## Seminar information archive

Seminar information archive ～05/23｜Today's seminar 05/24 | Future seminars 05/25～

### 2013/07/23

#### PDE Real Analysis Seminar

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

Analysis of the Simplified Ericksen-Leslie Model for Liquid Crystals (ENGLISH)

**Matthias Hieber**(Technische Universität Darmstadt)Analysis of the Simplified Ericksen-Leslie Model for Liquid Crystals (ENGLISH)

[ Abstract ]

Consider the Ericksen-Leslie model for the flow of liquid crystals in a bounded domain $\\Omega \\subset \\R^n$. In this talk we discuss various simplifications of the general model and describe a dynamic theory for the simplified equations by analyzing it as a quasilinear system. In particular, we show the existence of a unique, global, strong solutions to this system provided the initial data are close to an equilibrium or the solution is eventually bounded in the norm of the underlying state space. In this case the solution converges exponentially to an equilibrium. Moreover, the solution is shown to be real analytic, jointly in time and space.

We further analyze a non-isothermal extension of this model safisfying the first and second law of thermodynamics and show that results of the above type hold as well in this setting.

This is joint work with M. Nesensohn, J. Prüss and K. Schade.

Consider the Ericksen-Leslie model for the flow of liquid crystals in a bounded domain $\\Omega \\subset \\R^n$. In this talk we discuss various simplifications of the general model and describe a dynamic theory for the simplified equations by analyzing it as a quasilinear system. In particular, we show the existence of a unique, global, strong solutions to this system provided the initial data are close to an equilibrium or the solution is eventually bounded in the norm of the underlying state space. In this case the solution converges exponentially to an equilibrium. Moreover, the solution is shown to be real analytic, jointly in time and space.

We further analyze a non-isothermal extension of this model safisfying the first and second law of thermodynamics and show that results of the above type hold as well in this setting.

This is joint work with M. Nesensohn, J. Prüss and K. Schade.

#### Numerical Analysis Seminar

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

Boundary Integral Equation Method for several Laplace equations with crack(s) (JAPANESE)

[ Reference URL ]

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

**Akira Sasamoto**(National Institute of Advanced Industrial Science and Technology)Boundary Integral Equation Method for several Laplace equations with crack(s) (JAPANESE)

[ Reference URL ]

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

#### Lectures

13:00-15:00 Room #002 (Graduate School of Math. Sci. Bldg.)

)

Moduli space approach for protein structures (ENGLISH)

**Joergen E Andersen**(Centre for Quantum Geometry of Moduli Spaces (QGM), Aarhus University, Denmark)

Moduli space approach for protein structures (ENGLISH)

### 2013/07/22

#### thesis presentations

13:30-14:45 Room #128 (Graduate School of Math. Sci. Bldg.)

The Stokes semigroup on non-decaying spaces(非減衰空間上のストークス半群) (JAPANESE)

**Ken ABE**(Guraduate School of Mathematical Sciences the University of Tokyo)The Stokes semigroup on non-decaying spaces(非減衰空間上のストークス半群) (JAPANESE)

#### thesis presentations

15:30-16:45 Room #128 (Graduate School of Math. Sci. Bldg.)

A few topics related to maximum principles(最大値原理に関連する諸課題) (JAPANESE)

**Nao HAMAMUKI**(Guraduate School of Mathematical Sciences the University of Tokyo)A few topics related to maximum principles(最大値原理に関連する諸課題) (JAPANESE)

#### Algebraic Geometry Seminar

15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Equivariant degenerations of spherical modules (ENGLISH)

**Stavros Papadakis**(RIMS)Equivariant degenerations of spherical modules (ENGLISH)

[ Abstract ]

Given a reductive algebraic group G and an invariant

Hilbert function h, Alexeev and Brion have defined

a moduli scheme M which parametrizes affine G-schemes X

with the property that the coordinate ring of X decomposes,

as G-module, according to the function h. The talk will

be about joint work with Bart Van Steirteghem (New York)

which studies the moduli scheme M under some additional

assumptions.

Given a reductive algebraic group G and an invariant

Hilbert function h, Alexeev and Brion have defined

a moduli scheme M which parametrizes affine G-schemes X

with the property that the coordinate ring of X decomposes,

as G-module, according to the function h. The talk will

be about joint work with Bart Van Steirteghem (New York)

which studies the moduli scheme M under some additional

assumptions.

#### Lectures

13:00-15:00 Room #126 (Graduate School of Math. Sci. Bldg.)

)

Moduli space approach for RNA structure analysis (ENGLISH)

**Joergen E Andersen**(Centre for Quantum Geometry of Moduli Spaces (QGM), Aarhus University, Denmark)

Moduli space approach for RNA structure analysis (ENGLISH)

### 2013/07/20

#### Harmonic Analysis Komaba Seminar

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

Existence of Weak Solutions for a Diffuse Interface Model of Non-Newtonian Two-Phase Flows

(JAPANESE)

On the smoothness conditions for bilinear Fourier multipliers (JAPANESE)

**Yutaka Terasawa**(The University of Tokyo) 13:30-15:00Existence of Weak Solutions for a Diffuse Interface Model of Non-Newtonian Two-Phase Flows

(JAPANESE)

**Naohito Tomita**(Osaka University) 15:30-17:00On the smoothness conditions for bilinear Fourier multipliers (JAPANESE)

### 2013/07/18

#### Mathematical Biology Seminar

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

Path integral representaion and Euler-Lotka equation in age-size structured population model (JAPANESE)

**Ryo Oizumi**(Graduate School of Environmental Science, Hokkaido University)Path integral representaion and Euler-Lotka equation in age-size structured population model (JAPANESE)

#### FMSP Lectures

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

Representations of reductive groups and L-functions (I) (ENGLISH)

**Birgit Speh**(Cornell University)Representations of reductive groups and L-functions (I) (ENGLISH)

[ Abstract ]

This is an introduction to the theory of L-functions and in particular of the local L-factors of representations in real and complex groups. Some familiarity with infinite dimensional representations would be very helpful, but I will not assume any knowledge of number theory. We will start in the first lecture by considering L-functions for Groessen characters and classical automorphic forms, in other words for automorphic representations of G(1) and GL(2). This will motivate the definition of the local L-factors of representations of GL(1,R) and GL(2,R). Then we will discuss Rankin convolutions and define the L-factors for infinite dimensional tempered representations of GL(n,R).

This is an introduction to the theory of L-functions and in particular of the local L-factors of representations in real and complex groups. Some familiarity with infinite dimensional representations would be very helpful, but I will not assume any knowledge of number theory. We will start in the first lecture by considering L-functions for Groessen characters and classical automorphic forms, in other words for automorphic representations of G(1) and GL(2). This will motivate the definition of the local L-factors of representations of GL(1,R) and GL(2,R). Then we will discuss Rankin convolutions and define the L-factors for infinite dimensional tempered representations of GL(n,R).

### 2013/07/17

#### Kavli IPMU Komaba Seminar

17:00-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Homological Mirror Symmetry for toric Calabi-Yau varieties (ENGLISH)

**Daniel Pomerleano**(Kavli IPMU)Homological Mirror Symmetry for toric Calabi-Yau varieties (ENGLISH)

[ Abstract ]

I will discuss some recent developments in Homological Mirror

Symmetry for toric Calabi-Yau varieties.

I will discuss some recent developments in Homological Mirror

Symmetry for toric Calabi-Yau varieties.

### 2013/07/16

#### Tuesday Seminar on Topology

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

On new models of real hyperbolic spaces (JAPANESE)

**Sumio Yamada**(Gakushuin University)On new models of real hyperbolic spaces (JAPANESE)

[ Abstract ]

In this talk, I will introduce several new realization of the real hyperbolic spaces, using classical tools. The constructions will involve aspects of convex geometry as well as projective geometry, and they are interesting from the view point of the history of mathematics. This work belongs to a joint project with Athanase Papadopoulos.

In this talk, I will introduce several new realization of the real hyperbolic spaces, using classical tools. The constructions will involve aspects of convex geometry as well as projective geometry, and they are interesting from the view point of the history of mathematics. This work belongs to a joint project with Athanase Papadopoulos.

#### Numerical Analysis Seminar

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

Numerical computation of motion of interface networks (JAPANESE)

[ Reference URL ]

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

**Karel Svadlenka**(Kanazawa University)Numerical computation of motion of interface networks (JAPANESE)

[ Reference URL ]

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

### 2013/07/11

#### Geometry Colloquium

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

Primitive forms via polyvector fields (ENGLISH)

**Changzheng Li**(IPMU)Primitive forms via polyvector fields (ENGLISH)

[ Abstract ]

The theory of primitive forms was introduced by Kyoji Saito in early 1980s, which was first known in singularity theory and has attracted much attention in mirror symmetry recently. In this talk, we will introduce a differential geometric approach to primitive forms, using compactly supported polyvector fields. We will first introduce the notion of primitive forms, making it acceptable to general audience. We will use the example of the mirror Laudau-Ginzberg model of P^1 to illustrate such approach. This is my joint work with Si Li and Kyoji Saito.

The theory of primitive forms was introduced by Kyoji Saito in early 1980s, which was first known in singularity theory and has attracted much attention in mirror symmetry recently. In this talk, we will introduce a differential geometric approach to primitive forms, using compactly supported polyvector fields. We will first introduce the notion of primitive forms, making it acceptable to general audience. We will use the example of the mirror Laudau-Ginzberg model of P^1 to illustrate such approach. This is my joint work with Si Li and Kyoji Saito.

### 2013/07/10

#### Number Theory Seminar

17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

On ramification filtration of local fields of equal characteristic (JAPANESE)

**Yuri Yatagawa**(University of Tokyo)On ramification filtration of local fields of equal characteristic (JAPANESE)

### 2013/07/09

#### Tuesday Seminar on Topology

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

Smooth 3-manifolds in the 4-sphere (ENGLISH)

**Ryan Budney**(University of Victoria)Smooth 3-manifolds in the 4-sphere (ENGLISH)

[ Abstract ]

Everyone who has studied topology knows the compact 2-manifolds that embed in the 3-sphere. One dimension up, the problem of which smooth 3-manifolds embed in the 4-sphere turns out to be much more involved with a handful of partial answers. I will describe what is known at the present moment.

Everyone who has studied topology knows the compact 2-manifolds that embed in the 3-sphere. One dimension up, the problem of which smooth 3-manifolds embed in the 4-sphere turns out to be much more involved with a handful of partial answers. I will describe what is known at the present moment.

#### Tuesday Seminar of Analysis

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

A Trace Formula for Long-Range Perturbations of the Landau Hamiltonian

(Joint work with Georgi Raikov) (ENGLISH)

**Tom\'as Lungenstrass**(Pontificia Universidad Catolica de Chile)A Trace Formula for Long-Range Perturbations of the Landau Hamiltonian

(Joint work with Georgi Raikov) (ENGLISH)

[ Abstract ]

The Landau Hamiltonian describes the dynamics of a two-dimensional

charged particle subject to a constant magnetic field. Its spectrum

consists in eigenvalues of infinite multiplicity given by $B(2q+1)$, $q\\in Z_+$. We

consider perturbations of this operator by including a continuous

electric potential that decays slowly at infinity (as $|x|^{-\\rho}$, $0<\\rho<1$).

The spectrum of the perturbed operator consists of eigenvalue clusters

which accumulate to the Landau levels. We provide estimates for the

rate at which the clusters shrink as we move up the energy levels.

Further, we obtain an explicit description of the asymptotic density

of eigenvalues for asymptotically homogeneous long-range potentials in

terms of a mean-value transform of the associated homogeneous

function.

The Landau Hamiltonian describes the dynamics of a two-dimensional

charged particle subject to a constant magnetic field. Its spectrum

consists in eigenvalues of infinite multiplicity given by $B(2q+1)$, $q\\in Z_+$. We

consider perturbations of this operator by including a continuous

electric potential that decays slowly at infinity (as $|x|^{-\\rho}$, $0<\\rho<1$).

The spectrum of the perturbed operator consists of eigenvalue clusters

which accumulate to the Landau levels. We provide estimates for the

rate at which the clusters shrink as we move up the energy levels.

Further, we obtain an explicit description of the asymptotic density

of eigenvalues for asymptotically homogeneous long-range potentials in

terms of a mean-value transform of the associated homogeneous

function.

### 2013/07/08

#### Seminar on Geometric Complex Analysis

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

Cohomologies and deformations of solvmanifolds (JAPANESE)

**Hisashi Kasuya**(Tokyo Institute of Technology)Cohomologies and deformations of solvmanifolds (JAPANESE)

[ Abstract ]

$G$を単連結可解リー群とし, $G$はココンパクト離散部分群$\Gamma$を持つとする. この時, コンパクト等質空間$G/\Gamma$をsolvmanifoldと呼ぶ. 本講演では, solvmanifoldのde Rhamコホモロジー, Dolbeaultコホモロジー, Bott-Chernコホモロジーの計算法を紹介する. さらにその計算法を用いた, ホッジ理論と変形理論の研究を紹介する.

$G$を単連結可解リー群とし, $G$はココンパクト離散部分群$\Gamma$を持つとする. この時, コンパクト等質空間$G/\Gamma$をsolvmanifoldと呼ぶ. 本講演では, solvmanifoldのde Rhamコホモロジー, Dolbeaultコホモロジー, Bott-Chernコホモロジーの計算法を紹介する. さらにその計算法を用いた, ホッジ理論と変形理論の研究を紹介する.

#### Kavli IPMU Komaba Seminar

17:00-18:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Elliptic genera and two dimensional gauge theories (ENGLISH)

**Richard Eager**(Kavli IPMU)Elliptic genera and two dimensional gauge theories (ENGLISH)

[ Abstract ]

The elliptic genus is an important invariant of two dimensional conformal field theories that generalizes the Witten index. In this talk, I will first review the geometric meaning of the elliptic genus and Witten's GLSM construction. Then I will explain how the elliptic genus can be computed directly from a two dimensional gauge theory using localization. The central example of this talk will be the quintic threefold. The GLSM description of the quintic threefold has both a large-volume sigma model description and a Landau-Ginzburg description. I will explain how the GLSM calculation of the index reproduces the old results in these two phases. Time permitting, further applications and generalizations will be discussed.

The elliptic genus is an important invariant of two dimensional conformal field theories that generalizes the Witten index. In this talk, I will first review the geometric meaning of the elliptic genus and Witten's GLSM construction. Then I will explain how the elliptic genus can be computed directly from a two dimensional gauge theory using localization. The central example of this talk will be the quintic threefold. The GLSM description of the quintic threefold has both a large-volume sigma model description and a Landau-Ginzburg description. I will explain how the GLSM calculation of the index reproduces the old results in these two phases. Time permitting, further applications and generalizations will be discussed.

#### Lectures

10:40-12:10 Room #128 (Graduate School of Math. Sci. Bldg.)

Meiji University)

Aggregation mechanism of biological species : from microscopic

and macroscopic viewpoints (JAPANESE)

**Hirofumi Izuhara**(Meiji Institute for Advanced Study of Mathematical Sciences,Meiji University)

Aggregation mechanism of biological species : from microscopic

and macroscopic viewpoints (JAPANESE)

[ Abstract ]

There are a lot of organisms which form aggregation in nature. In order to describe the dynamics of such biological species, a particle model is often proposed, which is based on the random walk from the microscopic point of view. On the other hand, when we take population densities of biological species into account, the dynamics is expressed as partial differential equations. We see that different models are proposed according to the viewpoints which we are focusing on. In this talk, we take aggregation phenomena of biological species as an example, and introduce a relation between a microscopic particle model and a macroscopic partial differential equation model.

There are a lot of organisms which form aggregation in nature. In order to describe the dynamics of such biological species, a particle model is often proposed, which is based on the random walk from the microscopic point of view. On the other hand, when we take population densities of biological species into account, the dynamics is expressed as partial differential equations. We see that different models are proposed according to the viewpoints which we are focusing on. In this talk, we take aggregation phenomena of biological species as an example, and introduce a relation between a microscopic particle model and a macroscopic partial differential equation model.

#### FMSP Lectures

16:15-17:15 Room #270 (Graduate School of Math. Sci. Bldg.)

Two-dimensional Calderon problems for Navier-Stokes equations and Lame system (ENGLISH)

**Oleg Emanouilov**(Colorado State Univ.)Two-dimensional Calderon problems for Navier-Stokes equations and Lame system (ENGLISH)

[ Abstract ]

We will prove the uniqueness in determining viscosity in two-dimensional Navier-Stokes equations by Dirichlet-to-Neumann map.

Moreover, without any smallness assumption, we establish the uniqueness in determining two Lame coefficients in two-dimensional isotropic Lame system Dirichlet-to-Neumann map.

We will prove the uniqueness in determining viscosity in two-dimensional Navier-Stokes equations by Dirichlet-to-Neumann map.

Moreover, without any smallness assumption, we establish the uniqueness in determining two Lame coefficients in two-dimensional isotropic Lame system Dirichlet-to-Neumann map.

### 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/

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