## Seminar information archive

Seminar information archive ～09/15｜Today's seminar 09/16 | Future seminars 09/17～

### 2013/07/05

#### FMSP Lectures

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

Geometric applications of Wasserstein distance,

Lecture (IV) Applications to differential geometry and foliations (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 (IV) Applications to differential geometry and foliations (ENGLISH)

[ Reference URL ]

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

### 2013/07/04

#### Seminar on Probability and Statistics

14:50-16:00 Room #052 (Graduate School of Math. Sci. Bldg.)

低ランク行列推定におけるベイズ推定法の性質 (JAPANESE)

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/02.html

**SUZUKI, Taiji**(Tokyo Institute of Technology)低ランク行列推定におけるベイズ推定法の性質 (JAPANESE)

[ Abstract ]

真のパラメータが低ランク行列の構造を持つような低ランク行列推定問題を考える. 低ランク行列推定問題の例としては,低ランク行列の一部が見えている時にその残りを 推定する行列補完の問題などがある.応用としてはユーザへの推薦システムなどがある. これまでの理論解析は主にスパース正則化を用いた経験誤差最小化を対象としてきたが, 本発表ではベイズ法を考え,その統計的性質を調べる.ベイズ法においては, 正則化付き経験誤差最小化による方法とは異なるやや緩い仮定のもと, ほぼ最適な収束レートが導けることを示す.また,テンソル型データ (多次元アレイデータ)へも同様の議論が拡張可能であることも述べる.

[ Reference URL ]真のパラメータが低ランク行列の構造を持つような低ランク行列推定問題を考える. 低ランク行列推定問題の例としては,低ランク行列の一部が見えている時にその残りを 推定する行列補完の問題などがある.応用としてはユーザへの推薦システムなどがある. これまでの理論解析は主にスパース正則化を用いた経験誤差最小化を対象としてきたが, 本発表ではベイズ法を考え,その統計的性質を調べる.ベイズ法においては, 正則化付き経験誤差最小化による方法とは異なるやや緩い仮定のもと, ほぼ最適な収束レートが導けることを示す.また,テンソル型データ (多次元アレイデータ)へも同様の議論が拡張可能であることも述べる.

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/02.html

### 2013/07/03

#### Number Theory Seminar

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

A general formula for the discriminant of polynomials over $¥mathbb{F}_2$ determining the parity of the number of prime factors

(JAPANESE)

**Takehito Yoshiki**(University of Tokyo)A general formula for the discriminant of polynomials over $¥mathbb{F}_2$ determining the parity of the number of prime factors

(JAPANESE)

[ Abstract ]

In order to find irreducible polynomials over $\\mathbb{F}_2$ efficiently, the method using Swan's theorem is known. Swan's theorem determines the parity of the numberof irreducible factors of a polynomial $f$ over $\\mathbb{F}_2$ with no repeated root, by using the discriminant ${\\rm D}(\\tilde{f})\\pmod 8$, where $\\tilde{f}$ is a monic polynomial over $\\mathbb{Z}_2$ such that $\\tilde{f}=f\\pmod 2$. In the lecture, we will give the formula for the discriminant ${\\rm D}(\\tilde{f}) \\pmod 8$ for a polynomial $f$ over $\\mathbb{F}_2$ with no repeated root. By applying this formula to various types of polynomials, we shall get the parity of the number of irreducible factors of them.

In order to find irreducible polynomials over $\\mathbb{F}_2$ efficiently, the method using Swan's theorem is known. Swan's theorem determines the parity of the numberof irreducible factors of a polynomial $f$ over $\\mathbb{F}_2$ with no repeated root, by using the discriminant ${\\rm D}(\\tilde{f})\\pmod 8$, where $\\tilde{f}$ is a monic polynomial over $\\mathbb{Z}_2$ such that $\\tilde{f}=f\\pmod 2$. In the lecture, we will give the formula for the discriminant ${\\rm D}(\\tilde{f}) \\pmod 8$ for a polynomial $f$ over $\\mathbb{F}_2$ with no repeated root. By applying this formula to various types of polynomials, we shall get the parity of the number of irreducible factors of them.

### 2013/07/02

#### Numerical Analysis Seminar

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

Numerical plasma simulation for reactive plasma deposition (JAPANESE)

[ Reference URL ]

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

**Masaru Miyashita**(Sumitomo Heavy Industries, Ltd.)Numerical plasma simulation for reactive plasma deposition (JAPANESE)

[ Reference URL ]

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

### 2013/06/29

#### Harmonic Analysis Komaba Seminar

13:00-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Critical Sobolev embedding of function spaces and the real interpolation functor

(JAPANESE)

On weighted estimates for multilinear Fourier multipliers with Sobolev regularity

(JAPANESE)

**Yoshihiro Sawano**(Tokyo Metropolitan University) 13:30-15:00Critical Sobolev embedding of function spaces and the real interpolation functor

(JAPANESE)

[ Abstract ]

We consider the endpoint case of the Sobolev embedding.

It is well known that the function spaces such as Sobolev spaces are not embedded into L^¥infty in the critical case.

One of the remedies is the Brezis-Gallouet-Wainger type

estimate. However, such an estimate involve the log term

and it can not be regarded as the norm.

In this talk, by using the real interpolation functor, we propose another formulation. We compare

the existing result with our new results.

If time permits, we mention some related results.

We consider the endpoint case of the Sobolev embedding.

It is well known that the function spaces such as Sobolev spaces are not embedded into L^¥infty in the critical case.

One of the remedies is the Brezis-Gallouet-Wainger type

estimate. However, such an estimate involve the log term

and it can not be regarded as the norm.

In this talk, by using the real interpolation functor, we propose another formulation. We compare

the existing result with our new results.

If time permits, we mention some related results.

**Mai Fujita**(Osaka University) 15:30-17:00On weighted estimates for multilinear Fourier multipliers with Sobolev regularity

(JAPANESE)

### 2013/06/28

#### FMSP Lectures

16:00-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Mathematical model for the electrodiffusion of ions, Lecture II (JAPANESE)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~fmsp/files/FMSPLectures_Mori.pdf

**Yoichiro Mori**(University of Minnesota)Mathematical model for the electrodiffusion of ions, Lecture II (JAPANESE)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~fmsp/files/FMSPLectures_Mori.pdf

#### Colloquium

16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)

The Geometry of protain modelling (JAPANESE)

**Hiroki Kodama**(Graduate School of Mathematical Sciences, The University of Tokyo)The Geometry of protain modelling (JAPANESE)

### 2013/06/27

#### FMSP Lectures

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

Geometric applications of Wasserstein distance,

Lecture (III) Curvature of metric measure spaces II

(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 (III) Curvature of metric measure spaces II

(ENGLISH)

[ Reference URL ]

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

#### Geometry Colloquium

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

On volume formulae in terms of orthospectrum (JAPANESE)

**MASAI, Hidetoshi**(Tokyo Institute of Technology)On volume formulae in terms of orthospectrum (JAPANESE)

[ Abstract ]

Bridgeman-Kahn and Calegari derived formulae to compute the volumes of compact hyperbolic n-manifolds with totally geodesic boundary in terms of orthospectrum. Here the orthospectrum is the set of length of geodesics perpendicular to the boundary at both ends. The two formulae are obtained by apparently different methods. In this talk, we prove that the two volume formulae coincide. We also discuss some interesting relationship between two formulae. This work is a joint work with Greg McShane.

Bridgeman-Kahn and Calegari derived formulae to compute the volumes of compact hyperbolic n-manifolds with totally geodesic boundary in terms of orthospectrum. Here the orthospectrum is the set of length of geodesics perpendicular to the boundary at both ends. The two formulae are obtained by apparently different methods. In this talk, we prove that the two volume formulae coincide. We also discuss some interesting relationship between two formulae. This work is a joint work with Greg McShane.

#### FMSP Lectures

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

Mathematical model for the electrodiffusion of ions, Lecture I (JAPANESE)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~fmsp/files/FMSPLectures_Mori.pdf

**Yoichiro Mori**(University of Minnesota)Mathematical model for the electrodiffusion of ions, Lecture I (JAPANESE)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~fmsp/files/FMSPLectures_Mori.pdf

### 2013/06/26

#### Number Theory Seminar

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

An explicit construction of point sets with large minimum Dick weight (JAPANESE)

**Kousuke Suzuki**(University of Tokyo)An explicit construction of point sets with large minimum Dick weight (JAPANESE)

[ Abstract ]

Walsh figure of merit WAFOM($P$) is a quality measure of point sets $P$ for quasi-Monte Carlo integration constructed by a digital net method. WAFOM($P$) is bounded by the minimum Dick weight of $P^¥perp$, where the Dick weight is a generalization of Hamming weight. In this talk, we give an explicit construction of point sets with large minimum Dick weight using Niederreiter-Xing sequences and Dick's interleaving construction. These point sets are also examples of low-WAFOM point sets.

Walsh figure of merit WAFOM($P$) is a quality measure of point sets $P$ for quasi-Monte Carlo integration constructed by a digital net method. WAFOM($P$) is bounded by the minimum Dick weight of $P^¥perp$, where the Dick weight is a generalization of Hamming weight. In this talk, we give an explicit construction of point sets with large minimum Dick weight using Niederreiter-Xing sequences and Dick's interleaving construction. These point sets are also examples of low-WAFOM point sets.

### 2013/06/25

#### Tuesday Seminar on Topology

17:10-18:10 Room #056 (Graduate School of Math. Sci. Bldg.)

Higher-order generalization of Fukaya's Morse homotopy

invariant of 3-manifolds (JAPANESE)

**Tadayuki Watanabe**(Shimane University)Higher-order generalization of Fukaya's Morse homotopy

invariant of 3-manifolds (JAPANESE)

[ Abstract ]

In his article published in 1996, K. Fukaya constructed

a 3-manifold invariant by using Morse homotopy theory. Roughly, his

invariant is defined by considering several Morse functions on a

3-manifold and counting with weights the ways that the theta-graph can

be immersed such that edges follow gradient lines. We generalize his

construction to 3-valent graphs with arbitrary number of loops for

integral homology 3-spheres. I will also discuss extension of our method

to 3-manifolds with positive first Betti numbers.

In his article published in 1996, K. Fukaya constructed

a 3-manifold invariant by using Morse homotopy theory. Roughly, his

invariant is defined by considering several Morse functions on a

3-manifold and counting with weights the ways that the theta-graph can

be immersed such that edges follow gradient lines. We generalize his

construction to 3-valent graphs with arbitrary number of loops for

integral homology 3-spheres. I will also discuss extension of our method

to 3-manifolds with positive first Betti numbers.

#### Numerical Analysis Seminar

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

Digital watermarking methods using the wavelet transforms and interval arithmetic (JAPANESE)

[ Reference URL ]

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

**Teruya Minamoto**(Saga University)Digital watermarking methods using the wavelet transforms and interval arithmetic (JAPANESE)

[ Reference URL ]

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

### 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.

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