## Seminar information archive

Seminar information archive ～08/09｜Today's seminar 08/10 | Future seminars 08/11～

#### Lie Groups and Representation Theory

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

Local Theta lifts of unitary lowest weight modules to the indefinite orthogonal groups (ENGLISH)

**Hung Yean Loke**(National University of Singapore)Local Theta lifts of unitary lowest weight modules to the indefinite orthogonal groups (ENGLISH)

[ Abstract ]

In this talk, I will discuss the local theta lifts of unitary lowest weight modules of $Sp(2p,R)$ to the indefinite orthogonal group $O(n,m)$. In a previous paper, Nishiyama and Zhu computed the associated cycles when the dual pair $Sp(2p,R) \\times O(m,n)$ lies in the stable range, ie. $2p \\leq \\min(m,n)$. In this talk, I will report on a joint work with Jiajun Ma and U-Liang Tang at NUS where we extend the computation beyond the stable range. Our approach is to analyze the coherent sheaves generated by the graded modules.

We will also need the Kobayashi's projection formula for discretely decomposable restrictions. Our study produces some interesting formulas on the $K$-types of the representations. In particular for some of these representations, the $K$-types formulas agree those in a conjecture of Vogan on the unipotent representations.

In this talk, I will discuss the local theta lifts of unitary lowest weight modules of $Sp(2p,R)$ to the indefinite orthogonal group $O(n,m)$. In a previous paper, Nishiyama and Zhu computed the associated cycles when the dual pair $Sp(2p,R) \\times O(m,n)$ lies in the stable range, ie. $2p \\leq \\min(m,n)$. In this talk, I will report on a joint work with Jiajun Ma and U-Liang Tang at NUS where we extend the computation beyond the stable range. Our approach is to analyze the coherent sheaves generated by the graded modules.

We will also need the Kobayashi's projection formula for discretely decomposable restrictions. Our study produces some interesting formulas on the $K$-types of the representations. In particular for some of these representations, the $K$-types formulas agree those in a conjecture of Vogan on the unipotent representations.

#### Tuesday Seminar on Topology

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

Remarks on filtrations of the singular homology of real varieties. (ENGLISH)

**Mircea Voineagu**(IPMU, The University of Tokyo)Remarks on filtrations of the singular homology of real varieties. (ENGLISH)

[ Abstract ]

We discuss various conjectures about filtrations on the singular homology of real and complex varieties. We prove that a conjecture relating niveau filtration on Borel-Moore homology of real varieties and the image of generalized cycle maps from reduced Lawson homology is false. In the end, we discuss a certain decomposition of Borel-Haeflinger cycle map. This is a joint work with J.Heller.

We discuss various conjectures about filtrations on the singular homology of real and complex varieties. We prove that a conjecture relating niveau filtration on Borel-Moore homology of real varieties and the image of generalized cycle maps from reduced Lawson homology is false. In the end, we discuss a certain decomposition of Borel-Haeflinger cycle map. This is a joint work with J.Heller.

### 2011/12/12

#### Seminar on Geometric Complex Analysis

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

Brody curves and mean dimension (JAPANESE)

**Shinichiroh MATSUO**(Kyoto University)Brody curves and mean dimension (JAPANESE)

[ Abstract ]

We study the mean dimensions of the spaces of Brody curves. In particular we give the formula of the mean dimension of the space of Brody curves in the Riemann sphere.

We study the mean dimensions of the spaces of Brody curves. In particular we give the formula of the mean dimension of the space of Brody curves in the Riemann sphere.

#### Algebraic Geometry Seminar

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

A version of Barth's theorem for singular varieties (cancelled) (JAPANESE)

**Robert Laterveer**(CNRS, IRMA, Université de Strasbourg)A version of Barth's theorem for singular varieties (cancelled) (JAPANESE)

### 2011/12/09

#### Lectures

10:40-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)

An iterative construction of solutions of the TAP equation (ENGLISH)

**Erwin Bolthausen**(University of Zurich)An iterative construction of solutions of the TAP equation (ENGLISH)

[ Abstract ]

The TAP equation (Thouless-Anderson-Palmer) describes the so-called pure states in the Sherrington-Kirkpatrick model. A mathematical rigorous derivation of the equation exists only in the high temperature regime. We propose an interative construction of solutions of the equations which is shown to converge up to the de Almayda-Thouless line. The iteration makes sense also beyond this line, but it fails to converge. However, some properties of the iteration can also been proved beyond the AT-line.

The TAP equation (Thouless-Anderson-Palmer) describes the so-called pure states in the Sherrington-Kirkpatrick model. A mathematical rigorous derivation of the equation exists only in the high temperature regime. We propose an interative construction of solutions of the equations which is shown to converge up to the de Almayda-Thouless line. The iteration makes sense also beyond this line, but it fails to converge. However, some properties of the iteration can also been proved beyond the AT-line.

#### Lectures

10:40-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)

An iterative construction of solutions of the TAP equation (ENGLISH)

**Erwin Bolthausen**(University of Zurich)An iterative construction of solutions of the TAP equation (ENGLISH)

[ Abstract ]

The TAP equation (Thouless-Anderson-Palmer) describes the so-called pure states in the Sherrington-Kirkpatrick model. A mathematical rigorous derivation of the equation exists only in the high temperature regime. We propose an interative construction of solutions of the equations which is shown to converge up to the de Almayda-Thouless line. The iteration makes sense also beyond this line, but it fails to converge. However, some properties of the iteration can also been proved beyond the AT-line.

The TAP equation (Thouless-Anderson-Palmer) describes the so-called pure states in the Sherrington-Kirkpatrick model. A mathematical rigorous derivation of the equation exists only in the high temperature regime. We propose an interative construction of solutions of the equations which is shown to converge up to the de Almayda-Thouless line. The iteration makes sense also beyond this line, but it fails to converge. However, some properties of the iteration can also been proved beyond the AT-line.

#### GCOE Seminars

11:40-12:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Eigenvalue order statistics and mass concentration in the parabolic Anderson model (ENGLISH)

**Wolfgang Koenig**(Weierstrass Institute Berlin)Eigenvalue order statistics and mass concentration in the parabolic Anderson model (ENGLISH)

[ Abstract ]

We consider the random Schr\\"odinger operator on the lattice with i.i.d. potential, which is double-exponentially distributed. In a large box, we look at the lowest eigenvalues, together with the location of the centering of the corresponding eigenfunction, and derive a Poisson process limit law, after suitable rescaling and shifting, towards an explicit Poisson point process. This is a strong form of Anderson localization at the bottom of the spectrum. Since the potential is unbounded, also the eigenvalues are, and it turns out that the gaps between them are much larger than of inverse volume order. We explain an application to concentration properties of the corresponding Cauchy problem, the parabolic Anderson model. In fact, it will turn out that the total mass of the solution comes from just one island, asymptotically for large times. This is joint work in progress with Marek Biskup (Los Angeles and Budweis).

We consider the random Schr\\"odinger operator on the lattice with i.i.d. potential, which is double-exponentially distributed. In a large box, we look at the lowest eigenvalues, together with the location of the centering of the corresponding eigenfunction, and derive a Poisson process limit law, after suitable rescaling and shifting, towards an explicit Poisson point process. This is a strong form of Anderson localization at the bottom of the spectrum. Since the potential is unbounded, also the eigenvalues are, and it turns out that the gaps between them are much larger than of inverse volume order. We explain an application to concentration properties of the corresponding Cauchy problem, the parabolic Anderson model. In fact, it will turn out that the total mass of the solution comes from just one island, asymptotically for large times. This is joint work in progress with Marek Biskup (Los Angeles and Budweis).

#### GCOE Seminars

14:00-14:50 Room #122 (Graduate School of Math. Sci. Bldg.)

Gradient Gibbs models with non-convex potentials (ENGLISH)

**Roman Kotecky**(Charles University Prague/University of Warwick)Gradient Gibbs models with non-convex potentials (ENGLISH)

[ Abstract ]

A motivation for gradient Gibbs measures in the study of macroscopic elasticity and in proving the Cauchy-Born rule will be explained. Results concerning strict convexity of the free energy will be formulated and discussed. Based on joint works with S. Adams and S. Mueller and with S. Luckhaus.

A motivation for gradient Gibbs measures in the study of macroscopic elasticity and in proving the Cauchy-Born rule will be explained. Results concerning strict convexity of the free energy will be formulated and discussed. Based on joint works with S. Adams and S. Mueller and with S. Luckhaus.

#### GCOE Seminars

15:00-15:50 Room #122 (Graduate School of Math. Sci. Bldg.)

Einstein relation and linear response for random walks in random environment (ENGLISH)

**Stefano Olla**(University Paris - Dauphine)Einstein relation and linear response for random walks in random environment (ENGLISH)

### 2011/12/08

#### Number Theory Seminar

18:30-19:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Nonabelian p-adic Hodge theory and Frobenius (ENGLISH)

**Gerd Faltings**(Max Planck Institute for Mathematics, Bonn)Nonabelian p-adic Hodge theory and Frobenius (ENGLISH)

[ Abstract ]

Some time ago, I constructed a relation between Higgs-bundles and p-adic etale sheaves, on curves over a p-adic field. This corresponds (say in the abelian case) to a Hodge-Tate picture. In the lecture I try to explain one way to introduce Frobenius into the theory. We do not get a complete theory but at least can treat p-adic sheaves close to trivial.

(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)

Some time ago, I constructed a relation between Higgs-bundles and p-adic etale sheaves, on curves over a p-adic field. This corresponds (say in the abelian case) to a Hodge-Tate picture. In the lecture I try to explain one way to introduce Frobenius into the theory. We do not get a complete theory but at least can treat p-adic sheaves close to trivial.

(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)

### 2011/12/07

#### Lectures

16:00-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)

"Inverse problems associated with linear and non-linear parabolic systems " (ENGLISH)

"Hautus test for the approximate controllability of linear systems" (ENGLISH)

**Michel Cristofol**(マルセイユ大学) 16:00-17:00"Inverse problems associated with linear and non-linear parabolic systems " (ENGLISH)

[ Abstract ]

In this talk, I present several inverse reconstruction results for linear and non linear parabolic systems with different coupling terms : for linear systems with reaction-convection terms and for cooperative systems like Lotka Volterra systems with strong coupling terms. I will show different approaches to prove uniqueness of the coefficients via Carleman inequalities or via regularities properties of the solutions.

In this talk, I present several inverse reconstruction results for linear and non linear parabolic systems with different coupling terms : for linear systems with reaction-convection terms and for cooperative systems like Lotka Volterra systems with strong coupling terms. I will show different approaches to prove uniqueness of the coefficients via Carleman inequalities or via regularities properties of the solutions.

**Guillaume Olive**(マルセイユ大学) 17:00-18:00"Hautus test for the approximate controllability of linear systems" (ENGLISH)

[ Abstract ]

We will introduce some generalization of the Hautus test to linear parabolic systems and give some applications to the distributed and boundary approximate controllability of such systems.

We will introduce some generalization of the Hautus test to linear parabolic systems and give some applications to the distributed and boundary approximate controllability of such systems.

### 2011/12/06

#### Numerical Analysis Seminar

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

Development of high order CFD solver for aerospace applications (JAPANESE)

[ Reference URL ]

http://www.infsup.jp/saito/

**Kanako Yasue**(JAXA)Development of high order CFD solver for aerospace applications (JAPANESE)

[ Reference URL ]

http://www.infsup.jp/saito/

### 2011/12/05

#### Algebraic Geometry Seminar

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

Obstructions to deforming curves on a uniruled 3-fold (JAPANESE)

**Hirokazu Nasu**(Tokai University)Obstructions to deforming curves on a uniruled 3-fold (JAPANESE)

[ Abstract ]

In this talk, I review some results from a joint work with Mukai:

1. a generalization of Mumford's example of a non-reduced component of the Hilbert scheme, and

2. a sufficient condition for a first order deformation of a curve on a uniruled 3-fold to be obstructed.

As a sequel of the study, we will discuss some obstructed deformations of degenerate curves on a higher dimensional scroll.

In this talk, I review some results from a joint work with Mukai:

1. a generalization of Mumford's example of a non-reduced component of the Hilbert scheme, and

2. a sufficient condition for a first order deformation of a curve on a uniruled 3-fold to be obstructed.

As a sequel of the study, we will discuss some obstructed deformations of degenerate curves on a higher dimensional scroll.

### 2011/12/01

#### Lectures

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

Stability of topological phases of matter (ENGLISH)

**Spyridon Michalakis**(Caltech)Stability of topological phases of matter (ENGLISH)

#### Algebraic Geometry Seminar

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

Cyclic K-theory (ENGLISH)

**Dmitry Kaledin**(Steklov Mathematics Institute/ KIAS)Cyclic K-theory (ENGLISH)

[ Abstract ]

Cyclic K-theory is a variant of algebraic K-theory introduced by Goodwillie 25 years ago and more-or-less forgotten by now. I will try to convince the audience that cyclic K-theory is actually quite useful -- in particular, it can be effectively computed for varieties over a finite field.

Cyclic K-theory is a variant of algebraic K-theory introduced by Goodwillie 25 years ago and more-or-less forgotten by now. I will try to convince the audience that cyclic K-theory is actually quite useful -- in particular, it can be effectively computed for varieties over a finite field.

### 2011/11/30

#### Seminar on Probability and Statistics

15:00-16:10 Room #002 (Graduate School of Math. Sci. Bldg.)

Information criteria for parametric and semi-parametric models (JAPANESE)

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/05.html

**HIROSE, Yuichi**(Victoria University of Wellington)Information criteria for parametric and semi-parametric models (JAPANESE)

[ Abstract ]

Since Akaike proposed an Information Criteria, this approach to

model selection has been important part of Statistical data analysis.

Since then many Information Criteria have been proposed and it is still

an active field of research. Despite there are many contributors in this

topic, we have not have proper Information Criteria for semiparametric

models. In this talk, we give ideas to develop an Information Criteria

for semiparametric models.

[ Reference URL ]Since Akaike proposed an Information Criteria, this approach to

model selection has been important part of Statistical data analysis.

Since then many Information Criteria have been proposed and it is still

an active field of research. Despite there are many contributors in this

topic, we have not have proper Information Criteria for semiparametric

models. In this talk, we give ideas to develop an Information Criteria

for semiparametric models.

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/05.html

### 2011/11/29

#### Lectures

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

Stability of topological phases of matter (ENGLISH)

**Spyridon Michalakis**(Caltech)Stability of topological phases of matter (ENGLISH)

#### Tuesday Seminar on Topology

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

Mapping class group actions (ENGLISH)

**Athanase Papadopoulos**(IRMA, Univ. de Strasbourg)Mapping class group actions (ENGLISH)

[ Abstract ]

I will describe and present some rigidity results on mapping

class group actions on spaces of foliations on surfaces, equipped with various topologies.

I will describe and present some rigidity results on mapping

class group actions on spaces of foliations on surfaces, equipped with various topologies.

#### Lie Groups and Representation Theory

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

Symmetries, (their) deformations, and physics: some perspectives and open problems from half a century of personal experience (ENGLISH)

**Daniel Sternheimer**(Rikkyo Univertiry and Université de Bourgogne)Symmetries, (their) deformations, and physics: some perspectives and open problems from half a century of personal experience (ENGLISH)

[ Abstract ]

This is a flexible general framework, based on quite a number of papers, some of which are reviewed in:

MR2285047 (2008c:53079) Sternheimer, Daniel. The geometry of space-time and its deformations from a physical perspective. From geometry to quantum mechanics, 287–301, Progr. Math., 252, Birkhäuser Boston, Boston, MA, 2007

http://monge.u-bourgogne.fr/d.sternh/papers/PiMOmori-DS.pdf

This is a flexible general framework, based on quite a number of papers, some of which are reviewed in:

MR2285047 (2008c:53079) Sternheimer, Daniel. The geometry of space-time and its deformations from a physical perspective. From geometry to quantum mechanics, 287–301, Progr. Math., 252, Birkhäuser Boston, Boston, MA, 2007

http://monge.u-bourgogne.fr/d.sternh/papers/PiMOmori-DS.pdf

### 2011/11/28

#### Algebraic Geometry Seminar

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

Comparison with Gieseker stability and slope stability via Bridgeland's stability (JAPANESE)

**Kotaro Kawatani**(Kyoto University)Comparison with Gieseker stability and slope stability via Bridgeland's stability (JAPANESE)

[ Abstract ]

In this talk we compare two classical notions of stability (Gieseker stability and slope stability) for sheaves on K3 surfaces by using stability conditions which was introduced by Bridgeland. As a consequence of this work, we give a classification of 2 dimensional moduli spaces of sheaves on K3 surface depending on the rank of the sheaves.

In this talk we compare two classical notions of stability (Gieseker stability and slope stability) for sheaves on K3 surfaces by using stability conditions which was introduced by Bridgeland. As a consequence of this work, we give a classification of 2 dimensional moduli spaces of sheaves on K3 surface depending on the rank of the sheaves.

#### Seminar on Geometric Complex Analysis

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

An ampleness criterion with the extendability of singular positive metrics (JAPANESE)

**Shin-ichi Matsumura**(University of Tokyo)An ampleness criterion with the extendability of singular positive metrics (JAPANESE)

[ Abstract ]

Coman, Guedj and Zeriahi proved that, for an ample line bundle $L$ on a projective manifold $X$, any singular positive metric on the line bundle $L|_{V}$ along a subvariety $V \subset X$ can be extended to a global singular positive metric of $L$. In this talk, we prove that the extendability of singular positive metrics on a line bundle along a subvariety implies the ampleness of the line bundle.

Coman, Guedj and Zeriahi proved that, for an ample line bundle $L$ on a projective manifold $X$, any singular positive metric on the line bundle $L|_{V}$ along a subvariety $V \subset X$ can be extended to a global singular positive metric of $L$. In this talk, we prove that the extendability of singular positive metrics on a line bundle along a subvariety implies the ampleness of the line bundle.

### 2011/11/25

#### Colloquium

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

Nonlinear dispersive evolution equations (JAPANESE)

**SHIMOMURA Akihiro**(Graduate School of mathematical Sciences, University of Tokyo)Nonlinear dispersive evolution equations (JAPANESE)

[ Abstract ]

I will talk about the time evolution of solutions to nonlinear dispersive equations.

I will talk about the time evolution of solutions to nonlinear dispersive equations.

### 2011/11/24

#### Lectures

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

Stability of topological phases of matter (ENGLISH)

**Spyridon Michalakis**(Caltech)Stability of topological phases of matter (ENGLISH)

### 2011/11/22

#### Operator Algebra Seminars

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

Stability of topological phases of matter (ENGLISH)

**( Institute for Quantum Information and Matter (Caltech))**

Spyridon MichalakisSpyridon Michalakis

Stability of topological phases of matter (ENGLISH)

[ Abstract ]

The first lecture will be an introduction to quantum mechanics and a proof of Lieb-Robinson bounds for constant range interaction Hamiltonians. The second lecture will build on the first to prove a powerful lemma on the transformation of the interactions of generic gapped Hamiltonians to a new set of rapidly-decaying interactions that commute with the groundstate subspace. I call this "The Energy Filtering Lemma". Then, the third lecture will be on the construction of the Spectral Flow unitary (Quasi-adiabatic evolution) and its properties; in particular, the perfect simulation of the evolution of the groundstate subspace within a gapped path. I will end with a presentation of the recent result on the stability of the spectral gap for frustration-free Hamiltonians, highlighting how the previous three lectures fit into the proof.

The first lecture will be an introduction to quantum mechanics and a proof of Lieb-Robinson bounds for constant range interaction Hamiltonians. The second lecture will build on the first to prove a powerful lemma on the transformation of the interactions of generic gapped Hamiltonians to a new set of rapidly-decaying interactions that commute with the groundstate subspace. I call this "The Energy Filtering Lemma". Then, the third lecture will be on the construction of the Spectral Flow unitary (Quasi-adiabatic evolution) and its properties; in particular, the perfect simulation of the evolution of the groundstate subspace within a gapped path. I will end with a presentation of the recent result on the stability of the spectral gap for frustration-free Hamiltonians, highlighting how the previous three lectures fit into the proof.

#### Tuesday Seminar on Topology

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

Quantum and homological representations of braid groups (JAPANESE)

**Toshitake Kohno**(The University of Tokyo)Quantum and homological representations of braid groups (JAPANESE)

[ Abstract ]

Homological representations of braid groups are defined as

the action of homeomorphisms of a punctured disk on

the homology of an abelian covering of its configuration space.

These representations were extensively studied by Lawrence,

Krammer and Bigelow. In this talk we show that specializations

of the homological representations of braid groups

are equivalent to the monodromy of the KZ equation with

values in the space of null vectors in the tensor product

of Verma modules when the parameters are generic.

To prove this we use representations of the solutions of the

KZ equation by hypergeometric integrals due to Schechtman,

Varchenko and others.

In the case of special parameters these representations

are extended to quantum representations of mapping

class groups. We describe the images of such representations

and show that the images of any Johnson subgroups

contain non-abelian free groups if the genus and the

level are sufficiently large. The last part is a joint

work with Louis Funar.

Homological representations of braid groups are defined as

the action of homeomorphisms of a punctured disk on

the homology of an abelian covering of its configuration space.

These representations were extensively studied by Lawrence,

Krammer and Bigelow. In this talk we show that specializations

of the homological representations of braid groups

are equivalent to the monodromy of the KZ equation with

values in the space of null vectors in the tensor product

of Verma modules when the parameters are generic.

To prove this we use representations of the solutions of the

KZ equation by hypergeometric integrals due to Schechtman,

Varchenko and others.

In the case of special parameters these representations

are extended to quantum representations of mapping

class groups. We describe the images of such representations

and show that the images of any Johnson subgroups

contain non-abelian free groups if the genus and the

level are sufficiently large. The last part is a joint

work with Louis Funar.

< Previous 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188 Next >