## Seminar information archive

Seminar information archive ～08/18｜Today's seminar 08/19 | Future seminars 08/20～

### 2013/06/22

#### Monthly Seminar on Arithmetic of Automorphic Forms

10:00-12:15 Room #123 (Graduate School of Math. Sci. Bldg.)

*** (JAPANESE)

*** (JAPANESE)

*******(***) 10:00-11:00*** (JAPANESE)

*******(***) 11:15-12:15*** (JAPANESE)

#### Monthly Seminar on Arithmetic of Automorphic Forms

10:00-12:15 Room #123 (Graduate School of Math. Sci. Bldg.)

On the computation of the ramified Siegel series associated with

trivial character (JAPANESE)

An explicit relative trace formula for Hilbert modular forms and its applications

(JAPANESE)

**Kei-ichi Gunji**(Chiba Inst. Tech) 10:00-11:00On the computation of the ramified Siegel series associated with

trivial character (JAPANESE)

[ Abstract ]

Please check the Japanese version of the web page.

Please check the Japanese version of the web page.

**Masao Tsuzuki**(Sophia University) 11:15-12:15An explicit relative trace formula for Hilbert modular forms and its applications

(JAPANESE)

[ Abstract ]

This is joint work with Shingo Sugiyama. In this talk, we report our recent result on relative trace formula on PGL(2) computing the spectral averages for the central L-values of quadratic base change of holomorphic Hilbert mudular forms. explicitly all local terms of the trace formula, dropping several assumptions which have always been assumed in existing works of similar theme. The following applications of our explicit relative trace formula will be explained:

(i) a spectral equidistribution result in the leve aspect for the Satake parameters weighted by central L-values;

(ii) a subconvexity bound of quadratic base change L-functions for holomorphic Hilbert cusp forms in the weight aspect;

(iii) Existence of infinitely many holomorphic Hilbert cusp forms with arbitrarily large field of definition and with non vanishing central $L$-values.

This is joint work with Shingo Sugiyama. In this talk, we report our recent result on relative trace formula on PGL(2) computing the spectral averages for the central L-values of quadratic base change of holomorphic Hilbert mudular forms. explicitly all local terms of the trace formula, dropping several assumptions which have always been assumed in existing works of similar theme. The following applications of our explicit relative trace formula will be explained:

(i) a spectral equidistribution result in the leve aspect for the Satake parameters weighted by central L-values;

(ii) a subconvexity bound of quadratic base change L-functions for holomorphic Hilbert cusp forms in the weight aspect;

(iii) Existence of infinitely many holomorphic Hilbert cusp forms with arbitrarily large field of definition and with non vanishing central $L$-values.

### 2013/06/20

#### FMSP Lectures

16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Geometric applications of Wasserstein distance,

Lecture (II) Curvature of metric measure spaces I (ENGLISH)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~topology/Walczak.pdf

**Szymon M. Walczak**(University of Lodz, Poland)Geometric applications of Wasserstein distance,

Lecture (II) Curvature of metric measure spaces I (ENGLISH)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~topology/Walczak.pdf

### 2013/06/19

#### Number Theory Seminar

16:40-17:40 Room #056 (Graduate School of Math. Sci. Bldg.)

A p-adic exponential map for the Picard group and its application to curves (JAPANESE)

**Wataru Kai**(University of Tokyo)A p-adic exponential map for the Picard group and its application to curves (JAPANESE)

[ Abstract ]

Let $\\mathcal{X}$ be a proper flat scheme over a complete discrete valuation ring $O_k$ of characteristic $(0,p)$. We define an exponential map from a subgroup of the first cohomology group of $O_¥mathcal{X}$ to the Picard group of $\\mathcal{X}$, mimicking the classical construction in complex geometry. This exponential map can be applied to prove a surjectivity property concerning the Albanese variety $Alb_{X}$ of a smooth variety $X$ over $k$.

Let $\\mathcal{X}$ be a proper flat scheme over a complete discrete valuation ring $O_k$ of characteristic $(0,p)$. We define an exponential map from a subgroup of the first cohomology group of $O_¥mathcal{X}$ to the Picard group of $\\mathcal{X}$, mimicking the classical construction in complex geometry. This exponential map can be applied to prove a surjectivity property concerning the Albanese variety $Alb_{X}$ of a smooth variety $X$ over $k$.

#### FMSP Lectures

14:40-16:10 Room #002 (Graduate School of Math. Sci. Bldg.)

Geometric applications of Wasserstein distance,

Lecture (I) Wasserstein distance and optimal transportation

(ENGLISH)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~topology/Walczak.pdf

**Szymon M. Walczak**(University of Lodz, Poland)Geometric applications of Wasserstein distance,

Lecture (I) Wasserstein distance and optimal transportation

(ENGLISH)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~topology/Walczak.pdf

#### Operator Algebra Seminars

16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

A generalization of the spectral flow and localization of index (ENGLISH)

**Yosuke Kubota**(Univ. Tokyo)A generalization of the spectral flow and localization of index (ENGLISH)

### 2013/06/18

#### Tuesday Seminar on Topology

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

Left-orderable, non-L-space surgeries on knots (JAPANESE)

**Kimihiko Motegi**(Nihon University)Left-orderable, non-L-space surgeries on knots (JAPANESE)

[ Abstract ]

A Dehn surgery is said to be left-orderable

if the resulting manifold of the surgery has the left-orderable fundamental group,

and a Dehn surgery is called an L-space surgery

if the resulting manifold of the surgery is an L-space.

We will focus on left-orderable, non-L-space surgeries on knots in the 3-sphere.

Once we have a knot with left-orderable surgeries,

the ``periodic construction" enables us to provide infinitely many knots with

left-orderable, non-L-space surgeries.

We apply the construction to present infinitely many hyperbolic knots on each

of which every nontrivial surgery is a left-orderable, non-L-space surgery.

This is a joint work with Masakazu Teragaito.

A Dehn surgery is said to be left-orderable

if the resulting manifold of the surgery has the left-orderable fundamental group,

and a Dehn surgery is called an L-space surgery

if the resulting manifold of the surgery is an L-space.

We will focus on left-orderable, non-L-space surgeries on knots in the 3-sphere.

Once we have a knot with left-orderable surgeries,

the ``periodic construction" enables us to provide infinitely many knots with

left-orderable, non-L-space surgeries.

We apply the construction to present infinitely many hyperbolic knots on each

of which every nontrivial surgery is a left-orderable, non-L-space surgery.

This is a joint work with Masakazu Teragaito.

#### Seminar on Probability and Statistics

13:00-14:10 Room #052 (Graduate School of Math. Sci. Bldg.)

Locally stable distribution approximation of high-frequency data (JAPANESE)

[ Reference URL ]

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/01.html

**MASUDA, Hiroki**(Institute of Mathematics for Industry, Kyushu University)Locally stable distribution approximation of high-frequency data (JAPANESE)

[ Reference URL ]

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/01.html

### 2013/06/17

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

有理曲面上の自己同型写像のエントロピー (JAPANESE)

**Takato Uehara**(Niigata University)有理曲面上の自己同型写像のエントロピー (JAPANESE)

### 2013/06/13

#### Lectures

16:30-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)

Introduction to inter-universal Teichmueller theory, extended version (JAPANESE)

**Shinichi Mochizuki**(Kyoto University, RIMS)Introduction to inter-universal Teichmueller theory, extended version (JAPANESE)

#### FMSP Lectures

17:00-18:00 Room #370 (Graduate School of Math. Sci. Bldg.)

Boundary Rigidity for Riemannian Manifolds (ENGLISH)

**Fikret Golgeleyen**(Bulent Ecevit University)Boundary Rigidity for Riemannian Manifolds (ENGLISH)

### 2013/06/12

#### Number Theory Seminar

17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Hodge index theorem for adelic line bundles (ENGLISH)

**Xinyi Yuan**(University of California, Berkeley)Hodge index theorem for adelic line bundles (ENGLISH)

[ Abstract ]

The Hodge index theorem of Faltings and Hriljac asserts that the Neron-Tate height pairing on a projective curve over a number field is equal to certain intersection pairing in the setting of Arakelov geometry. In the talk, I will present an extension of the result to adelic line bundles on higher dimensional varieties over finitely generated fields. Then we will talk about its relation to the non-archimedean Calabi-Yau theorem and the its application to algebraic dynamics. This is a joint work with Shou-Wu Zhang.

The Hodge index theorem of Faltings and Hriljac asserts that the Neron-Tate height pairing on a projective curve over a number field is equal to certain intersection pairing in the setting of Arakelov geometry. In the talk, I will present an extension of the result to adelic line bundles on higher dimensional varieties over finitely generated fields. Then we will talk about its relation to the non-archimedean Calabi-Yau theorem and the its application to algebraic dynamics. This is a joint work with Shou-Wu Zhang.

#### thesis presentations

16:30-17:45 Room #122 (Graduate School of Math. Sci. Bldg.)

Quasi-Likelihood Analysis for Diffusion Processes and Diffusion

Processes with Jumps (JAPANESE)

**Teppei OGIHARA**(Center for the Study of Finance and Insurance, Osaka University)Quasi-Likelihood Analysis for Diffusion Processes and Diffusion

Processes with Jumps (JAPANESE)

### 2013/06/11

#### Tuesday Seminar on Topology

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

On an analogue of Culler-Shalen theory for higher-dimensional

representations

(JAPANESE)

**Takahiro Kitayama**(The University of Tokyo)On an analogue of Culler-Shalen theory for higher-dimensional

representations

(JAPANESE)

[ Abstract ]

Culler and Shalen established a way to construct incompressible surfaces

in a 3-manifold from ideal points of the SL_2-character variety. We

present an analogous theory to construct certain kinds of branched

surfaces from limit points of the SL_n-character variety. Such a

branched surface induces a nontrivial presentation of the fundamental

group as a 2-dimensional complex of groups. This is a joint work with

Takashi Hara (Osaka University).

Culler and Shalen established a way to construct incompressible surfaces

in a 3-manifold from ideal points of the SL_2-character variety. We

present an analogous theory to construct certain kinds of branched

surfaces from limit points of the SL_n-character variety. Such a

branched surface induces a nontrivial presentation of the fundamental

group as a 2-dimensional complex of groups. This is a joint work with

Takashi Hara (Osaka University).

#### Seminar on Mathematics for various disciplines

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

脳の同一源性推定を仮定した聴覚時間知覚のベイズモデル (JAPANESE)

**Ken-ichi SAWAI**(Institute of Industrial Science, the University of Tokyo)脳の同一源性推定を仮定した聴覚時間知覚のベイズモデル (JAPANESE)

### 2013/06/10

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

A Nadel vanishing theorem for metrics with minimal singularities on big line bundles (JAPANESE)

**Shin-ichi Matsumura**(Kagoshima University)A Nadel vanishing theorem for metrics with minimal singularities on big line bundles (JAPANESE)

[ Abstract ]

In this talk, we study singular metrics with non-algebraic singularities, their multiplier ideal sheaves and a Nadel type vanishing theorem, from the view point of complex geometry. The Nadel vanishing theorem can be seen as an analytic version of the Kawamata-Viehweg vanishing theorem of algebraic geometry. The main purpose of this talk is to establish such a theorem for the multiplier ideal sheaf of a metric with minimal singularities, for the cohomology with values in a big line bundle.

In this talk, we study singular metrics with non-algebraic singularities, their multiplier ideal sheaves and a Nadel type vanishing theorem, from the view point of complex geometry. The Nadel vanishing theorem can be seen as an analytic version of the Kawamata-Viehweg vanishing theorem of algebraic geometry. The main purpose of this talk is to establish such a theorem for the multiplier ideal sheaf of a metric with minimal singularities, for the cohomology with values in a big line bundle.

### 2013/06/06

#### Geometry Colloquium

10:00-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Equivariant local index and transverse index for circle action (JAPANESE)

**Hajime Fujita**(Japan Women's University)Equivariant local index and transverse index for circle action (JAPANESE)

[ Abstract ]

In our joint work with Furuta and Yoshida we gave a formulation of index theory of Dirac-type operator on open Riemannian manifolds. We used a torus fibration and a perturbation by Dirac-type operator along fibers. In this talk we develop an equivariant version for circle action and apply it for Hamiltonian circle action case. We investigate the relation between our equivariant index and index of transverse elliptic operator/symbol developed by Atiyah, Paradan-Vergne and Braverman. We give a computation for the standard cylinder, which shows the difference between two equivariant indices.

In our joint work with Furuta and Yoshida we gave a formulation of index theory of Dirac-type operator on open Riemannian manifolds. We used a torus fibration and a perturbation by Dirac-type operator along fibers. In this talk we develop an equivariant version for circle action and apply it for Hamiltonian circle action case. We investigate the relation between our equivariant index and index of transverse elliptic operator/symbol developed by Atiyah, Paradan-Vergne and Braverman. We give a computation for the standard cylinder, which shows the difference between two equivariant indices.

#### FMSP Lectures

16:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Real-valued and circle-valued Morse theory:

an introduction

(ENGLISH)

**Andrei Pajitnov**(Univ. de Nantes)Real-valued and circle-valued Morse theory:

an introduction

(ENGLISH)

[ Abstract ]

Classical Morse theory relates the number of critical points of a Morse

function f on a manifold M to the topology of M. The main technical

ingredient of this theory is a chain complex generated by the critical points

of the function. In 1981 S.P. Novikov generalized this theory to the case of

circle-valued Morse functions. In this talk we describe the construction of

both chain complexes, based on the idea of E. Witten (1982), which allows, in

particular, to compute the boundary operators in the Morse complex from

the count of flow lines of the gradient of f. We discuss geometric applications

of these constructions.

Classical Morse theory relates the number of critical points of a Morse

function f on a manifold M to the topology of M. The main technical

ingredient of this theory is a chain complex generated by the critical points

of the function. In 1981 S.P. Novikov generalized this theory to the case of

circle-valued Morse functions. In this talk we describe the construction of

both chain complexes, based on the idea of E. Witten (1982), which allows, in

particular, to compute the boundary operators in the Morse complex from

the count of flow lines of the gradient of f. We discuss geometric applications

of these constructions.

#### Applied Analysis

16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)

The Geometry of Critical Points of Green functions On Tori (ENGLISH)

**Chang-Shou Lin**(National Taiwan University)The Geometry of Critical Points of Green functions On Tori (ENGLISH)

[ Abstract ]

The Green function of a torus can be expressed by elliptic functions or Jacobic theta functions. It is not surprising the geometry of its critical points would be involved with behaviors of those classical functions. Thus, the non-degeneracy of critical points gives rise to some inequality for elliptic functions. One of consequences of our analysis is to prove any saddle point is non-degenerate, i.e., the Hessian is negative.

We will also show that the number of the critical points of Green function in any torus is either three or five critical points. Furthermore, the moduli space of tori which Green function has five critical points is a simple-connected connected set. The proof of these results use a nonlinear PDE (mean field equation) and the formula for counting zeros of modular form. For a N torsion point,the related modular form is the Eisenstein series of weight one, which was discovered by Hecke (1926). Thus, our PDE method gives a deformation of those Eisenstein series and allows us to find the zeros of those Eisenstein series.

We can generalize our results to a sum of two Green functions.

The Green function of a torus can be expressed by elliptic functions or Jacobic theta functions. It is not surprising the geometry of its critical points would be involved with behaviors of those classical functions. Thus, the non-degeneracy of critical points gives rise to some inequality for elliptic functions. One of consequences of our analysis is to prove any saddle point is non-degenerate, i.e., the Hessian is negative.

We will also show that the number of the critical points of Green function in any torus is either three or five critical points. Furthermore, the moduli space of tori which Green function has five critical points is a simple-connected connected set. The proof of these results use a nonlinear PDE (mean field equation) and the formula for counting zeros of modular form. For a N torsion point,the related modular form is the Eisenstein series of weight one, which was discovered by Hecke (1926). Thus, our PDE method gives a deformation of those Eisenstein series and allows us to find the zeros of those Eisenstein series.

We can generalize our results to a sum of two Green functions.

### 2013/06/04

#### Tuesday Seminar on Topology

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

Low-dimensional linear representations of mapping class groups. (ENGLISH)

**Mustafa Korkmaz**(Middle East Technical University)Low-dimensional linear representations of mapping class groups. (ENGLISH)

[ Abstract ]

For a compact connected orientable surface, the mapping class group

of it is defined as the group of isotopy classes of orientation-preserving

self-diffeomorphisms of S which are identity on the boundary. The action

of the mapping class group on the first homology of the surface

gives rise to the classical 2g-dimensional symplectic representation.

The existence of a faithful linear representation of the mapping class

group is still unknown. In my talk, I will show the following three results;

there is no lower dimensional (complex) linear representation,

up to conjugation the symplectic representation is the unique nontrivial representation in dimension 2g, and there is no faithful linear representation

of the mapping class group in dimensions up to 3g-3. I will also discuss a few applications of these theorems, including some algebraic consequences.

For a compact connected orientable surface, the mapping class group

of it is defined as the group of isotopy classes of orientation-preserving

self-diffeomorphisms of S which are identity on the boundary. The action

of the mapping class group on the first homology of the surface

gives rise to the classical 2g-dimensional symplectic representation.

The existence of a faithful linear representation of the mapping class

group is still unknown. In my talk, I will show the following three results;

there is no lower dimensional (complex) linear representation,

up to conjugation the symplectic representation is the unique nontrivial representation in dimension 2g, and there is no faithful linear representation

of the mapping class group in dimensions up to 3g-3. I will also discuss a few applications of these theorems, including some algebraic consequences.

#### Numerical Analysis Seminar

16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)

On the theories of discrete differential forms and their applications to structure-preserving numerical methods (JAPANESE)

[ Reference URL ]

http://www.infsup.jp/utnas/

**Takaharu Yaguchi**(Kobe University )On the theories of discrete differential forms and their applications to structure-preserving numerical methods (JAPANESE)

[ Reference URL ]

http://www.infsup.jp/utnas/

### 2013/06/03

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Generalized deformation theory of CR structures (JAPANESE)

**Takao Akahori**(University of Hyogo)Generalized deformation theory of CR structures (JAPANESE)

[ Abstract ]

Let $(M, {}^0 T^{''})$ be a compact strongly pseudo convex CR manifold with dimension $2n-1 \geq 5$, embedded in a complex manifold $N$ as a real hypersurface. In our former papers (T. Akahori, Invent. Math. 63 (1981); T. Akahori, P. M. Garfield, and J. M. Lee, Michigan Math. J. 50 (2002)), we constructed the versal family of CR structures. The purpose of this talk is to show that in more wide scope, our family is versal.

Let $(M, {}^0 T^{''})$ be a compact strongly pseudo convex CR manifold with dimension $2n-1 \geq 5$, embedded in a complex manifold $N$ as a real hypersurface. In our former papers (T. Akahori, Invent. Math. 63 (1981); T. Akahori, P. M. Garfield, and J. M. Lee, Michigan Math. J. 50 (2002)), we constructed the versal family of CR structures. The purpose of this talk is to show that in more wide scope, our family is versal.

### 2013/05/31

#### Colloquium

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

Stable patterns and the nonlinear ``hot spots'' conjecture (JAPANESE)

**Yasuhito MIYAMOTO**(Graduate School of Mathematical Sciences, The University of Tokyo)Stable patterns and the nonlinear ``hot spots'' conjecture (JAPANESE)

### 2013/05/30

#### FMSP Lectures

13:00-14:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Low-dimensional linear representations of mapping class groups (III) (ENGLISH)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~topology/Korkmaz.pdf

**Mustafa Korkmaz**(Middle East Technical University)Low-dimensional linear representations of mapping class groups (III) (ENGLISH)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~topology/Korkmaz.pdf

### 2013/05/29

#### FMSP Lectures

13:00-14:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Low-dimensional linear representations of mapping class groups (II) (ENGLISH)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~topology/Korkmaz.pdf

**Mustafa Korkmaz**(Middle East Technical University)Low-dimensional linear representations of mapping class groups (II) (ENGLISH)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~topology/Korkmaz.pdf

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