplectic structure. If
the time allows, we also discuss the existence of such structures on
globally convex symplectic manifolds.

### 2011/12/19

#### Number Theory Seminar

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)
Tamas Szamuely (Budapest)
Galois Theory: Past and Present (ENGLISH)

### 2011/12/17

#### Monthly Seminar on Arithmetic of Automorphic Forms

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Masami Ohta (Professor Emeritus of Tokai Univeristy) 13:30-14:30
On the finite order Q-rational points on J_1 (N) (JAPANESE)
Shushi Harashita (Yokohama National University
) 15:00-16:00
On the affineness of distinguished Deligne-Lusztig varieties (JAPANESE)

### 2011/12/16

#### Colloquium

16:30-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)
TAKAGI, Shunsuke (Graduate School of Mathematical Sciences, University of Tokyo)
Application of positive characteristic methods to singularity theory (JAPANESE)
[ Abstract ]
As an application of positive characteristic methods to singularity theory, I will talk about a characterization of singularities in characteristic zero using Frobenius maps. Log canonical singularities form a class of singularities associated to the minimal model program. It is conjectured that they correspond to $F$-pure singularities, which form a class of singularities defined via splitting of Frobenius maps. In this talk, I will explain a recent progress on this conjecture, especially its connection to another conjecture on ordinary reductions of Calabi-Yau varieties defined over number fields.

### 2011/12/14

#### Number Theory Seminar

17:30-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Lucien Szpiro (City University of New York)
Good and bad reduction for algebraic dynamical systems (ENGLISH)
[ Abstract ]
We will report on a recent work with collaborators in New York on the
different ways to look at degenerations of a dynamical system in a one
parameter family. Resultants, conductors and isotriviality will be analyzed.

### 2011/12/13

#### Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Wolfram Bauer (Mathematisches Institut, Georg-August-Universität)
Trivializable subriemannian structures and spectral analysis of associated operators (ENGLISH)

#### Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Hung Yean Loke (National University of Singapore)
Local Theta lifts of unitary lowest weight modules to the indefinite orthogonal groups (ENGLISH)
[ Abstract ]

In this talk, I will discuss the local theta lifts of unitary lowest weight modules of $Sp(2p,R)$ to the indefinite orthogonal group $O(n,m)$. In a previous paper, Nishiyama and Zhu computed the associated cycles when the dual pair $Sp(2p,R) \\times O(m,n)$ lies in the stable range, ie. $2p \\leq \\min(m,n)$. In this talk, I will report on a joint work with Jiajun Ma and U-Liang Tang at NUS where we extend the computation beyond the stable range. Our approach is to analyze the coherent sheaves generated by the graded modules.
We will also need the Kobayashi's projection formula for discretely decomposable restrictions. Our study produces some interesting formulas on the $K$-types of the representations. In particular for some of these representations, the $K$-types formulas agree those in a conjecture of Vogan on the unipotent representations.

#### Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Hung Yean Loke (National University of Singapore)
Local Theta lifts of unitary lowest weight modules to the indefinite orthogonal groups (ENGLISH)
[ Abstract ]

In this talk, I will discuss the local theta lifts of unitary lowest weight modules of $Sp(2p,R)$ to the indefinite orthogonal group $O(n,m)$. In a previous paper, Nishiyama and Zhu computed the associated cycles when the dual pair $Sp(2p,R) \\times O(m,n)$ lies in the stable range, ie. $2p \\leq \\min(m,n)$. In this talk, I will report on a joint work with Jiajun Ma and U-Liang Tang at NUS where we extend the computation beyond the stable range. Our approach is to analyze the coherent sheaves generated by the graded modules.
We will also need the Kobayashi's projection formula for discretely decomposable restrictions. Our study produces some interesting formulas on the $K$-types of the representations. In particular for some of these representations, the $K$-types formulas agree those in a conjecture of Vogan on the unipotent representations.

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Mircea Voineagu (IPMU, The University of Tokyo)
Remarks on filtrations of the singular homology of real varieties. (ENGLISH)
[ Abstract ]
We discuss various conjectures about filtrations on the singular homology of real and complex varieties. We prove that a conjecture relating niveau filtration on Borel-Moore homology of real varieties and the image of generalized cycle maps from reduced Lawson homology is false. In the end, we discuss a certain decomposition of Borel-Haeflinger cycle map. This is a joint work with J.Heller.

### 2011/12/12

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Shinichiroh MATSUO (Kyoto University)
Brody curves and mean dimension (JAPANESE)
[ Abstract ]
We study the mean dimensions of the spaces of Brody curves. In particular we give the formula of the mean dimension of the space of Brody curves in the Riemann sphere.

#### Algebraic Geometry Seminar

15:30-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Robert Laterveer (CNRS, IRMA, Université de Strasbourg)
A version of Barth's theorem for singular varieties (cancelled) (JAPANESE)

### 2011/12/09

#### Lectures

10:40-11:30   Room #122 (Graduate School of Math. Sci. Bldg.)
Erwin Bolthausen (University of Zurich)
An iterative construction of solutions of the TAP equation (ENGLISH)
[ Abstract ]
The TAP equation (Thouless-Anderson-Palmer) describes the so-called pure states in the Sherrington-Kirkpatrick model. A mathematical rigorous derivation of the equation exists only in the high temperature regime. We propose an interative construction of solutions of the equations which is shown to converge up to the de Almayda-Thouless line. The iteration makes sense also beyond this line, but it fails to converge. However, some properties of the iteration can also been proved beyond the AT-line.

#### Lectures

10:40-11:30   Room #122 (Graduate School of Math. Sci. Bldg.)
Erwin Bolthausen (University of Zurich)
An iterative construction of solutions of the TAP equation (ENGLISH)
[ Abstract ]
The TAP equation (Thouless-Anderson-Palmer) describes the so-called pure states in the Sherrington-Kirkpatrick model. A mathematical rigorous derivation of the equation exists only in the high temperature regime. We propose an interative construction of solutions of the equations which is shown to converge up to the de Almayda-Thouless line. The iteration makes sense also beyond this line, but it fails to converge. However, some properties of the iteration can also been proved beyond the AT-line.