## Seminar information archive

Seminar information archive ～10/22｜Today's seminar 10/23 | Future seminars 10/24～

#### Lie Groups and Representation Theory

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

Categorification of cluster algebras arising from unipotent subgroups of non-simply laced Lie groups (ENGLISH)

**Laurant Demonet**(Nagoya University)Categorification of cluster algebras arising from unipotent subgroups of non-simply laced Lie groups (ENGLISH)

[ Abstract ]

We introduce an abstract framework to categorify some antisymetrizable cluster algebras by using actions of finite groups on stably 2-Calabi-Yau exact categories. We introduce the notion of the equivariant category and, with similar technics as in [K], [CK], [GLS1], [GLS2], [DK], [FK], [P], we construct some examples of such categorifications. For example, if we let Z/2Z act on the category of representations of the preprojective algebra of type A2n-1 via the only non trivial action on the diagram, we obtain the cluster structure on the coordinate ring of the maximal unipotent subgroup of the semi-simple Lie group of type Bn [D]. Hence, we can get relations between the cluster algebras categorified by some exact subcategories of these two categories. We also prove by the same methods as in [FK] a conjecture of Fomin and Zelevinsky stating that the cluster monomials are linearly independent.

References

[CK] P. Caldero, B. Keller, From triangulated categories to cluster algebras, Invent. Math. 172 (2008), no. 1, 169--211.

[DK] R. Dehy, B. Keller, On the combinatorics of rigid objects in 2-Calabi-Yau categories, arXiv: 0709.0882.

[D] L. Demonet, Cluster algebras and preprojective algebras: the non simply-laced case, C. R. Acad. Sci. Paris, Ser. I 346 (2008), 379--384.

[FK] C. Fu, B. Keller, On cluster algebras with coefficients and 2-Calabi-Yau categories, arXiv: 0710.3152.

[GLS1] C. Geiss, B. Leclerc, J. Schröer, Rigid modules over preprojective algebras, Invent. Math. 165 (2006), no. 3, 589--632.

[GLS2] C. Geiss, B. Leclerc, J. Schröer, Cluster algebra structures and semicanoncial bases for unipotent groups, arXiv: math/0703039.

[K] B. Keller, Categorification of acyclic cluster algebras: an introduction, arXiv: 0801.3103.

[P] Y. Palu, Cluster characters for triangulated 2-Calabi--Yau categories, arXiv: math/0703540.

We introduce an abstract framework to categorify some antisymetrizable cluster algebras by using actions of finite groups on stably 2-Calabi-Yau exact categories. We introduce the notion of the equivariant category and, with similar technics as in [K], [CK], [GLS1], [GLS2], [DK], [FK], [P], we construct some examples of such categorifications. For example, if we let Z/2Z act on the category of representations of the preprojective algebra of type A2n-1 via the only non trivial action on the diagram, we obtain the cluster structure on the coordinate ring of the maximal unipotent subgroup of the semi-simple Lie group of type Bn [D]. Hence, we can get relations between the cluster algebras categorified by some exact subcategories of these two categories. We also prove by the same methods as in [FK] a conjecture of Fomin and Zelevinsky stating that the cluster monomials are linearly independent.

References

[CK] P. Caldero, B. Keller, From triangulated categories to cluster algebras, Invent. Math. 172 (2008), no. 1, 169--211.

[DK] R. Dehy, B. Keller, On the combinatorics of rigid objects in 2-Calabi-Yau categories, arXiv: 0709.0882.

[D] L. Demonet, Cluster algebras and preprojective algebras: the non simply-laced case, C. R. Acad. Sci. Paris, Ser. I 346 (2008), 379--384.

[FK] C. Fu, B. Keller, On cluster algebras with coefficients and 2-Calabi-Yau categories, arXiv: 0710.3152.

[GLS1] C. Geiss, B. Leclerc, J. Schröer, Rigid modules over preprojective algebras, Invent. Math. 165 (2006), no. 3, 589--632.

[GLS2] C. Geiss, B. Leclerc, J. Schröer, Cluster algebra structures and semicanoncial bases for unipotent groups, arXiv: math/0703039.

[K] B. Keller, Categorification of acyclic cluster algebras: an introduction, arXiv: 0801.3103.

[P] Y. Palu, Cluster characters for triangulated 2-Calabi--Yau categories, arXiv: math/0703540.

### 2011/11/14

#### GCOE lecture series

17:00-18:00 Room #470 (Graduate School of Math. Sci. Bldg.)

Recovery of weakly coupled system from partial Cauchy data (ENGLISH)

**Oleg Emanouilov**(Colorado State University)Recovery of weakly coupled system from partial Cauchy data (ENGLISH)

[ Abstract ]

We consider the inverse problem for recovery of coefficients of weakly coupled system of elliptic equations in a bounded 2D domain.

We consider the inverse problem for recovery of coefficients of weakly coupled system of elliptic equations in a bounded 2D domain.

#### Algebraic Geometry Seminar

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

On projective manifolds swept out by cubic varieties (JAPANESE)

**Kiwamu Watanabe**(University of Tokyo)On projective manifolds swept out by cubic varieties (JAPANESE)

[ Abstract ]

The structures of embedded complex projective manifolds swept out by varieties with preassigned properties have been studied by several authors. In this talk, we study structures of embedded projective manifolds swept out by cubic varieties.

The structures of embedded complex projective manifolds swept out by varieties with preassigned properties have been studied by several authors. In this talk, we study structures of embedded projective manifolds swept out by cubic varieties.

### 2011/11/10

#### GCOE lecture series

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

Inverse boundary value problem for Schroedinger equation in two dimensions (ENGLISH)

**Oleg Emanouilov**(Colorado State University)Inverse boundary value problem for Schroedinger equation in two dimensions (ENGLISH)

[ Abstract ]

We relax the regularity condition on potentials of Schroedinger equations in uniqueness results on the inverse boundary value problem recently proved in A.Bukhgeim (2008) and O. Imanuvilov, G.Uhlmann and M. Yamamoto (2010).

We relax the regularity condition on potentials of Schroedinger equations in uniqueness results on the inverse boundary value problem recently proved in A.Bukhgeim (2008) and O. Imanuvilov, G.Uhlmann and M. Yamamoto (2010).

#### Applied Analysis

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

Mathematical Modeling of Cellular Electrodiffusion and Osmosis (JAPANESE)

**Yoichiro Mori**(University of Minnesota )Mathematical Modeling of Cellular Electrodiffusion and Osmosis (JAPANESE)

#### Applied Analysis

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

Schoenflies spheres in Sturm attractors (ENGLISH)

**Bernold Fiedler**(Free University of Berlin)Schoenflies spheres in Sturm attractors (ENGLISH)

[ Abstract ]

In gradient systems on compact manifolds the boundary of the unstable manifold of an equilibrium need not be homeomorphic to a sphere, or to any compact manifold.

For scalar parabolic equations in one space dimension, however, we can exlude complications like Reidemeister torsion and the Alexander horned sphere. Instead the boundary is a Schoenflies embedded sphere. This is due to Sturm nodal properties related to the Matano lap number.

In gradient systems on compact manifolds the boundary of the unstable manifold of an equilibrium need not be homeomorphic to a sphere, or to any compact manifold.

For scalar parabolic equations in one space dimension, however, we can exlude complications like Reidemeister torsion and the Alexander horned sphere. Instead the boundary is a Schoenflies embedded sphere. This is due to Sturm nodal properties related to the Matano lap number.

### 2011/11/09

#### Number Theory Seminar

18:00-19:00 Room #056 (Graduate School of Math. Sci. Bldg.)

On extension and restriction of overconvergent isocrystals (ENGLISH)

**Atsushi Shiho**(University of Tokyo)On extension and restriction of overconvergent isocrystals (ENGLISH)

[ Abstract ]

First we explain two theorems concerning (log) extension of overconvergent isocrystals. One is a p-adic analogue of the theorem of logarithmic extension of regular integrable connections, and the other is a p-adic analogue of Zariski-Nagata purity. Next we explain a theorem which says that we can check certain property of overconvergent isocrystals by restricting them to curves.

(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。)

First we explain two theorems concerning (log) extension of overconvergent isocrystals. One is a p-adic analogue of the theorem of logarithmic extension of regular integrable connections, and the other is a p-adic analogue of Zariski-Nagata purity. Next we explain a theorem which says that we can check certain property of overconvergent isocrystals by restricting them to curves.

(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。)

### 2011/11/08

#### Tuesday Seminar on Topology

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

Fiberwise bordism groups and related topics (JAPANESE)

**Shoji Yokura**(Kagoshima University )Fiberwise bordism groups and related topics (JAPANESE)

[ Abstract ]

We have recently introduced the notion of fiberwise bordism. In this talk, after a quick review of some of the classical (co)bordism theories, we will explain motivations of considering fiberwise bordism and some results and connections with other known works, such as M. Kreck's bordism groups of orientation preserving diffeomorphisms and Emerson-Meyer's bivariant K-theory etc. An essential motivation is our recent work towards constructing a bivariant-theoretic analogue (in the sense of Fulton-MacPherson) of Levine-Morel's or Levine-Pandharipande's algebraic cobordism.

We have recently introduced the notion of fiberwise bordism. In this talk, after a quick review of some of the classical (co)bordism theories, we will explain motivations of considering fiberwise bordism and some results and connections with other known works, such as M. Kreck's bordism groups of orientation preserving diffeomorphisms and Emerson-Meyer's bivariant K-theory etc. An essential motivation is our recent work towards constructing a bivariant-theoretic analogue (in the sense of Fulton-MacPherson) of Levine-Morel's or Levine-Pandharipande's algebraic cobordism.

#### Tuesday Seminar of Analysis

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

The University of Tokyo (JSPS Research Fellow))

Stochastic Power-Law Fluid equations: Existence and Uniqueness of weak solutions (joint work with Nobuo Yoshida) (JAPANESE)

**Yutaka Terasawa**(Graduate School of Mathematical Sciences,The University of Tokyo (JSPS Research Fellow))

Stochastic Power-Law Fluid equations: Existence and Uniqueness of weak solutions (joint work with Nobuo Yoshida) (JAPANESE)

#### Seminar on Mathematics for various disciplines

16:30-17:30 Room #052 (Graduate School of Math. Sci. Bldg.)

Interactive Data Visualization challenges, approaches and examples (ENGLISH)

**Ralph Bruckschen**(ベルリン工科大学、MATHEON)Interactive Data Visualization challenges, approaches and examples (ENGLISH)

[ Abstract ]

Data visualization is probably the most important method to analyze scientific datasets. In the time of petaflop supercomputers and high resolution sensors, the visualization of such datasets became a challenge because of the sheer magnitude. Using the latest technology I will describe some of the challenges and approaches to visualize large and massive datasets. The main bottle necks will be explained, as some algorithms and data structures to widen them. Finally I will show some examples of data visualization using a CAVE environment and virtual prototyping from the 3D Labor at the Technical University of Berlin.

Data visualization is probably the most important method to analyze scientific datasets. In the time of petaflop supercomputers and high resolution sensors, the visualization of such datasets became a challenge because of the sheer magnitude. Using the latest technology I will describe some of the challenges and approaches to visualize large and massive datasets. The main bottle necks will be explained, as some algorithms and data structures to widen them. Finally I will show some examples of data visualization using a CAVE environment and virtual prototyping from the 3D Labor at the Technical University of Berlin.

### 2011/11/07

#### GCOE lecture series

17:00-18:00 Room #470 (Graduate School of Math. Sci. Bldg.)

Inverse boundary value problem for Schroedinger equation in two dimensions (ENGLISH)

**Oleg Emanouilov**(Colorado State University)Inverse boundary value problem for Schroedinger equation in two dimensions (ENGLISH)

[ Abstract ]

We relax the regularity condition on potentials of Schroedinger equations in uniqueness results on the inverse boundary value problem recently proved in A.Bukhgeim (2008) and O. Imanuvilov, G.Uhlmann and M. Yamamoto (2010).

We relax the regularity condition on potentials of Schroedinger equations in uniqueness results on the inverse boundary value problem recently proved in A.Bukhgeim (2008) and O. Imanuvilov, G.Uhlmann and M. Yamamoto (2010).

#### Algebraic Geometry Seminar

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

Okounkov bodies and Seshadri constants (JAPANESE)

**Atsushi Ito**(University of Tokyo)Okounkov bodies and Seshadri constants (JAPANESE)

[ Abstract ]

Okounkov bodies, which are convex bodies associated to big line bundles, have rich information of the line bundles. On the other hand, Seshadri constants are invariants which measure the positivities of line bundles. In this talk, I will explain a relation between Okounkov bodies and Seshadri constants.

Okounkov bodies, which are convex bodies associated to big line bundles, have rich information of the line bundles. On the other hand, Seshadri constants are invariants which measure the positivities of line bundles. In this talk, I will explain a relation between Okounkov bodies and Seshadri constants.

#### Seminar on Geometric Complex Analysis

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

Oka's extra-zero problem and related topics (JAPANESE)

**Junjiro Nocuchi**(University of Tokyo)Oka's extra-zero problem and related topics (JAPANESE)

[ Abstract ]

The main part of this talk is a joint work with my colleagues, M. Abe and S. Hamano. After the solution of Cousin II problem by K. Oka III in 1939, he thought an extra-zero problem in 1945 (his posthumous paper) asking if it is possible to solve an arbitrarily given Cousin II problem adding some extra-zeros whose support is disjoint from the given one. Some special case was affirmatively confirmed in dimension two and a counter-example in dimension three or more was obtained. We will give a complete solution of this problem with examples and to discuss some new questions. An example on a toric variety of which idea is based on K. Stein's paper in 1941 has some special interest and will be discussed. I would like also to discuss some analytic intersections form the viewpoint of Nevanlinna theory.

The main part of this talk is a joint work with my colleagues, M. Abe and S. Hamano. After the solution of Cousin II problem by K. Oka III in 1939, he thought an extra-zero problem in 1945 (his posthumous paper) asking if it is possible to solve an arbitrarily given Cousin II problem adding some extra-zeros whose support is disjoint from the given one. Some special case was affirmatively confirmed in dimension two and a counter-example in dimension three or more was obtained. We will give a complete solution of this problem with examples and to discuss some new questions. An example on a toric variety of which idea is based on K. Stein's paper in 1941 has some special interest and will be discussed. I would like also to discuss some analytic intersections form the viewpoint of Nevanlinna theory.

### 2011/11/04

#### Colloquium

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

Cross ratio, and all that

(JAPANESE)

**KANAI Masahiko**(Graduate School of Mathematical Sciences, University of Tokyo)Cross ratio, and all that

(JAPANESE)

[ Abstract ]

Although the origin of cross ratio goes back to ancient Greek mathematics, new discoveries about it has been made even in the past few decades. It seems that our understanding as to cross ratio is still limited. I am going to show you the present status and my own concerns, as well.

Although the origin of cross ratio goes back to ancient Greek mathematics, new discoveries about it has been made even in the past few decades. It seems that our understanding as to cross ratio is still limited. I am going to show you the present status and my own concerns, as well.

### 2011/11/02

#### Number Theory Seminar

16:30-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Hypergeometric series and arithmetic-geometric mean over 2-adic fields (JAPANESE)

**Kensaku Kinjo**(University of Tokyo)Hypergeometric series and arithmetic-geometric mean over 2-adic fields (JAPANESE)

[ Abstract ]

Dwork proved that the Gaussian hypergeometric function on p-adic numbers

can be extended to a function which takes values of the unit roots of

ordinary elliptic curves over a finite field of characteristic p>2.

We present an analogous theory in the case p=2.

As an application, we give a relation between the canonical lift

and the unit root of an elliptic curve over a finite field of

characteristic 2

by using the 2-adic arithmetic-geometric mean.

Dwork proved that the Gaussian hypergeometric function on p-adic numbers

can be extended to a function which takes values of the unit roots of

ordinary elliptic curves over a finite field of characteristic p>2.

We present an analogous theory in the case p=2.

As an application, we give a relation between the canonical lift

and the unit root of an elliptic curve over a finite field of

characteristic 2

by using the 2-adic arithmetic-geometric mean.

### 2011/11/01

#### Tuesday Seminar on Topology

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

Motivic Milnor fibers and Jordan normal forms of monodromies (JAPANESE)

**Kiyoshi Takeuchi**(University of Tsukuba)Motivic Milnor fibers and Jordan normal forms of monodromies (JAPANESE)

[ Abstract ]

We introduce a method to calculate the equivariant

Hodge-Deligne numbers of toric hypersurfaces.

Then we apply it to motivic Milnor

fibers introduced by Denef-Loeser and study the Jordan

normal forms of the local and global monodromies

of polynomials maps in various situations.

Especially we focus our attention on monodromies

at infinity studied by many people. The results will be

explicitly described by the ``convexity" of

the Newton polyhedra of polynomials. This is a joint work

with Y. Matsui and A. Esterov.

We introduce a method to calculate the equivariant

Hodge-Deligne numbers of toric hypersurfaces.

Then we apply it to motivic Milnor

fibers introduced by Denef-Loeser and study the Jordan

normal forms of the local and global monodromies

of polynomials maps in various situations.

Especially we focus our attention on monodromies

at infinity studied by many people. The results will be

explicitly described by the ``convexity" of

the Newton polyhedra of polynomials. This is a joint work

with Y. Matsui and A. Esterov.

### 2011/10/31

#### Algebraic Geometry Seminar

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

Minimal model theory for log surfaces (JAPANESE)

**Osamu Fujino**(Kyoto University)Minimal model theory for log surfaces (JAPANESE)

[ Abstract ]

We discuss the log minimal model theory for log sur- faces. We show that the log minimal model program, the finite generation of log canonical rings, and the log abundance theorem for log surfaces hold true under assumptions weaker than the usual framework of the log minimal model theory.

We discuss the log minimal model theory for log sur- faces. We show that the log minimal model program, the finite generation of log canonical rings, and the log abundance theorem for log surfaces hold true under assumptions weaker than the usual framework of the log minimal model theory.

#### PDE Real Analysis Seminar

13:30-14:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Stationary Weak Solutions of the Navier-Stokes Equations Past an Obstacle (ENGLISH)

**Horst Heck**

(Technische Universität Darmstadt)Stationary Weak Solutions of the Navier-Stokes Equations Past an Obstacle (ENGLISH)

[ Abstract ]

Consider the stationary Navier-Stokes equations in an exterior smooth domain $\\Omega$. If the flow condition $u_\\infty$ for $u$ at infinity is non-zero and the external force $f\\in \\dot H^{-1}_2(\\Omega)$ is given Leray constructed a weak solution $u\\in \\dot H^1_2(\\Omega)$, the homogeneous Sobolev space, with $u-u_\\infty\\in L^6(\\Omega)$.

We show that if in addition $f\\in \\dot H^{-1}_q(\\Omega)$ for some $q\\in (4/3,4)$ then the weak solution has the property $u-u_\\infty\\in L^{4q/(4-q)}(\\Omega)$.

This additional integrability implies that $u$ satisfies the energy identity. Further consequences are uniqueness results for small $u_\\infty$ and $f$ and continuous dependence of the solution with respect to $u_\\infty$.

The presented results are joint work with Hyunseok Kim and Hideo Kozono.

Consider the stationary Navier-Stokes equations in an exterior smooth domain $\\Omega$. If the flow condition $u_\\infty$ for $u$ at infinity is non-zero and the external force $f\\in \\dot H^{-1}_2(\\Omega)$ is given Leray constructed a weak solution $u\\in \\dot H^1_2(\\Omega)$, the homogeneous Sobolev space, with $u-u_\\infty\\in L^6(\\Omega)$.

We show that if in addition $f\\in \\dot H^{-1}_q(\\Omega)$ for some $q\\in (4/3,4)$ then the weak solution has the property $u-u_\\infty\\in L^{4q/(4-q)}(\\Omega)$.

This additional integrability implies that $u$ satisfies the energy identity. Further consequences are uniqueness results for small $u_\\infty$ and $f$ and continuous dependence of the solution with respect to $u_\\infty$.

The presented results are joint work with Hyunseok Kim and Hideo Kozono.

#### Seminar on Geometric Complex Analysis

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

Classification of Moishezon twistor spaces on 4CP^2 (JAPANESE)

**Nobuhiro Honda**(Tohoku Univeristy)Classification of Moishezon twistor spaces on 4CP^2 (JAPANESE)

### 2011/10/29

#### Infinite Analysis Seminar Tokyo

11:00-14:30 Room #117 (Graduate School of Math. Sci. Bldg.)

CKP Hierarchy, Bosonic Tau Function, Bosonization Formulae and Orthogonal Polynomials both in Odd and Even Variables

(based on a joint work with Johan van de Leur and Takahiro Shiota) (ENGLISH)

Kernel function identities associated with van Diejen's $q$-difference operators

and transformation formulas for multiple $q$-hypergeometric series (JAPANESE)

**Alexander Orlov**(Nonlinear Wave Processes Laboratory, Oceanology Institute (Moscow)) 11:00-12:00CKP Hierarchy, Bosonic Tau Function, Bosonization Formulae and Orthogonal Polynomials both in Odd and Even Variables

(based on a joint work with Johan van de Leur and Takahiro Shiota) (ENGLISH)

[ Abstract ]

We develop the theory of CKP hierarchy introduced in the papers of Kyoto school where the CKP tau function is written as a vacuum expectation value in terms of free bosons. We show that a sort of odd currents naturaly appear. We consider bosonization formulae which relate bosonic Fock vectors to polynomials in even and odd Grassmannian variables, where both sets play a role of higher times.

We develop the theory of CKP hierarchy introduced in the papers of Kyoto school where the CKP tau function is written as a vacuum expectation value in terms of free bosons. We show that a sort of odd currents naturaly appear. We consider bosonization formulae which relate bosonic Fock vectors to polynomials in even and odd Grassmannian variables, where both sets play a role of higher times.

**Yasuho Masuda**(Kobe Univ. ) 13:30-14:30Kernel function identities associated with van Diejen's $q$-difference operators

and transformation formulas for multiple $q$-hypergeometric series (JAPANESE)

### 2011/10/26

#### Seminar on Probability and Statistics

15:00-16:10 Room #000 (Graduate School of Math. Sci. Bldg.)

Statistical models constructed by optimal stationary coupling (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/04.html

**SEI, Tomonari**(Department of Mathematics, Keio University)Statistical models constructed by optimal stationary coupling (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/04.html

### 2011/10/25

#### Tuesday Seminar on Topology

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

Circle-valued Morse theory for complex hyperplane arrangements (ENGLISH)

**Andrei Pajitnov**(Univ. de Nantes, Univ. of Tokyo)Circle-valued Morse theory for complex hyperplane arrangements (ENGLISH)

[ Abstract ]

Let A be a complex hyperplane arrangement

in an n-dimensional complex vector space V.

Denote by H the union of the hyperplanes

and by M the complement to H in V.

We develop the real-valued and circle-valued Morse

theory on M. We prove that if A is essential then

M has the homotopy type of a space

obtained from a finite n-dimensional

CW complex fibered over a circle,

by attaching several cells of dimension n.

We compute the Novikov homology of M and show

that its structure is similar to the

homology with generic local coefficients:

it vanishes for all dimensions except n.

This is a joint work with Toshitake Kohno.

Let A be a complex hyperplane arrangement

in an n-dimensional complex vector space V.

Denote by H the union of the hyperplanes

and by M the complement to H in V.

We develop the real-valued and circle-valued Morse

theory on M. We prove that if A is essential then

M has the homotopy type of a space

obtained from a finite n-dimensional

CW complex fibered over a circle,

by attaching several cells of dimension n.

We compute the Novikov homology of M and show

that its structure is similar to the

homology with generic local coefficients:

it vanishes for all dimensions except n.

This is a joint work with Toshitake Kohno.

#### Lie Groups and Representation Theory

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

Localization of Cohomological Induction (ENGLISH)

**Yoshiki Oshima**(Graduate School of Mathematical Sciences, the University of Tokyo)Localization of Cohomological Induction (ENGLISH)

[ Abstract ]

Cohomological induction is defined for (g,K)-modules in an algebraic way and construct important representations such as (Harish-Chandra modules of) discrete series representations,

principal series representations and Zuckerman's modules of

semisimple Lie groups.

Hecht, Milicic, Schmid, and Wolf proved that modules induced from

one-dimensional representations of Borel subalgebra can be realized as D-modules on the flag variety.

In this talk, we show a similar result for modules induced from

more general representations.

Cohomological induction is defined for (g,K)-modules in an algebraic way and construct important representations such as (Harish-Chandra modules of) discrete series representations,

principal series representations and Zuckerman's modules of

semisimple Lie groups.

Hecht, Milicic, Schmid, and Wolf proved that modules induced from

one-dimensional representations of Borel subalgebra can be realized as D-modules on the flag variety.

In this talk, we show a similar result for modules induced from

more general representations.

### 2011/10/22

#### Infinite Analysis Seminar Tokyo

13:30-16:00 Room #117 (Graduate School of Math. Sci. Bldg.)

Department of Mathematics) 13:30-14:30

Quantization of Quasimaps' Spaces (joint work with M. Finkelberg) (ENGLISH)

Instituteof Biochemical Physics) 15:00-16:00

Quantum integrable models with elliptic R-matrices

and elliptic hypergeometric series (ENGLISH)

**Leonid Rybnikov**(IITP, and State University Higher School of Economics,Department of Mathematics) 13:30-14:30

Quantization of Quasimaps' Spaces (joint work with M. Finkelberg) (ENGLISH)

[ Abstract ]

Quasimaps' space Z_d (also known as Drinfeld's Zastava space) is a

remarkable compactification of the space of based degree d maps from

the projective line to the flag variety of type A. The space Z_d has a

natural Poisson structure,

which goes back to Atiyah and Hitchin. We describe

the Quasimaps' space as some quiver variety, and define the

Atiyah-Hitchin Poisson structure in quiver terms.

This gives a natural way to quantize this Poisson structure.

The quantization of the coordinate ring of the Quasimaps' space turns

to be some natural subquotient of the Yangian of type A.

I will also discuss some generalization of this result to the BCD types.

Quasimaps' space Z_d (also known as Drinfeld's Zastava space) is a

remarkable compactification of the space of based degree d maps from

the projective line to the flag variety of type A. The space Z_d has a

natural Poisson structure,

which goes back to Atiyah and Hitchin. We describe

the Quasimaps' space as some quiver variety, and define the

Atiyah-Hitchin Poisson structure in quiver terms.

This gives a natural way to quantize this Poisson structure.

The quantization of the coordinate ring of the Quasimaps' space turns

to be some natural subquotient of the Yangian of type A.

I will also discuss some generalization of this result to the BCD types.

**Anton Zabrodin**(Instituteof Biochemical Physics) 15:00-16:00

Quantum integrable models with elliptic R-matrices

and elliptic hypergeometric series (ENGLISH)

[ Abstract ]

Intertwining operators for infinite-dimensional representations of the

Sklyanin algebra with spins l and -l-1 are constructed using the technique of

intertwining vectors for elliptic L-operator. They are expressed in

terms of

elliptic hypergeometric series with operator argument. The intertwining

operators obtained (W-operators) serve as building blocks for the

elliptic R-matrix

which intertwines tensor product of two L-operators taken in

infinite-dimensional

representations of the Sklyanin algebra with arbitrary spin. The

Yang-Baxter equation

for this R-matrix follows from simpler equations of the star-triangle

type for the

W-operators. A natural graphic representation of the objects and

equations involved

in the construction is used.

Intertwining operators for infinite-dimensional representations of the

Sklyanin algebra with spins l and -l-1 are constructed using the technique of

intertwining vectors for elliptic L-operator. They are expressed in

terms of

elliptic hypergeometric series with operator argument. The intertwining

operators obtained (W-operators) serve as building blocks for the

elliptic R-matrix

which intertwines tensor product of two L-operators taken in

infinite-dimensional

representations of the Sklyanin algebra with arbitrary spin. The

Yang-Baxter equation

for this R-matrix follows from simpler equations of the star-triangle

type for the

W-operators. A natural graphic representation of the objects and

equations involved

in the construction is used.

### 2011/10/20

#### GCOE Seminars

16:30-18:00 Room #270 (Graduate School of Math. Sci. Bldg.)

On reconstruction of Lame coefficients from partial Cauchy data (ENGLISH)

**O. Emanouilov**(Colorado State University)On reconstruction of Lame coefficients from partial Cauchy data (ENGLISH)

[ Abstract ]

For the isotropic Lame system, we prove that if the Lame coefficient ¥mu is a positive constant, then both Lame coefficients can be recovered from the partial Cauchy data.

For the isotropic Lame system, we prove that if the Lame coefficient ¥mu is a positive constant, then both Lame coefficients can be recovered from the partial Cauchy data.

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