## Seminar information archive

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

### 2014/05/13

#### Tuesday Seminar of Analysis

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

Ultra-differentiable classes and intersection theorems (JAPANESE)

**Yasunori Okada**(Graduate School of Science and Technology, Chiba University)Ultra-differentiable classes and intersection theorems (JAPANESE)

[ Abstract ]

There are two ways to define notions of

ultra-differentiability: one in terms of estimates on derivatives, and

the other in terms of growth properties of Fourier transforms of

suitably localized functions.

In this talk, we study the relation between BMT-classes and

inhomogeneous Gevrey classes, which are examples of such two kinds of

notions of ultra-differentiability.

We also mention intersection theorems on these classes.

This talk is based on a joint work with Otto Liess (Bologna University).

There are two ways to define notions of

ultra-differentiability: one in terms of estimates on derivatives, and

the other in terms of growth properties of Fourier transforms of

suitably localized functions.

In this talk, we study the relation between BMT-classes and

inhomogeneous Gevrey classes, which are examples of such two kinds of

notions of ultra-differentiability.

We also mention intersection theorems on these classes.

This talk is based on a joint work with Otto Liess (Bologna University).

#### Seminar on Probability and Statistics

13:00-14:10 Room #052 (Graduate School of Math. Sci. Bldg.)

On High Frequency Estimation of the Frictionless Price: The Use of Observed Liquidity Variables (ENGLISH)

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2014/01.html

**Selma Chaker**(Bank of Canada)On High Frequency Estimation of the Frictionless Price: The Use of Observed Liquidity Variables (ENGLISH)

[ Abstract ]

Observed high-frequency prices are always contaminated with liquidity costs or market microstructure noise. Inspired by the market microstructure literature, I explicitly model this noise and remove it from observed prices to obtain an estimate of the frictionless price. I then formally test whether the prices adjusted for the estimated liquidity costs are either totally or partially free from noise. If the liquidity costs are only partially removed, the residual noise is smaller and closer to an exogenous white noise than the original noise is. To illustrate my approach, I use the adjusted prices to improve volatility estimation in the presence of noise. If the noise is totally absorbed, I show that the sum of squared returns - which would be inconsistent for return variance when based on observed returns - becomes consistent when based on adjusted returns.

[ Reference URL ]Observed high-frequency prices are always contaminated with liquidity costs or market microstructure noise. Inspired by the market microstructure literature, I explicitly model this noise and remove it from observed prices to obtain an estimate of the frictionless price. I then formally test whether the prices adjusted for the estimated liquidity costs are either totally or partially free from noise. If the liquidity costs are only partially removed, the residual noise is smaller and closer to an exogenous white noise than the original noise is. To illustrate my approach, I use the adjusted prices to improve volatility estimation in the presence of noise. If the noise is totally absorbed, I show that the sum of squared returns - which would be inconsistent for return variance when based on observed returns - becomes consistent when based on adjusted returns.

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2014/01.html

#### Tuesday Seminar on Topology

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

Transverse projective structures of foliations and deformations of the Godbillon-Vey class (JAPANESE)

**Taro Asuke**(The University of Tokyo)Transverse projective structures of foliations and deformations of the Godbillon-Vey class (JAPANESE)

[ Abstract ]

Given a smooth family of foliations, we can define the derivative of the Godbillon-Vey class

with respect to the family. The derivative is known to be represented in terms of the projective

Schwarzians of holonomy maps. In this talk, we will study transverse projective structures

and connections, and show that the derivative is in fact determined by the projective structure

and the family.

Given a smooth family of foliations, we can define the derivative of the Godbillon-Vey class

with respect to the family. The derivative is known to be represented in terms of the projective

Schwarzians of holonomy maps. In this talk, we will study transverse projective structures

and connections, and show that the derivative is in fact determined by the projective structure

and the family.

#### Lie Groups and Representation Theory

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

)

Global q,t-hypergeometric and q-Whittaker functions (ENGLISH)

**Ivan Cherednik**(The University of North Carolina at Chapel Hill, RIMS)

Global q,t-hypergeometric and q-Whittaker functions (ENGLISH)

[ Abstract ]

The lectures will be devoted to the new theory of global

difference hypergeometric and Whittaker functions, one of

the major applications of the double affine Hecke algebras

and a breakthrough in the classical harmonic analysis. They

integrate the Ruijsenaars-Macdonald difference QMBP and

"Q-Toda" (any root systems), and are analytic everywhere

("global") with superb asymptotic behavior.

The definition of the global functions was suggested about

14 years ago; it is conceptually different from the definition

Heine gave in 1846, which remained unchanged and unchallenged

since then. Algebraically, the new functions are closer to

Bessel functions than to the classical hypergeometric and

Whittaker functions. The analytic theory of these functions was

completed only recently (the speaker and Jasper Stokman).

The construction is based on DAHA. The global functions are defined

as reproducing kernels of Fourier-DAHA transforms. Their

specializations are Macdonald polynomials, which is a powerful

generalization of the Shintani and Casselman-Shalika p-adic formulas.

If time permits, the connection of the Harish-Chandra theory of global

q-Whittaker functions will be discussed with the Givental-Lee formula

(Gromov-Witten invariants of flag varieties) and its generalizations due

to Braverman and Finkelberg (algebraic theory of affine flag varieties).

The lectures will be devoted to the new theory of global

difference hypergeometric and Whittaker functions, one of

the major applications of the double affine Hecke algebras

and a breakthrough in the classical harmonic analysis. They

integrate the Ruijsenaars-Macdonald difference QMBP and

"Q-Toda" (any root systems), and are analytic everywhere

("global") with superb asymptotic behavior.

The definition of the global functions was suggested about

14 years ago; it is conceptually different from the definition

Heine gave in 1846, which remained unchanged and unchallenged

since then. Algebraically, the new functions are closer to

Bessel functions than to the classical hypergeometric and

Whittaker functions. The analytic theory of these functions was

completed only recently (the speaker and Jasper Stokman).

The construction is based on DAHA. The global functions are defined

as reproducing kernels of Fourier-DAHA transforms. Their

specializations are Macdonald polynomials, which is a powerful

generalization of the Shintani and Casselman-Shalika p-adic formulas.

If time permits, the connection of the Harish-Chandra theory of global

q-Whittaker functions will be discussed with the Givental-Lee formula

(Gromov-Witten invariants of flag varieties) and its generalizations due

to Braverman and Finkelberg (algebraic theory of affine flag varieties).

### 2014/05/12

#### Seminar on Geometric Complex Analysis

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

Resolution of singularities via Newton polyhedra and its application to analysis (JAPANESE)

**Joe Kamimoto**(Kyushu university)Resolution of singularities via Newton polyhedra and its application to analysis (JAPANESE)

[ Abstract ]

In the 1970s, A. N. Varchenko precisely investigated the leading term of the asymptotic expansion of an oscillatory integral with real analytic phase by using the geometry of the Newton polyhedron of the phase. Since his study, the importance of the resolution of singularities by means of Newton polyhedra has been strongly recognized. The purpose of this talk is to consider studies around this theme and to explain their relationship with some problems in several complex variables.

In the 1970s, A. N. Varchenko precisely investigated the leading term of the asymptotic expansion of an oscillatory integral with real analytic phase by using the geometry of the Newton polyhedron of the phase. Since his study, the importance of the resolution of singularities by means of Newton polyhedra has been strongly recognized. The purpose of this talk is to consider studies around this theme and to explain their relationship with some problems in several complex variables.

#### Algebraic Geometry Seminar

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

Higher Nash blowup on normal toric varieties and a higher order version of Nobile's theorem (ENGLISH)

**Andrés Daniel Duarte**(Institut de Mathématiques de Toulouse)Higher Nash blowup on normal toric varieties and a higher order version of Nobile's theorem (ENGLISH)

[ Abstract ]

The higher Nash blowup of an algebraic variety replaces singular points with limits of certain vector spaces carrying first or higher order data associated to the variety at non-singular points. In the case of normal toric varieties, the higher Nash blowup has a combinatorial description in terms of the Gröbner fan. This description will allows us to prove a higher version of Nobile's theorem in this context: for a normal toric variety, the higher Nash blowup is an isomorphism if and only if the variety is non-singular. We will also present some further observations coming from computational experiments.

The higher Nash blowup of an algebraic variety replaces singular points with limits of certain vector spaces carrying first or higher order data associated to the variety at non-singular points. In the case of normal toric varieties, the higher Nash blowup has a combinatorial description in terms of the Gröbner fan. This description will allows us to prove a higher version of Nobile's theorem in this context: for a normal toric variety, the higher Nash blowup is an isomorphism if and only if the variety is non-singular. We will also present some further observations coming from computational experiments.

#### Numerical Analysis Seminar

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

On the finite difference approximation for blow-up solutions of the nonlinear wave equation (JAPANESE)

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

**Chien-Hong Cho**(National Chung Cheng University)On the finite difference approximation for blow-up solutions of the nonlinear wave equation (JAPANESE)

[ Abstract ]

We consider in this paper the 1-dim nonlinear wave equation $u_{tt}=u_{xx}+u^{1+\\alpha}$ $(\\alpha > 0)$ and its finite difference analogue. It is known that the solutions of the current equation becomes unbounded in finite time, a phenomenon which is often called blow-up. Numerical approaches on such kind of problems are widely investigated in the last decade. However, those results are mainly about parabolic blow-up problems. Compared with the parabolic ones, there is a remarkable property for the solution of the nonlinear wave equation -- the existence of the blow-up curve. That is, even though the solution has become unbounded at certain points, the solution continues to exist at other points and blows up at later times. We are concerned in this paper as to how a finite difference scheme can reproduce such a phenomenon.

[ Reference URL ]We consider in this paper the 1-dim nonlinear wave equation $u_{tt}=u_{xx}+u^{1+\\alpha}$ $(\\alpha > 0)$ and its finite difference analogue. It is known that the solutions of the current equation becomes unbounded in finite time, a phenomenon which is often called blow-up. Numerical approaches on such kind of problems are widely investigated in the last decade. However, those results are mainly about parabolic blow-up problems. Compared with the parabolic ones, there is a remarkable property for the solution of the nonlinear wave equation -- the existence of the blow-up curve. That is, even though the solution has become unbounded at certain points, the solution continues to exist at other points and blows up at later times. We are concerned in this paper as to how a finite difference scheme can reproduce such a phenomenon.

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

### 2014/05/08

#### Geometry Colloquium

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

On non Hamiltonian volume minimizing H-stable Lagrangian tori (JAPANESE)

**Hajime Ono**(Saitama University)On non Hamiltonian volume minimizing H-stable Lagrangian tori (JAPANESE)

[ Abstract ]

Y. –G. Oh investigated the volume of Lagrangian submanifolds in a Kaehler manifold and introduced the notion of Hamiltonian minimality, Hamiltonian stability and Hamiltonian volume minimizing property. For example, it is known that standard tori in complex Euclidean spaces and torus orbits in complex projective spaces are H-minimal and H-stable. In this talk I show that

1. Almost all of standard tori in the complex Euclidean space of dimension greater than two are not Hamiltonian volume minimizing.

2. There are non Hamiltonian volume minimizing torus orbits in any compact toric Kaehler manifold of dimension greater than two.

Y. –G. Oh investigated the volume of Lagrangian submanifolds in a Kaehler manifold and introduced the notion of Hamiltonian minimality, Hamiltonian stability and Hamiltonian volume minimizing property. For example, it is known that standard tori in complex Euclidean spaces and torus orbits in complex projective spaces are H-minimal and H-stable. In this talk I show that

1. Almost all of standard tori in the complex Euclidean space of dimension greater than two are not Hamiltonian volume minimizing.

2. There are non Hamiltonian volume minimizing torus orbits in any compact toric Kaehler manifold of dimension greater than two.

### 2014/05/07

#### Mathematical Biology Seminar

14:50-16:20 Room #128 (Graduate School of Math. Sci. Bldg.)

Asymptotic behavior of differential equation systems for age-structured epidemic models (JAPANESE)

**Yoichi Enatsu**(Graduate School of Mathematical Sciences, University fo Tokyo)Asymptotic behavior of differential equation systems for age-structured epidemic models (JAPANESE)

### 2014/05/02

#### Colloquium

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

From hyperplane arrangements to Deligne-Mumford moduli spaces: Kohno-Drinfeld way (ENGLISH)

**A.P. Veselov**(Loughborough, UK and Tokyo, Japan)From hyperplane arrangements to Deligne-Mumford moduli spaces: Kohno-Drinfeld way (ENGLISH)

[ Abstract ]

Gaudin subalgebras are abelian Lie subalgebras of maximal

dimension spanned by generators of the Kohno-Drinfeld Lie algebra t_n,

associated to A-type hyperplane arrangement.

It turns out that Gaudin subalgebras form a smooth algebraic variety

isomorphic to the Deligne-Mumford moduli space \\bar M_{0,n+1} of

stable genus zero curves with n+1 marked points.

A real version of this result allows to describe the

moduli space of integrable n-dimensional tops and

separation coordinates on the unit sphere

in terms of the geometry of Stasheff polytope.

The talk is based on joint works with L. Aguirre and G. Felder and with K.

Schoebel.

Gaudin subalgebras are abelian Lie subalgebras of maximal

dimension spanned by generators of the Kohno-Drinfeld Lie algebra t_n,

associated to A-type hyperplane arrangement.

It turns out that Gaudin subalgebras form a smooth algebraic variety

isomorphic to the Deligne-Mumford moduli space \\bar M_{0,n+1} of

stable genus zero curves with n+1 marked points.

A real version of this result allows to describe the

moduli space of integrable n-dimensional tops and

separation coordinates on the unit sphere

in terms of the geometry of Stasheff polytope.

The talk is based on joint works with L. Aguirre and G. Felder and with K.

Schoebel.

### 2014/04/30

#### Number Theory Seminar

16:40-17:40 Room #056 (Graduate School of Math. Sci. Bldg.)

An effective upper bound for the number of principally polarized Abelian schemes (JAPANESE)

**Takuya Maruyama**(University of Tokyo)An effective upper bound for the number of principally polarized Abelian schemes (JAPANESE)

#### Operator Algebra Seminars

16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Noncommutative real algebraic geometry of Kazhdan's property (T) (ENGLISH)

**Narutaka Ozawa**(RIMS, Kyoto University)Noncommutative real algebraic geometry of Kazhdan's property (T) (ENGLISH)

### 2014/04/28

#### Seminar on Geometric Complex Analysis

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

On the existence problem of Kähler-Ricci solitons (JAPANESE)

**Sunsuke Saito**(The University of Tokyo)On the existence problem of Kähler-Ricci solitons (JAPANESE)

#### Algebraic Geometry Seminar

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

Syzygies of jacobian ideals and Torelli properties (ENGLISH)

**Alexandru Dimca**(Institut Universitaire de France )Syzygies of jacobian ideals and Torelli properties (ENGLISH)

[ Abstract ]

Let $C$ be a reduced complex projective plane curve defined by a homogeneous equation $f(x,y,z)=0$. We consider syzygies of the type $af_x+bf_y+cf_z=0$, where $a,b,c$ are homogeneous polynomials and $f_x,f_y,f_z$ stand for the partial derivatives of $f$. In our talk we relate such syzygies with stable or splittable rank two vector bundles on the projective plane, and to Torelli properties of plane curves in the sense of Dolgachev-Kapranov.

Let $C$ be a reduced complex projective plane curve defined by a homogeneous equation $f(x,y,z)=0$. We consider syzygies of the type $af_x+bf_y+cf_z=0$, where $a,b,c$ are homogeneous polynomials and $f_x,f_y,f_z$ stand for the partial derivatives of $f$. In our talk we relate such syzygies with stable or splittable rank two vector bundles on the projective plane, and to Torelli properties of plane curves in the sense of Dolgachev-Kapranov.

### 2014/04/26

#### Monthly Seminar on Arithmetic of Automorphic Forms

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

The estimate of integral points of F(X,Y)=1, with F being a integral homogeneous quartic form F of degree 4 (JAPANESE)

Moduli of teh pairs of algebraic curve of genus 2 and its unramified cover of degree 7 (joint work with Hoffmann) (JAPANESE)

**Ryutarou Okazaki**(Doushisha Univ. until March, 2014) 13:30-14:30The estimate of integral points of F(X,Y)=1, with F being a integral homogeneous quartic form F of degree 4 (JAPANESE)

**Ryutarou Okazaki**(Doushisha Univ. until March, 2014) 15:00-16:00Moduli of teh pairs of algebraic curve of genus 2 and its unramified cover of degree 7 (joint work with Hoffmann) (JAPANESE)

### 2014/04/24

#### Geometry Colloquium

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

On rigidity of Lie foliations (JAPANESE)

**Hiraku Nozawa**(Ritsumeikan University)On rigidity of Lie foliations (JAPANESE)

[ Abstract ]

If the leaves of a Lie foliation are isometric to a symmetric space of noncompact type of higher rank, then, by a theorem of Zimmer, the holonomy group of the Lie foliation has rigidity similar to that of lattices of semisimple Lie groups of higher rank. The main result of this talk is a generalization of Zimmer's theorem including the case of real rank one based on an application of a variant of Mostow rigidity. (This talk is based on a joint work with Ga¥"el Meigniez.)

If the leaves of a Lie foliation are isometric to a symmetric space of noncompact type of higher rank, then, by a theorem of Zimmer, the holonomy group of the Lie foliation has rigidity similar to that of lattices of semisimple Lie groups of higher rank. The main result of this talk is a generalization of Zimmer's theorem including the case of real rank one based on an application of a variant of Mostow rigidity. (This talk is based on a joint work with Ga¥"el Meigniez.)

### 2014/04/23

#### Operator Algebra Seminars

16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Bost-Connes system for local fields of characteristic zero (ENGLISH)

**Takuya Takeishi**(Univ. Tokyo)Bost-Connes system for local fields of characteristic zero (ENGLISH)

#### Number Theory Seminar

16:40-17:40 Room #002 (Graduate School of Math. Sci. Bldg.)

Non-tempered A-packets and the Rapoport-Zink spaces (JAPANESE)

**Yoichi Mieda**(University of Tokyo)Non-tempered A-packets and the Rapoport-Zink spaces (JAPANESE)

#### Mathematical Biology Seminar

14:50-16:20 Room #128 (Graduate School of Math. Sci. Bldg.)

Age-structured epidemic model with infection during transportation (JAPANESE)

**Yukihiko Nakata**(Graduate School of Mathematical Sciences, University of Tokyo)Age-structured epidemic model with infection during transportation (JAPANESE)

### 2014/04/22

#### Tuesday Seminar of Analysis

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

Bounded small solutions to a chemotaxis system with

non-diffusive chemical (JAPANESE)

**Yohei Tsutsui**(The University of Tokyo)Bounded small solutions to a chemotaxis system with

non-diffusive chemical (JAPANESE)

[ Abstract ]

We consider a chemotaxis system with a logarithmic

sensitivity and a non-diffusive chemical substance. For some chemotactic

sensitivity constants, Ahn and Kang proved the existence of bounded

global solutions to the system. An entropy functional was used in their

argument to control the cell density by the density of the chemical

substance. Our purpose is to show the existence of bounded global

solutions for all the chemotactic sensitivity constants. Assuming the

smallness on the initial data in some sense, we can get uniform

estimates for time. These estimates are used to extend local solutions.

This talk is partially based on joint work with Yoshie Sugiyama (Kyusyu

Univ.) and Juan J. L. Vel\\'azquez (Univ. of Bonn).

We consider a chemotaxis system with a logarithmic

sensitivity and a non-diffusive chemical substance. For some chemotactic

sensitivity constants, Ahn and Kang proved the existence of bounded

global solutions to the system. An entropy functional was used in their

argument to control the cell density by the density of the chemical

substance. Our purpose is to show the existence of bounded global

solutions for all the chemotactic sensitivity constants. Assuming the

smallness on the initial data in some sense, we can get uniform

estimates for time. These estimates are used to extend local solutions.

This talk is partially based on joint work with Yoshie Sugiyama (Kyusyu

Univ.) and Juan J. L. Vel\\'azquez (Univ. of Bonn).

### 2014/04/21

#### Numerical Analysis Seminar

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

Shape optimization problems for time-periodic solutions of the Navier-Stokes equations (JAPANESE)

[ Reference URL ]

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

**Takashi Nakazawa**(Tohoku University)Shape optimization problems for time-periodic solutions of the Navier-Stokes equations (JAPANESE)

[ Reference URL ]

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

#### Seminar on Geometric Complex Analysis

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

Lagrangian mean curvature flows and some examples (JAPANESE)

**Hikaru Yamamoto**(The University of Tokyo)Lagrangian mean curvature flows and some examples (JAPANESE)

### 2014/04/19

#### Harmonic Analysis Komaba Seminar

13:30-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Strichartz estimates for incompressible rotating fluids (JAPANESE)

On the interpolation of functions for scattered data on random infinite points with a sharp error estimate (JAPANESE)

**Ryo Takada**(Tohoku University) 13:30-15:00Strichartz estimates for incompressible rotating fluids (JAPANESE)

**Masami Okada**(Tokyo Metropolitan Unversity) 15:30-16:30On the interpolation of functions for scattered data on random infinite points with a sharp error estimate (JAPANESE)

### 2014/04/16

#### Number Theory Seminar

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

On the cycle class map for zero-cycles over local fields (ENGLISH)

**Olivier Wittenberg**(ENS and CNRS)On the cycle class map for zero-cycles over local fields (ENGLISH)

[ Abstract ]

The Chow group of zero-cycles of a smooth and projective variety defined over a field k is an invariant of an arithmetic and geometric nature which is well understood only when k is a finite field (by higher-dimensional class field theory). In this talk, we will discuss the case of local and strictly local fields. We prove in particular the injectivity of the cycle class map to integral l-adic cohomology for a large class of surfaces with positive geometric genus over p-adic fields. The same statement holds for semistable K3 surfaces over C((t)), but does not hold in general for surfaces over C((t)) or over the maximal unramified extension of a p-adic field. This is a joint work with Hélène Esnault.

The Chow group of zero-cycles of a smooth and projective variety defined over a field k is an invariant of an arithmetic and geometric nature which is well understood only when k is a finite field (by higher-dimensional class field theory). In this talk, we will discuss the case of local and strictly local fields. We prove in particular the injectivity of the cycle class map to integral l-adic cohomology for a large class of surfaces with positive geometric genus over p-adic fields. The same statement holds for semistable K3 surfaces over C((t)), but does not hold in general for surfaces over C((t)) or over the maximal unramified extension of a p-adic field. This is a joint work with Hélène Esnault.

### 2014/04/15

#### Tuesday Seminar on Topology

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

On the rational string operations of classifying spaces and the

Hochschild cohomology (JAPANESE)

**Takahito Naito**(The University of Tokyo)On the rational string operations of classifying spaces and the

Hochschild cohomology (JAPANESE)

[ Abstract ]

Chataur and Menichi initiated the theory of string topology of

classifying spaces.

In particular, the cohomology of the free loop space of a classifying

space is endowed with a product

called the dual loop coproduct. In this talk, I will discuss the

algebraic structure and relate the rational dual loop coproduct to the

cup product on the Hochschild cohomology via the Van den Bergh isomorphism.

Chataur and Menichi initiated the theory of string topology of

classifying spaces.

In particular, the cohomology of the free loop space of a classifying

space is endowed with a product

called the dual loop coproduct. In this talk, I will discuss the

algebraic structure and relate the rational dual loop coproduct to the

cup product on the Hochschild cohomology via the Van den Bergh isomorphism.

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