## Seminar information archive

### 2014/01/27

#### Seminar on Geometric Complex Analysis

11:00-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Junjiro Noguchi (The University of Tokyo)
Logarithmic 1-forms and distributions of entire curves and integral points (JAPANESE)
[ Abstract ]
The Log-Bloch-Ochiai Theorem says, in the most general form so far, that every entire curve in a Zariski open $X$ of a compact Kahler manifold $\bar{X}$ must be degenerate, if $\bar{q}(X)> \dim X$ ([NW02] Noguchi-Winkelmann, Math.\ Z. 239, 2002). If $X$ is defined a quasi-projective algebraic variety defined over a number field, then there is no Zariski dense $(S, D)$-integral subset in $X$ ($D=\partial X=\bar{X}\subset X$). We discuss this kind of properties more.
In the talk we will fix an error in an application in [NW02], and we will show
Theorem 1. (i) Let $M$ be a complex projective algebraic manifold, and let $D=\sum_{j=1}^l D_j$ be a sum of divisors on $M$ which are independent in supports. If $l> \dim M+r(\{D_j\})-q(M)$, then every entire curve $f:\mathbf{C} \to M\setminus D$ must be degenerate.
(ii) Let $M$ and $D_j$ be defined over a number field. If $l> \dim M+r(\{D_j\})-q(M)$, then there is no Zariski-dense $(S,D)$-integral subset of $M\setminus D$.
For the finiteness we obtain
Theorem 2. Let the notation be as above.
(i) If $l \geq 2 \dim M+r(\{D_j\})$, then $M\setminus D$ is completehyperbolic and hyperbolically embedded into $M$.
(ii) Let $M$ and $D_j$ be defined over a number field. If $l> 2\dim M+r(\{D_j\})$, then every $(S,D)$-integral subset of $M\setminus D$ is finite.

Precise definitions will be given in the talk. We will also discuss an application of Theorem 1 (ii) to generalize Siegel's Theorem on integral points on affine curves,
recent due to A. Levin.

### 2014/01/25

#### Harmonic Analysis Komaba Seminar

13:00-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Jayson Cunanan (Nagoya University) 13:30-15:00
Unimodular Fourier multipliers on Wiener Amalgam Spaces (JAPANESE)
Satoshi Masaki (Hiroshima University) 15:30-17:00
Analysis of mass-subcritical nonlinear Schrödinger equation (JAPANESE)

### 2014/01/24

#### Number Theory Seminar

16:40-18:50   Room #056 (Graduate School of Math. Sci. Bldg.)
Christopher Davis (University of Copenhagen) 16:40-17:40
An approach to p-adic Hodge theory over number fields (ENGLISH)
[ Abstract ]
As motivation from classical Hodge theory, we will first compare singular cohomology and (algebraic) de Rham cohomology for a complex analytic variety. We will also describe a sense in which this comparison does not have a natural analogue over the real numbers. We think of the complex numbers as a "big" ring which is necessary for the comparison isomorphism to work. In the p-adic setting, the analogous study is known as p-adic Hodge theory, and the "big" rings there are even bigger. There are many approaches to p-adic Hodge theory, and we will introduce one tool in particular: (phi, Gamma)-modules. The goal of this talk is to describe a preliminary attempt to find an analogue of this theory (and analogues of its "big" rings) which makes sense over number fields (rather than p-adic fields). This is joint work with Kiran Kedlaya.
Bryden Cais (University of Arizona) 17:50-18:50
Canonical lifts of norm fields and applications (ENGLISH)
[ Abstract ]
In this talk, we begin by outlining the Fontaine-Wintenberger theory of norm fields and explain its application to the classification of p-adic Galois representations on F_p-vector spaces. In order to lift this to a classification of p-adic representations on Z_p-modules, it is necessary to lift the characteristic p norm field constructions of Fontaine-Wintenberger to characteristic zero. We will explain how to canonically perform such lifting in many interesting cases, as well as applications to generalizing a theorem of Kisin on the restriction of crystalline p-adic Galois representations. This is joint work with Christopher Davis.

#### Colloquium

16:30-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Bo Berndtsson (Chalmers University of Technology)
Complex Brunn-Minkowski theory (ENGLISH)
[ Abstract ]
The classical Brunn-Minkowski theory deals with the volume of convex sets.
It can be formulated as a statement about how the volume of slices of a convex set varies when the slice changes. Its complex counterpart deals with slices of pseudo convex sets, or more generally fibers of a complex fibration. It describes how $L^2$-norms of holomorphic functions, or sections of a line bundle, vary when the fibers change, and says essentially that a certain associated vector bundle has positive curvature. In the presence of enough symmetry this implies convexity properties of volumes; the real Brunn-Minkowski theorem corresponding to maximal symmetry. There are also applications and relations in other directions, like variations of Kahler metrics, variations of complex structures and the study of plurisubharmonic functions.

### 2014/01/23

#### Applied Analysis

16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Thomas Giletti (Univ. of Lorraine at Nancy)
Inside dynamics of pushed and pulled fronts (ENGLISH)
[ Abstract ]
Mathematical analysis of reaction-diffusion equations is a powerful tool in the understanding of dynamics of many real-life propagation phenomena. A feature of particular interest is the fact that dynamics and their underlying mechanisms vary greatly, depending on the choice of the nonlinearity in the reaction term. In this talk, we will discuss the pushed/pulled front terminology, based upon the role of each component of the front inside the whole propagating structure.

### 2014/01/22

#### Number Theory Seminar

18:00-19:00   Room #117 (Graduate School of Math. Sci. Bldg.)
Masaki Kashiwara (RIMS, Kyoto University)
Riemann-Hilbert correspondence for irregular holonomic D-modules (ENGLISH)
[ Abstract ]
The classical Riemann-Hilbert correspondence establishes an equivalence between the derived category of regular holonomic D-modules and the derived category of constructible sheaves. Recently, I, with Andrea D'Agnolo, proved a Riemann-Hilbert correspondence for holonomic D-modules which are not necessarily regular (arXiv:1311.2374). In this correspondence, we have to replace the derived category of constructible sheaves with a full subcategory of ind-sheaves on the product of the base space and the real projective line. The construction is therefore based on the theory of ind-sheaves by Kashiwara-Schapira, and also it is influenced by Tamarkin's work. Among the main ingredients of our proof is the description of the structure of flat meromorphic connections due to Takuro Mochizuki and Kiran Kedlaya.

#### Algebraic Geometry Seminar

15:00-16:30   Room #122 (Graduate School of Math. Sci. Bldg.)
Thomas Ducat (University of Warwick)
Divisorial Extractions from Singular Curves in Smooth 3-Folds (ENGLISH)
[ Abstract ]
Consider a singular curve C contained in a smooth 3-fold X.
Assuming the existence of a Du Val general elephant S containing C,
I give a normal form for the equations of C in X and an outline of how to
construct a divisorial extraction from this curve. If the general S is
Du Val of type D_{2k}, E_6 or E_7 then I can give some explicit
conditions for the existence of a terminal extraction. A treatment of
the D_{2k+1} case should be possible by similar means.

### 2014/01/21

#### Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Nao Hamamuki (Graduate shool of Mathematical Sciences, the University of Tokyo)
An improved level set method based on comparison with a signed distance function (JAPANESE)
[ Abstract ]
In the classical level set method, a slope of a solution to level set
equations can be close to zero as time develops even if the initial
slope is large, and this prevents one from computing interfaces given as
the level set of the solution. To overcome this issue we introduce an
improved equation by adding an extra term to the original equation.
Then, by applying a comparison principle to the signed distance function
to the interface, we prove that, globally in time, the slope of a
solution of the initial value problem is preserved near the zero level set.

#### Tuesday Seminar on Topology

16:30-17:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Naohiko Kasuya (The University of Tokyo)
On contact submanifolds of the odd dimensional Euclidean space (JAPANESE)
[ Abstract ]
We prove that the Chern class of a closed contact manifold is an
obstruction for codimension two contact embeddings in the odd
dimensional Euclidean space.
By Gromov's h-principle,
for any closed contact $3$-manifold with trivial first Chern class,
there is a contact structure on $\\mathbb{R}^5$ which admits a contact
embedding.

#### Tuesday Seminar on Topology

17:30-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Xiaolong Li (The University of Tokyo)
Weak eigenvalues in homoclinic classes: perturbations from saddles
with small angles (ENGLISH)
[ Abstract ]
For 3-dimensional homoclinic classes of saddles with index 2, a
new sufficient condition for creating weak contracting eigenvalues is
provided. Our perturbation makes use of small angles between stable and
unstable subspaces of saddles. In particular, by recovering the unstable
eigenvector, we can designate that the newly created weak eigenvalue is
contracting. As applications, we obtain C^1-generic non-trivial index-
intervals of homoclinic classes and the C^1-approximation of robust
heterodimensional cycles. In particular, this sufficient condition is
satisfied by a substantial class of saddles with homoclinic tangencies.

### 2014/01/20

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Hideki Miyachi (Osaka University)
タイヒミュラー距離の幾何学とその応用 (JAPANESE)

#### GCOE Seminars

16:00-17:00   Room #118 (Graduate School of Math. Sci. Bldg.)
Victor Isakov (The Wichita State University)
Increasing stability in the inverse problems for the Helmholtz type prposed equations (ENGLISH)
[ Abstract ]
We report on new stability estimates for recovery of the near field from the prposed scattering amplitude prposed and for Schroedinger potential from the Dirichlet-to Neumann map. In these prposed esrtimates prposed unstable (logarithmic part) goes to zero as the wave number grows. Proofs prposed are using prposed new bounds for Hankel functions and complex and real geometrical optics prposed solutions.

#### Algebraic Geometry Seminar

15:30-17:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Taro Sano (University of Warwick)
Deforming elephants of Q-Fano 3-folds (ENGLISH)
[ Abstract ]
Shokurov and Reid proved that a Fano 3-fold with canonical
Gorenstein singularities has a Du Val elephant, that is,
a member of the anticanonical linear system with only Du Val singularities.
The classification of Fano 3-folds is based on this fact.
However, for a Fano 3-fold with non-Gorenstein terminal singularities,
the anticanonical system does not contain such a member in general.
Alt{\\i}nok--Brown--Reid conjectured that, if the anticanonical system is non-empty,
a Q-Fano 3-fold can be deformed to that with a Du Val elephant.
In this talk, I will explain how to deform an elephant with isolated
singularities to a Du Val elephant.

### 2014/01/15

#### FMSP Lectures

14:50-16:20   Room #056 (Graduate School of Math. Sci. Bldg.)
Rinat Kashaev (University of Geneva)
Lectures on quantum Teichmüller theory IV (ENGLISH)
[ Abstract ]
Quantum Teichmüller theory leads to a family of unitary infinite dimensional projective representations of the mapping class groups of punctured surfaces. One of the recent applications of this theory is the construction of state integral three-manifold invariants related with hyperbolic geometry.
In these lectures it is planned to address the following subjects:
1) Penner’s coordinates in the decorated Teichmüller space.
2) Ratio coordinates.
3) Quantization.
4) The length spectrum of simple closed curves.
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Kashaev.pdf

#### Operator Algebra Seminars

16:30-18:00   Room #118 (Graduate School of Math. Sci. Bldg.)
Yoh Tanimoto (Univ. Tokyo)
Wedge-local fields in integrable models with bound states (JAPANESE)

#### GCOE Seminars

16:00-17:00   Room #370 (Graduate School of Math. Sci. Bldg.)
Victor Isakov (The Wichita State University)
Increasing stability of the continuation for the Helmholtz type equations (ENGLISH)
[ Abstract ]
We derive conditional stability estimates for the Helmholtz type equations which are becoming of Lipschitz type for large frequencies/wave numbers. Proofs use splitting solutions into low and high frequencies parts where we use energy (in particular) Carleman estimates. We discuss numerical confirmation and open problems.

#### GCOE Seminars

17:00-18:00   Room #370 (Graduate School of Math. Sci. Bldg.)
Jin Cheng (Fudan University)
A numerical method for solving the inverse heat conduction problem without initial value (ENGLISH)
[ Abstract ]
In this talk, we will present some results for the inverse heat conduction problem for the heat equation of determining a boundary value at in an unreachable part of the boundary. The main difficulty for this problem is that the initial value is unknown by the practical reason. A new method is prposed to solve this problem and the nuemrical tests show the effective of this method. Some theoretic analysis will be presented. This is a joint work with J Nakagawa, YB Wang, M Yamamoto.

#### Number Theory Seminar

16:40-17:40   Room #056 (Graduate School of Math. Sci. Bldg.)
Stephen Lichtenbaum (Brown University)
Special values of zeta-functions of schemes (ENGLISH)
[ Abstract ]
We will give conjectured formulas giving the behavior of the
seta-function of regular schemes projective and flat over Spec Z at
non-positive integers in terms of Weil-etale cohomology. We will also
explain the conjectured relationship of Weil-etale cohomology to etale
cohomology, which makes it possible to express these formulas also in terms
of etale cohomology.

### 2014/01/14

#### FMSP Lectures

14:50-16:20   Room #056 (Graduate School of Math. Sci. Bldg.)
Rinat Kashaev (University of Geneva)
Lectures on quantum Teichmüller theory III (ENGLISH)
[ Abstract ]
Quantum Teichmüller theory leads to a family of unitary infinite dimensional projective representations of the mapping class groups of punctured surfaces. One of the recent applications of this theory is the construction of state integral three-manifold invariants related with hyperbolic geometry.
In these lectures it is planned to address the following subjects:
1) Penner’s coordinates in the decorated Teichmüller space.
2) Ratio coordinates.
3) Quantization.
4) The length spectrum of simple closed curves.
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Kashaev.pdf

#### Tuesday Seminar on Topology

17:00-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Rinat Kashaev (University of Geneva)
State-integral partition functions on shaped triangulations (ENGLISH)
[ Abstract ]
Quantum Teichm\\"uller theory can be promoted to a
generalized TQFT within the combinatorial framework of shaped
triangulations with the tetrahedral weight functions given in
terms of the Weil-Gelfand-Zak transformation of Faddeev.FN"s
quantum dilogarithm. By using simple examples, I will
illustrate the connection of this theory with the hyperbolic
geometry in three dimensions.

#### Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Kenichi Ito (University of Tsukuba)
Threshold properties for one-dimensional discrete Schr\\"odinger operators (JAPANESE)
[ Abstract ]
We study the relation between the generalized eigenspace and the asymptotic expansion of the resolvent around the threshold $0$ for the one-dimensional discrete Schr\\"odinger operator on $\\mathbb Z$. We decompose the generalized eigenspace into the subspaces corresponding to the eigenstates and the resonance states only by their asymptotics at infinity, and classify the coefficient operators of the singlar part of resolvent expansion completely in terms of these eigenspaces. Here the generalized eigenspace we consider is largest possible. For an explicit computation of the resolvent expansion we apply the expansion scheme of Jensen-Nenciu (2001). This talk is based on the recent joint work with Arne Jensen (Aalborg University).

#### Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Masaki Mori (the University of Tokyo)
A cellular classification of simple modules of the Hecke-Clifford
superalgebra (JAPANESE)
[ Abstract ]
The Hecke--Clifford superalgebra is a super version of
the Iwahori--Hecke algebra of type A. Its simple modules
are classified by Brundan, Kleshchev and Tsuchioka using
a method of categorification of affine Lie algebras.
However their constructions are too abstract to study in practice.
In this talk, we introduce a more concrete way to produce its
simple modules with a generalized theory of cellular algebras
which is originally developed by Graham and Lehrer.
In our construction the key is that there is a right action of
the Clifford superalgebra on the super-analogue of the Specht module.
With the help of the notion of the Morita context, a simple module
of the Hecke--Clifford superalgebra is made from that of
the Clifford superalgebra.

#### GCOE Seminars

15:00-16:00   Room #118 (Graduate School of Math. Sci. Bldg.)
Calderon problem for Maxwell's equations in cylindrical domain (ENGLISH)
[ Abstract ]
We prove some uniqueness results in determination of the conductivity, the permeability and the permittivity of Maxwell's equations from partial Dirichlet-to-Neumann map.

### 2014/01/11

#### Monthly Seminar on Arithmetic of Automorphic Forms

14:00-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Dihua Jiang (School of Mathematics, University of Minnesota) 14:00-14:45
A product of tensor product L-functions of quasi-split classical groups of Hermitian type. (jointly with Lei Zhang) (ENGLISH)
Dihua Jiang (School of Mathematics, University of Minnesota) 15:00-15:45
A product of tensor product L-functions of quasi-split classical groups of Hermitian type, Part II. (jointly with Lei Zhang) (ENGLISH)

### 2014/01/10

#### FMSP Lectures

14:50-16:20   Room #056 (Graduate School of Math. Sci. Bldg.)
Rinat Kashaev (University of Geneva)
Lectures on quantum Teichmüller theory II (ENGLISH)
[ Abstract ]
Quantum Teichmüller theory leads to a family of unitary infinite dimensional projective representations of the mapping class groups of punctured surfaces. One of the recent applications of this theory is the construction of state integral three-manifold invariants related with hyperbolic geometry.
In these lectures it is planned to address the following subjects:
1) Penner’s coordinates in the decorated Teichmüller space.
2) Ratio coordinates.
3) Quantization.
4) The length spectrum of simple closed curves.
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Kashaev.pdf