## Seminar information archive

Seminar information archive ～05/25｜Today's seminar 05/26 | Future seminars 05/27～

#### FMSP Lectures

15:30-16:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Lifting of maps between surfaces (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_ZhiChen.pdf

**Zhi Chen**(Hefei University of Technology)Lifting of maps between surfaces (ENGLISH)

[ Abstract ]

The Thom conjecture says the algebraic curves have minimal genus among those surfaces Imbedded in CP^2 having fixed degree. This conjecture was solved by Kronheimer and Mrowka by using Seiberg-Witten invariants. In this talk we try to understand the content of this conjecture. We will construct these imbedded surface with minimal genus explicitly, and present some kind of generalization of this conjecture.

[ Reference URL ]The Thom conjecture says the algebraic curves have minimal genus among those surfaces Imbedded in CP^2 having fixed degree. This conjecture was solved by Kronheimer and Mrowka by using Seiberg-Witten invariants. In this talk we try to understand the content of this conjecture. We will construct these imbedded surface with minimal genus explicitly, and present some kind of generalization of this conjecture.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_ZhiChen.pdf

### 2015/09/09

#### Number Theory Seminar

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

The hyperbolic Ax-Lindemann conjecture (English)

**Emmanuel Ullmo**(IHES)The hyperbolic Ax-Lindemann conjecture (English)

[ Abstract ]

The hyperbolic Ax Lindemann conjecture is a functional transcendental statement which describes the Zariski closure of "algebraic flows" on Shimura varieties. We will describe the proof of this conjecture and its consequences for the André-Oort conjecture. This is a joint work with Bruno Klingler and Andrei Yafaev.

The hyperbolic Ax Lindemann conjecture is a functional transcendental statement which describes the Zariski closure of "algebraic flows" on Shimura varieties. We will describe the proof of this conjecture and its consequences for the André-Oort conjecture. This is a joint work with Bruno Klingler and Andrei Yafaev.

### 2015/09/08

#### Seminar on Mathematics for various disciplines

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

Duality based approaches to total variation-like flows with applications to image processing (English)

**Monika Muszkieta**(Wroclaw University of Technology)Duality based approaches to total variation-like flows with applications to image processing (English)

[ Abstract ]

During the last years, total variation models have became very popular in image processing and analysis. They have been used to solve such problems as image restoration, image deblurring or image inpainting. Their interesting and successful applications became the motivation for many authors to rigorous analysis of properties of solutions to the corresponding total variation flows. The main difficulty in numerical approximation of solutions to these flows is caused by the lack of differentiability of the total variation term, and the commonly used approach to overcome this difficulty consists in considering of the dual formulation. In the talk, we consider two total variation flow models. The first one is the anisotropic total variation flow on $L^2$ with additional regularization, and the second one, is the total variation flow on $H^{-s}$. We introduce duality based numerical schemes for approximate solutions to corresponding equations and present some applications to image processing.

This talk is based on joint work with Y. Giga, P. Mucha and P. Rybka.

During the last years, total variation models have became very popular in image processing and analysis. They have been used to solve such problems as image restoration, image deblurring or image inpainting. Their interesting and successful applications became the motivation for many authors to rigorous analysis of properties of solutions to the corresponding total variation flows. The main difficulty in numerical approximation of solutions to these flows is caused by the lack of differentiability of the total variation term, and the commonly used approach to overcome this difficulty consists in considering of the dual formulation. In the talk, we consider two total variation flow models. The first one is the anisotropic total variation flow on $L^2$ with additional regularization, and the second one, is the total variation flow on $H^{-s}$. We introduce duality based numerical schemes for approximate solutions to corresponding equations and present some applications to image processing.

This talk is based on joint work with Y. Giga, P. Mucha and P. Rybka.

#### Tuesday Seminar of Analysis

16:50-18:20 Room #126 (Graduate School of Math. Sci. Bldg.)

Global-in-time Strichartz estimates for Schr\"odinger equations with long-range repulsive potentials (Japanese)

**Haruya Mizutani**(School of Science, Osaka University)Global-in-time Strichartz estimates for Schr\"odinger equations with long-range repulsive potentials (Japanese)

[ Abstract ]

We will discuss a resent result on global-in-time Strichartz estimates for Schr\"odinger equations with slowly decreasing repulsive potentials. If the potential is of very short-range type, there is a simple method due to Rodnianski-Schlag or Burq et al, which seems to be difficult to apply for the present case. The proof instead follows a similar line as in speaker’s resent joint work with J.-M. Bouclet. In particular, we employ both Morawetz type estimates and the methods of micro local analysis such as the Isozaki-Kitada parametrix, even in the low frequency regime.

We will discuss a resent result on global-in-time Strichartz estimates for Schr\"odinger equations with slowly decreasing repulsive potentials. If the potential is of very short-range type, there is a simple method due to Rodnianski-Schlag or Burq et al, which seems to be difficult to apply for the present case. The proof instead follows a similar line as in speaker’s resent joint work with J.-M. Bouclet. In particular, we employ both Morawetz type estimates and the methods of micro local analysis such as the Isozaki-Kitada parametrix, even in the low frequency regime.

### 2015/09/02

#### FMSP Lectures

17:00-18:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Operads and their applications to Mathematical Physics (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Voronov.pdf

**Alexander Voronov**(Univ. of Minnesota)Operads and their applications to Mathematical Physics (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Voronov.pdf

### 2015/08/31

#### thesis presentations

16:30-17:45 Room #128 (Graduate School of Math. Sci. Bldg.)

Approximate Controllability, Non-homogeneous Boundary Value Problems and Inverse Source Problems for Fractional Diffusion Equations（非整数階拡散方程式に対する近似可制御性、非斉次境界値問題およびソース項決定逆問題） (JAPANESE)

**藤城 謙一**(東京大学大学院数理科学研究科)Approximate Controllability, Non-homogeneous Boundary Value Problems and Inverse Source Problems for Fractional Diffusion Equations（非整数階拡散方程式に対する近似可制御性、非斉次境界値問題およびソース項決定逆問題） (JAPANESE)

### 2015/08/28

#### Colloquium

16:50-17:50 Room #002 (Graduate School of Math. Sci. Bldg.)

On the development of Riemann surfaces and moduli (ENGLISH)

**Athanase Papadopoulos**(Institut de Recherche Mathématique Avancée, Université de Strasbourg et CNRS)On the development of Riemann surfaces and moduli (ENGLISH)

[ Abstract ]

I will describe a selection of major fundamental ideas in the theory

of Riemann surfaces and moduli, starting from the work of Riemann, and

ending with recent works.

I will describe a selection of major fundamental ideas in the theory

of Riemann surfaces and moduli, starting from the work of Riemann, and

ending with recent works.

### 2015/08/07

#### Seminar on Probability and Statistics

14:40-15:50 Room #052 (Graduate School of Math. Sci. Bldg.)

Effectiveness of time-varying minimum value at risk and expected shortfall hedging

**UBUKATA, Masato**(Kushiro Public University of Economics)Effectiveness of time-varying minimum value at risk and expected shortfall hedging

[ Abstract ]

This paper assesses the incremental value of time-varying minimum value at risk (VaR) and expected shortfall (ES) hedging strategies over unconditional hedging strategy. The conditional futures hedge ratios are calculated through estimation of multivariate volatility models under a skewed and leptokurtic distribution and Monte Carlo simulation for conditional skewness and kurtosis of hedged portfolio returns. We examine DCC-GJR models with or without encompassing realized covariance measure (RCM) from high-frequency data under a multivariate skewed Student's t-distribution. In the out-of-sample analysis with a daily rebalancing approach, the empirical results show that the conditional minimum VaR and ES hedging strategies outperform the unconditional hedging strategy. We find that the use of RCM improves the futures hedging performance for a short hedge, although the degree of improvement is small relative to that when switching from unconditional to conditional.

This paper assesses the incremental value of time-varying minimum value at risk (VaR) and expected shortfall (ES) hedging strategies over unconditional hedging strategy. The conditional futures hedge ratios are calculated through estimation of multivariate volatility models under a skewed and leptokurtic distribution and Monte Carlo simulation for conditional skewness and kurtosis of hedged portfolio returns. We examine DCC-GJR models with or without encompassing realized covariance measure (RCM) from high-frequency data under a multivariate skewed Student's t-distribution. In the out-of-sample analysis with a daily rebalancing approach, the empirical results show that the conditional minimum VaR and ES hedging strategies outperform the unconditional hedging strategy. We find that the use of RCM improves the futures hedging performance for a short hedge, although the degree of improvement is small relative to that when switching from unconditional to conditional.

#### Seminar on Probability and Statistics

13:20-14:30 Room #052 (Graduate School of Math. Sci. Bldg.)

ESTIMATION OF INTEGRATED QUADRATIC COVARIATION BETWEEN TWO ASSETS WITH ENDOGENOUS SAMPLING TIMES

**Yoann Potiron**(University of Chicago)ESTIMATION OF INTEGRATED QUADRATIC COVARIATION BETWEEN TWO ASSETS WITH ENDOGENOUS SAMPLING TIMES

[ Abstract ]

When estimating integrated covariation between two assets based on high-frequency data,simple assumptions are usually imposed on the relationship between the price processes and the observation times. In this paper, we introduce an endogenous 2-dimensional model and show that it is more general than the existing endogenous models of the literature. In addition, we establish a central limit theorem for the Hayashi-Yoshida estimator in this general endogenous model in the case where prices follow pure-diffusion processes.

When estimating integrated covariation between two assets based on high-frequency data,simple assumptions are usually imposed on the relationship between the price processes and the observation times. In this paper, we introduce an endogenous 2-dimensional model and show that it is more general than the existing endogenous models of the literature. In addition, we establish a central limit theorem for the Hayashi-Yoshida estimator in this general endogenous model in the case where prices follow pure-diffusion processes.

### 2015/07/30

#### thesis presentations

10:30-11:45 Room #128 (Graduate School of Math. Sci. Bldg.)

Theory and application of a meta lambda calculus with cross-level computation （レベル横断的計算機構を持つメタラムダ計算の理論と応用） (JAPANESE)

**飛澤 和則**(東京大学大学院数理科学研究科)Theory and application of a meta lambda calculus with cross-level computation （レベル横断的計算機構を持つメタラムダ計算の理論と応用） (JAPANESE)

### 2015/07/29

#### thesis presentations

16:00-17:15 Room #128 (Graduate School of Math. Sci. Bldg.)

Accelerating convergence and tractability of multivariate numerical integration when the L1-norms of the higher order derivatives of the integrand grow at most exponentially（被積分関数の高階偏微分のL1ノルムの増大度が高々指数的である場合の多次元数値積分の加速的な収束と計算容易性） (JAPANESE)

**鈴木 航介**(東京大学大学院数里科学研究科)Accelerating convergence and tractability of multivariate numerical integration when the L1-norms of the higher order derivatives of the integrand grow at most exponentially（被積分関数の高階偏微分のL1ノルムの増大度が高々指数的である場合の多次元数値積分の加速的な収束と計算容易性） (JAPANESE)

#### thesis presentations

17:30-18:45 Room #128 (Graduate School of Math. Sci. Bldg.)

Research on Walsh figure of merit for higher order convergent Quasi-Monte Carlo integration（高次収束準モンテカルロ積分のためのWalsh figure of meritの研究） (JAPANESE)

**芳木 武仁**(東京大学大学院数理科学研究科)Research on Walsh figure of merit for higher order convergent Quasi-Monte Carlo integration（高次収束準モンテカルロ積分のためのWalsh figure of meritの研究） (JAPANESE)

### 2015/07/28

#### Lectures

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

Convergence of some horocyclic deformations to the Gardiner-Masur

boundary of Teichmueller space. (ENGLISH)

**Vincent Alberge**(Université de Strasbourg)Convergence of some horocyclic deformations to the Gardiner-Masur

boundary of Teichmueller space. (ENGLISH)

[ Abstract ]

It is well known that a point of the Teichmueller space and a measured foliation determine an isometric embedding of the hyperbolic disc to the Teichmueller space equipped with the so-called Teichmueller metric. In this talk, we will consider the image by this embedding of a particular horocycle whose points will be called an horocyclic deformation. To be more precise, we will be interested in the closure of this subset in the Gardiner-Masur compactification. As the embedding of the disc does not admit a continuous extension to boundaries, we cannot say that the boundary of the set of horocyclic deformations consists of one point.

However, according to Miyachi's results, we will see that it is the case if the given foliation is either a simple closed curve or a uniquely ergodic foliation.

It is well known that a point of the Teichmueller space and a measured foliation determine an isometric embedding of the hyperbolic disc to the Teichmueller space equipped with the so-called Teichmueller metric. In this talk, we will consider the image by this embedding of a particular horocycle whose points will be called an horocyclic deformation. To be more precise, we will be interested in the closure of this subset in the Gardiner-Masur compactification. As the embedding of the disc does not admit a continuous extension to boundaries, we cannot say that the boundary of the set of horocyclic deformations consists of one point.

However, according to Miyachi's results, we will see that it is the case if the given foliation is either a simple closed curve or a uniquely ergodic foliation.

#### Lie Groups and Representation Theory

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

On g,K-modules over arbitrary fields and applications to special values of L-functions

**Fabian Januszewski**(Karlsruhe Institute of Technology)On g,K-modules over arbitrary fields and applications to special values of L-functions

[ Abstract ]

I will introduce g,K-modules over arbitrary fields of characteristic 0 and discuss their fundamental properties and constructions, including Zuckerman functors. This may be applied to produce models of certain standard modules over number fields, which has applications to special values of automorphic L-functions, and also furnishes the space of regular algebraic cusp forms of GL(n) with a natural global Q-structure.

I will introduce g,K-modules over arbitrary fields of characteristic 0 and discuss their fundamental properties and constructions, including Zuckerman functors. This may be applied to produce models of certain standard modules over number fields, which has applications to special values of automorphic L-functions, and also furnishes the space of regular algebraic cusp forms of GL(n) with a natural global Q-structure.

### 2015/07/27

#### Tokyo Probability Seminar

16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)

Convergence of Brownian motions on RCD*(K,N) spaces

**Kohei Suzuki**(Graduate School of Science, Kyoto University)Convergence of Brownian motions on RCD*(K,N) spaces

### 2015/07/24

#### Operator Algebra Seminars

16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)

Applications of Boltzmann's S=k log W in algebra and analysis

**Mikael Pichot**(McGill Univ.)Applications of Boltzmann's S=k log W in algebra and analysis

#### Geometry Colloquium

10:00-11:30 Room #126 (Graduate School of Math. Sci. Bldg.)

High-dimensional metric-measure limit of Stiefel manifolds (Japanese)

**Asuka Takatsu**(Tokyo Metropolitan University)High-dimensional metric-measure limit of Stiefel manifolds (Japanese)

[ Abstract ]

A metric measure space is the triple of a complete separable metric space with a Borel measure on this space. Gromov defined a concept of convergence of metric measure spaces by the convergence of the sets of 1-Lipschitz functions on the spaces. We study and specify the high-dimensional limit of Stiefel manifolds in the sense of this convergence; the limit is the infinite-dimensional Gaussian space, which is drastically different from the manifolds. This is a joint work with Takashi SHIOYA (Tohoku univ).

A metric measure space is the triple of a complete separable metric space with a Borel measure on this space. Gromov defined a concept of convergence of metric measure spaces by the convergence of the sets of 1-Lipschitz functions on the spaces. We study and specify the high-dimensional limit of Stiefel manifolds in the sense of this convergence; the limit is the infinite-dimensional Gaussian space, which is drastically different from the manifolds. This is a joint work with Takashi SHIOYA (Tohoku univ).

#### FMSP Lectures

16:00-19:00 Room #268 (Graduate School of Math. Sci. Bldg.)

Solvability and approximate solution of a coefficient inverse problem for the kinetic equation (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Fikret.pdf

**Fikret Golgeleyen**(Bulent Ecevit University)Solvability and approximate solution of a coefficient inverse problem for the kinetic equation (ENGLISH)

[ Abstract ]

The existence, uniqueness and stability of the solution of a coefficient inverse problem for the kinetic equation are proven.

The approximate solution of the problem in one-dimensional case is investigated by using two different techniques: finite difference approximation (FDA) and symbolic computation approach (SCA).

A comparison among the exact solution of the problem, the numerical solution obtained from FDA and the approximate analytical solution obtained from SCA is presented.

[ Reference URL ]The existence, uniqueness and stability of the solution of a coefficient inverse problem for the kinetic equation are proven.

The approximate solution of the problem in one-dimensional case is investigated by using two different techniques: finite difference approximation (FDA) and symbolic computation approach (SCA).

A comparison among the exact solution of the problem, the numerical solution obtained from FDA and the approximate analytical solution obtained from SCA is presented.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Fikret.pdf

### 2015/07/23

#### Number Theory Seminar

13:00-16:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Representation of squares by cubic forms - Estimates for the appearing exponential sums (English)

Ramification and nearby cycles for $\ell$-adic sheaves on relative curves (English)

Explicit computation of the number of dormant opers and duality (Japanese)

**Lasse Grimmelt**(University of Göttingen/Waseda University) 13:00-14:00Representation of squares by cubic forms - Estimates for the appearing exponential sums (English)

**Haoyu Hu**(University of Tokyo) 14:15-15:15Ramification and nearby cycles for $\ell$-adic sheaves on relative curves (English)

[ Abstract ]

I will present a new approach for a formula of Deligne and Kato that computes the dimension of the nearby cycle complex of an $\ell$-adic sheaf on a smooth relative curve over a strictly henselian trait such that $p$ is not one of its uniformizer. Deligne considered the case where the sheaf has no vertical ramification and Kato extended the formula to the general case. My approach is based on ramification theory of Abbes and Saito. It computes the nearby cycle complex in terms of the refined Swan conductor. In fact, I compare Abbes-Saito's refined Swan conductor with Kato's Swan conductor with differential values, which is the key ingredient in Kato's formula; the case of rank one sheaves is due to Abbes and Saito. My approach provides also a new independent proof of Deligne-Kato's formula.

I will present a new approach for a formula of Deligne and Kato that computes the dimension of the nearby cycle complex of an $\ell$-adic sheaf on a smooth relative curve over a strictly henselian trait such that $p$ is not one of its uniformizer. Deligne considered the case where the sheaf has no vertical ramification and Kato extended the formula to the general case. My approach is based on ramification theory of Abbes and Saito. It computes the nearby cycle complex in terms of the refined Swan conductor. In fact, I compare Abbes-Saito's refined Swan conductor with Kato's Swan conductor with differential values, which is the key ingredient in Kato's formula; the case of rank one sheaves is due to Abbes and Saito. My approach provides also a new independent proof of Deligne-Kato's formula.

**Yasuhiro Wakabayashi**(University of Tokyo) 15:30-16:30Explicit computation of the number of dormant opers and duality (Japanese)

### 2015/07/22

#### Operator Algebra Seminars

16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)

Recent progress in the classification of amenable $C^*$-algebras

**George Elliott**(Univ. Toronto)Recent progress in the classification of amenable $C^*$-algebras

#### FMSP Lectures

16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)

Recent progress in the classification of amenable C*-algebras (ENGLISH)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

**George Elliott**(Univ. Toronto)Recent progress in the classification of amenable C*-algebras (ENGLISH)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

### 2015/07/21

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Ribbon concordance and 0-surgeries along knots (JAPANESE)

**Keiji Tagami**(Tokyo Institute of Technology)Ribbon concordance and 0-surgeries along knots (JAPANESE)

[ Abstract ]

Akbulut and Kirby conjectured that two knots with

the same 0-surgery are concordant. Recently, Yasui

gave a counterexample of this conjecture.

In this talk, we introduce a technique to construct

non-ribbon concordant knots with the same 0-surgery.

Moreover, we give a potential counterexample of the

slice-ribbon conjecture. This is a joint work with

Tetsuya Abe (Osaka City University, OCAMI).

Akbulut and Kirby conjectured that two knots with

the same 0-surgery are concordant. Recently, Yasui

gave a counterexample of this conjecture.

In this talk, we introduce a technique to construct

non-ribbon concordant knots with the same 0-surgery.

Moreover, we give a potential counterexample of the

slice-ribbon conjecture. This is a joint work with

Tetsuya Abe (Osaka City University, OCAMI).

#### Tuesday Seminar of Analysis

16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Born-Oppenheimer approximation for an atom in constant magnetic fields (Japanese)

**Sohei Ashida**(Department of Mathematics, Kyoto University)Born-Oppenheimer approximation for an atom in constant magnetic fields (Japanese)

[ Abstract ]

We obtain a reduction scheme for the study of the quantum evolution of an atom in constant magnetic fields using the method developed by Martinez, Nenciu and Sordoni based on the construction of almost invariant subspace. Martinez and Sordoni also dealt with such a case but their reduced Hamiltonian includes the vector potential terms. Using the center of mass coordinates and constructing the almost invariant subspace different from theirs, we obtain the reduced Hamiltonian which does not include the vector potential terms. Using the reduced evolution we also obtain the asymptotic expantion of the evolution for a specific localized initial data, which verifies the straight motion of an atom in constatnt magnetic fields.

We obtain a reduction scheme for the study of the quantum evolution of an atom in constant magnetic fields using the method developed by Martinez, Nenciu and Sordoni based on the construction of almost invariant subspace. Martinez and Sordoni also dealt with such a case but their reduced Hamiltonian includes the vector potential terms. Using the center of mass coordinates and constructing the almost invariant subspace different from theirs, we obtain the reduced Hamiltonian which does not include the vector potential terms. Using the reduced evolution we also obtain the asymptotic expantion of the evolution for a specific localized initial data, which verifies the straight motion of an atom in constatnt magnetic fields.

#### Lie Groups and Representation Theory

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

GEOMETRIC STRUCTURE IN SMOOTH DUAL

**Paul Baum**(Penn State University)GEOMETRIC STRUCTURE IN SMOOTH DUAL

[ Abstract ]

Let G be a connected split reductive p-adic group. Examples are GL(n, F) , SL(n, F) , SO(n, F) , Sp(2n, F) , PGL(n, F) where n can be any positive integer and F can be any finite extension of the field Q_p of p-adic numbers. The smooth (or admissible) dual of G is the set of equivalence classes of smooth irreducible representations of G. This talk will first review the theory of the Bernstein center. According to this theory, the smooth dual of G is the disjoint union of subsets known as the Bernstein components. The talk will then explain the ABPS (Aubert-Baum-Plymen-Solleveld) conjecture which states that each Bernstein component is a complex affine variety. Each of these complex affine varieties is explicitly identified as the extended quotient associated to the given Bernstein component.

The ABPS conjecture has been proved for GL(n, F), SO(n, F), and Sp(2n, F).

Let G be a connected split reductive p-adic group. Examples are GL(n, F) , SL(n, F) , SO(n, F) , Sp(2n, F) , PGL(n, F) where n can be any positive integer and F can be any finite extension of the field Q_p of p-adic numbers. The smooth (or admissible) dual of G is the set of equivalence classes of smooth irreducible representations of G. This talk will first review the theory of the Bernstein center. According to this theory, the smooth dual of G is the disjoint union of subsets known as the Bernstein components. The talk will then explain the ABPS (Aubert-Baum-Plymen-Solleveld) conjecture which states that each Bernstein component is a complex affine variety. Each of these complex affine varieties is explicitly identified as the extended quotient associated to the given Bernstein component.

The ABPS conjecture has been proved for GL(n, F), SO(n, F), and Sp(2n, F).

#### Lie Groups and Representation Theory

15:30-16:30 Room #122 (Graduate School of Math. Sci. Bldg.)

(Japanese)

**Toshiaki Hattori**(Tokyo Institute of Technology)(Japanese)

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