## Seminar information archive

Seminar information archive ～09/14｜Today's seminar 09/15 | Future seminars 09/16～

#### thesis presentations

13:00-14:15 Room #128 (Graduate School of Math. Sci. Bldg.)

Topology, symplectic geometry and complex geometry of solvmanifolds -From nilpotent to solvable- (JAPANESE)

**Hisashi KASUYA**(Guraduate School of Mathematical Sciences the University of Tokyo)Topology, symplectic geometry and complex geometry of solvmanifolds -From nilpotent to solvable- (JAPANESE)

#### thesis presentations

14:15-15:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Discretization and ultradiscretization of differential equations preserving characters of their solutions (JAPANESE)

**Keisuke MATSUYA**(Guraduate School of Mathematical Sciences the University of Tokyo)Discretization and ultradiscretization of differential equations preserving characters of their solutions (JAPANESE)

### 2013/02/07

#### Operator Algebra Seminars

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

Combinatorial independence, amenability, and sofic entropy (ENGLISH)

**David Kerr**(東大数理/Texas A&M Univ.)Combinatorial independence, amenability, and sofic entropy (ENGLISH)

#### thesis presentations

09:45-11:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Lie foliations transversely modeled on nilpotent Lie algebras

(JAPANESE)

**Naoki KATO**(Guraduate School of Mathematical Sciences the University of Tokyo)Lie foliations transversely modeled on nilpotent Lie algebras

(JAPANESE)

#### thesis presentations

11:00-12:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Mathematical Analysis for Epidemic Models with Heterogeneity (JAPANESE)

**Toshikazu KUNIYA**(Guradate School of Mathematical Sciences the University of Tokyo)Mathematical Analysis for Epidemic Models with Heterogeneity (JAPANESE)

#### thesis presentations

13:00-14:15 Room #118 (Graduate School of Math. Sci. Bldg.)

MONOMIAL DEFORMATIONS OF CERTAIN HYPERSURFACES AND TWO HYPERGEOMETRIC FUNCTIONS

(JAPANESE)

**Kazuaki MIYATANI**(Guraduate School of Mathematical Sciences the University of Tokyo)MONOMIAL DEFORMATIONS OF CERTAIN HYPERSURFACES AND TWO HYPERGEOMETRIC FUNCTIONS

(JAPANESE)

#### thesis presentations

14:15-15:30 Room #118 (Graduate School of Math. Sci. Bldg.)

Proper actions and designs on homogeneous spaces (JAPANESE)

**Takayuki OKUDA**(Guraduate School of Mathematical Sciences the University of Tokyo)Proper actions and designs on homogeneous spaces (JAPANESE)

#### thesis presentations

15:45-17:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Symmetrized Max-Plus Algebra and Ultradiscrete sine-Gordon Equation (JAPANESE)

**Kenichi KONDO**(Guraduate School of Mathematical Sciences the University of Tokyo)Symmetrized Max-Plus Algebra and Ultradiscrete sine-Gordon Equation (JAPANESE)

#### thesis presentations

09:45-11:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Asymptotic analysis of Bergman kernels for linear series and its application to Kahler Geometry (JAPANESE)

**Tomoyuki HISAMOTO**(Guraduate School of Mathematical Sciences the University of Tokyo)Asymptotic analysis of Bergman kernels for linear series and its application to Kahler Geometry (JAPANESE)

#### thesis presentations

11:00-12:15 Room #128 (Graduate School of Math. Sci. Bldg.)

Asymptotically complex hyperbolic Einstein metrics and CR geometry (JAPANESE)

**Yoshihiko MATSUMOTO**(Guraduate School of Mathematical Sciences the University of Tokyo)Asymptotically complex hyperbolic Einstein metrics and CR geometry (JAPANESE)

#### thesis presentations

13:00-14:15 Room #128 (Graduate School of Math. Sci. Bldg.)

Analytic semigroup approach to higher order quasilinear parabolic problems (JAPANESE)

**Tomoro ASAI**(Guraduate School of Mathematical Sciences the University of Tokyo)Analytic semigroup approach to higher order quasilinear parabolic problems (JAPANESE)

#### thesis presentations

14:15-15:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Hibi toric varieties and mirror symmetry (JAPANESE)

**Makoto MIURA**(Guraduate School of Mathematical Sciences the University of Tokyo)Hibi toric varieties and mirror symmetry (JAPANESE)

#### thesis presentations

15:45-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Quasi-morphisms on the group of area-preserving diffeomorphisms of the 2-disk (JAPANESE)

**Tomohiko ISHIDA**(Guraduate School of Mathematical Sciences the University of Tokyo)Quasi-morphisms on the group of area-preserving diffeomorphisms of the 2-disk (JAPANESE)

#### GCOE Seminars

17:00-18:30 Room #370 (Graduate School of Math. Sci. Bldg.)

Identification of quantum potentials in the Schrodinger equation (ENGLISH)

**Asaf Iskandarov**(Lenkaran State University)Identification of quantum potentials in the Schrodinger equation (ENGLISH)

[ Abstract ]

In this lecture I will consider the identification problem of determining the unknown time-dependent coefficients of nonlinear Schrodinger equation.We applied the variational method and studied the correctness of direct and identification problems. We find a necessary condition of the solution and give a stable methed for solution.

In this lecture I will consider the identification problem of determining the unknown time-dependent coefficients of nonlinear Schrodinger equation.We applied the variational method and studied the correctness of direct and identification problems. We find a necessary condition of the solution and give a stable methed for solution.

#### Seminar on Probability and Statistics

11:00-12:10 Room #006 (Graduate School of Math. Sci. Bldg.)

On L^p model selection for discretely observed diffusion processes (JAPANESE)

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/14.html

**Stefano M. Iacus**(Dipartimento di Economia, Managemente Metodi Quantitativi Universita' di Milano)On L^p model selection for discretely observed diffusion processes (JAPANESE)

[ Abstract ]

The LASSO is a widely used L^2 statistical methodology for simultaneous estimation and variable selection. In the last years, many authors analyzed this technique from a theoretical and applied point of view. In the first part of the seminar, we introduce and study the adaptive LASSO problem for discretely observed ergodic diffusion processes We prove oracle properties also deriving the asymptotic distribution of the LASSO estimator. In the second part of the seminar we present general L^p approach for stochastic differential equations with small diffusion noise. Finally, we present simulated and real data analysis to provide some evidence on the applicability of this method.

FMSP Lectures

http://faculty.ms.u-tokyo.ac.jp/~fmsp/jpn/conferences/fmsp.html

[ Reference URL ]The LASSO is a widely used L^2 statistical methodology for simultaneous estimation and variable selection. In the last years, many authors analyzed this technique from a theoretical and applied point of view. In the first part of the seminar, we introduce and study the adaptive LASSO problem for discretely observed ergodic diffusion processes We prove oracle properties also deriving the asymptotic distribution of the LASSO estimator. In the second part of the seminar we present general L^p approach for stochastic differential equations with small diffusion noise. Finally, we present simulated and real data analysis to provide some evidence on the applicability of this method.

FMSP Lectures

http://faculty.ms.u-tokyo.ac.jp/~fmsp/jpn/conferences/fmsp.html

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/14.html

### 2013/02/05

#### Lie Groups and Representation Theory

17:30-19:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Dunkl processes assciated with dihedral systems, II (ENGLISH)

**Nizar Demni**(Université de Rennes 1)Dunkl processes assciated with dihedral systems, II (ENGLISH)

[ Abstract ]

I'll focus on dihedral systems and its semi group density. I'll show how one can write down this density using probabilistic techniques and give some interpretation using spherical harmonics. I'll also present some results attempting to get a close formula for the density: the main difficulty comes then from the inversion (in composition sense) of Tchebycheff polynomials of the first kind in some neighborhood. Finally, I'll display expressions through known special functions for even dihedral groups, and the unexplained connection between the obtained formulas and those of Ben Said-Kobayashi-Orsted.

I'll focus on dihedral systems and its semi group density. I'll show how one can write down this density using probabilistic techniques and give some interpretation using spherical harmonics. I'll also present some results attempting to get a close formula for the density: the main difficulty comes then from the inversion (in composition sense) of Tchebycheff polynomials of the first kind in some neighborhood. Finally, I'll display expressions through known special functions for even dihedral groups, and the unexplained connection between the obtained formulas and those of Ben Said-Kobayashi-Orsted.

### 2013/02/04

#### Lie Groups and Representation Theory

17:30-19:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Dunkl processes assciated with dihedral systems, I (ENGLISH)

**Nizar Demni**(Université de Rennes 1)Dunkl processes assciated with dihedral systems, I (ENGLISH)

[ Abstract ]

I'll first give a brief and needed account on root systems and finite reflection groups. Then, I'll introduce Dunkl operators and give some properties. Once I'll do, I'll introduce Dunkl processes and their continuous components, so-called radial Dunkl processes. The latter generalize eigenvalues processes of some matrix-valued processes and reduces to reflected Brownian motion in Weyl chambers. Besides, Brownian motion in Weyl chambers corresponds to all multiplicity values equal one are constructed from a Brownian motion killed when it first hits the boundary of the Weyl chamber using the unique positive harmonic function (up to a constant) on the Weyl chamber. In the analytic side, determinantal formulas appear and are related to harmonic analysis on the Gelfand pair (Gl(n,C), U(n)). This is in agreement on the one side with the so-called reflection principle in stochastic processes theory and matches on the other side the so-called shift principle introduced by E. Opdam. Finally, I'll discuss the spectacular result of Biane-Bougerol-O'connell yielding to a Duistermaat-Heckman distribution for non crystallographic systems.

I'll first give a brief and needed account on root systems and finite reflection groups. Then, I'll introduce Dunkl operators and give some properties. Once I'll do, I'll introduce Dunkl processes and their continuous components, so-called radial Dunkl processes. The latter generalize eigenvalues processes of some matrix-valued processes and reduces to reflected Brownian motion in Weyl chambers. Besides, Brownian motion in Weyl chambers corresponds to all multiplicity values equal one are constructed from a Brownian motion killed when it first hits the boundary of the Weyl chamber using the unique positive harmonic function (up to a constant) on the Weyl chamber. In the analytic side, determinantal formulas appear and are related to harmonic analysis on the Gelfand pair (Gl(n,C), U(n)). This is in agreement on the one side with the so-called reflection principle in stochastic processes theory and matches on the other side the so-called shift principle introduced by E. Opdam. Finally, I'll discuss the spectacular result of Biane-Bougerol-O'connell yielding to a Duistermaat-Heckman distribution for non crystallographic systems.

### 2013/01/30

#### Geometry Colloquium

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Hamiltonian Volume Minimizing Property of Maximal Torus Orbits in the Complex Projective Space (JAPANESE)

**Ryoichi Kobayashi**(Nagoya University)Hamiltonian Volume Minimizing Property of Maximal Torus Orbits in the Complex Projective Space (JAPANESE)

[ Abstract ]

We prove that any $U(1)^n$-orbit in $\\Bbb P^n$ is volume minimizing under Hamiltonian deformation.

The idea of the proof is :

- (1) We extend one $U(1)^n$-orbit to the momentum torus fibration $\\{T_t\\}_{t\\in\\Delta^n}$ and consider its Hamiltonian deformation $\\{\\phi(T_t)\\}_{t\\in\\Delta^n}$ where $\\phi$ is a Hamiltobian diffeomorphism of $\\Bbb P^n$,

and then :

- (2) We compare each $U(1)^n$-orbit and its Hamiltonian deformation by compaing the large $k$ asymptotic behavior of the sequence of projective embeddings defined, for each $k$, by the basis of $H^0(\\Bbb P^n,\\Cal O(k))$ obtained by semi-classical approximation of the $\\Cal O(k)$ Bohr-Sommerfeld tori of the Lagrangian torus fibration $\\{T_t\\}_{t\\in\\Delta^n}$ and its Hamiltonian deformation $\\{\\phi(T_t)\\}_{t\\in\\Delta^n}$.

We prove that any $U(1)^n$-orbit in $\\Bbb P^n$ is volume minimizing under Hamiltonian deformation.

The idea of the proof is :

- (1) We extend one $U(1)^n$-orbit to the momentum torus fibration $\\{T_t\\}_{t\\in\\Delta^n}$ and consider its Hamiltonian deformation $\\{\\phi(T_t)\\}_{t\\in\\Delta^n}$ where $\\phi$ is a Hamiltobian diffeomorphism of $\\Bbb P^n$,

and then :

- (2) We compare each $U(1)^n$-orbit and its Hamiltonian deformation by compaing the large $k$ asymptotic behavior of the sequence of projective embeddings defined, for each $k$, by the basis of $H^0(\\Bbb P^n,\\Cal O(k))$ obtained by semi-classical approximation of the $\\Cal O(k)$ Bohr-Sommerfeld tori of the Lagrangian torus fibration $\\{T_t\\}_{t\\in\\Delta^n}$ and its Hamiltonian deformation $\\{\\phi(T_t)\\}_{t\\in\\Delta^n}$.

#### Lectures

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

Integrable nonlinear wave equations, nonlocal interaction and spectral methods (ENGLISH)

**Antonio Degasperis**(La Sapienza, University of Rome)Integrable nonlinear wave equations, nonlocal interaction and spectral methods (ENGLISH)

[ Abstract ]

A general class of integrable nonlinear multi-component wave equations are discussed to show that integrability, as implied by Lax pair, does not necessarily imply solvability of the initial value problem by spectral methods. A simple instance of this class, with applicative relevance to nonlinear optics, is discussed as a prototype model. Conservation laws and special solutions of this model are displayed to underline the integrability issue.

A general class of integrable nonlinear multi-component wave equations are discussed to show that integrability, as implied by Lax pair, does not necessarily imply solvability of the initial value problem by spectral methods. A simple instance of this class, with applicative relevance to nonlinear optics, is discussed as a prototype model. Conservation laws and special solutions of this model are displayed to underline the integrability issue.

#### Lectures

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

Integrable nonlinear wave equations, nonlocal interaction and spectral methods (ENGLISH)

**Antonio Degasperis**(La Sapienza, University of Rome)Integrable nonlinear wave equations, nonlocal interaction and spectral methods (ENGLISH)

[ Abstract ]

A general class of integrable nonlinear multi-component wave equations are discussed to show that integrability, as implied by Lax pair, does not necessarily imply solvability of the initial value problem by spectral methods. A simple instance of this class, with applicative relevance to nonlinear optics, is discussed as a prototype model. Conservation laws and special solutions of this model are displayed to underline the integrability issue.

A general class of integrable nonlinear multi-component wave equations are discussed to show that integrability, as implied by Lax pair, does not necessarily imply solvability of the initial value problem by spectral methods. A simple instance of this class, with applicative relevance to nonlinear optics, is discussed as a prototype model. Conservation laws and special solutions of this model are displayed to underline the integrability issue.

#### Lectures

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

Integrable nonlinear wave equations, nonlocal interaction and spectral methods (ENGLISH)

**Antonio Degasperis**(La Sapienza, University of Rome)Integrable nonlinear wave equations, nonlocal interaction and spectral methods (ENGLISH)

[ Abstract ]

A general class of integrable nonlinear multi-component wave equations are discussed to show that integrability, as implied by Lax pair, does not necessarily imply solvability of the initial value problem by spectral methods. A simple instance of this class, with applicative relevance to nonlinear optics, is discussed as a prototype model. Conservation laws and special solutions of this model are displayed to underline the integrability issue.

A general class of integrable nonlinear multi-component wave equations are discussed to show that integrability, as implied by Lax pair, does not necessarily imply solvability of the initial value problem by spectral methods. A simple instance of this class, with applicative relevance to nonlinear optics, is discussed as a prototype model. Conservation laws and special solutions of this model are displayed to underline the integrability issue.

#### Lectures

09:45-10:45 Room #123 (Graduate School of Math. Sci. Bldg.)

Stability of Fredholm property of regular operators on Hilbert $C^*$-modules (ENGLISH)

**Marzieh Forough**(Ferdowsi Univ. Mashhad)Stability of Fredholm property of regular operators on Hilbert $C^*$-modules (ENGLISH)

#### Lectures

11:00-12:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Scaling algebras, superselection theory and asymptotic morphisms (ENGLISH)

**Gerardo Morsella**(Univ. Roma II)Scaling algebras, superselection theory and asymptotic morphisms (ENGLISH)

#### Lectures

13:30-14:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Tracially $\\mathcal{Z}$-absorbing $C^*$-algebras (ENGLISH)

**Joav Orovitz**(Ben-Gurion Univ.)Tracially $\\mathcal{Z}$-absorbing $C^*$-algebras (ENGLISH)

#### Lectures

14:45-15:45 Room #118 (Graduate School of Math. Sci. Bldg.)

Noncommutative covering dimension (ENGLISH)

**Nicola Watson**(Univ. Toronto)Noncommutative covering dimension (ENGLISH)

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