## Seminar information archive

Seminar information archive ～05/21｜Today's seminar 05/22 | Future seminars 05/23～

### 2009/11/18

#### Lectures

15:30-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)

The stochastic Burgers equation and its discretization

**Herbert Spohn**(ミュンヘン工科大学・九州大学)The stochastic Burgers equation and its discretization

#### Number Theory Seminar

16:30-18:45 Room #056 (Graduate School of Math. Sci. Bldg.)

Elementary computation of ramified component of the Jacobi sum

P-divisible groups and the p-adic Corona problem

**津嶋 貴弘**(東京大学大学院数理科学研究科) 16:30-17:30Elementary computation of ramified component of the Jacobi sum

[ Abstract ]

R. Coleman and W. McCallum calculated the Jacobi sum Hecke characters using their computation of the stable reduction of the Fermat curve in 1988. In my talk, we give an elementary proof of the main result of them without using rigid geometry or the stable model of the Fermat curve.

R. Coleman and W. McCallum calculated the Jacobi sum Hecke characters using their computation of the stable reduction of the Fermat curve in 1988. In my talk, we give an elementary proof of the main result of them without using rigid geometry or the stable model of the Fermat curve.

**Christopher Deninger**(Universität Münster) 17:45-18:45P-divisible groups and the p-adic Corona problem

### 2009/11/17

#### Tuesday Seminar on Topology

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

On the $SO(N)$ and $Sp(N)$ free energy of a closed oriented 3-manifold

**高田 敏恵**(新潟大学)On the $SO(N)$ and $Sp(N)$ free energy of a closed oriented 3-manifold

[ Abstract ]

We give an explicit formula of the $SO(N)$ and $Sp(N)$ free energy

of a lens space and show that the genus $g$ terms of it are analytic

in a neighborhood at zero, where we can choose the neighborhood

independently of $g$.

Moreover, it is proved that for any closed oriented 3-manifold $M$

and any $g$, the genus $g$ terms of $SO(N)$ and $Sp(N)$ free energy

of $M$ coincide up to sign.

We give an explicit formula of the $SO(N)$ and $Sp(N)$ free energy

of a lens space and show that the genus $g$ terms of it are analytic

in a neighborhood at zero, where we can choose the neighborhood

independently of $g$.

Moreover, it is proved that for any closed oriented 3-manifold $M$

and any $g$, the genus $g$ terms of $SO(N)$ and $Sp(N)$ free energy

of $M$ coincide up to sign.

### 2009/11/16

#### Seminar on Geometric Complex Analysis

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

Weighted Green functions of polynomial skew products on C^2

**上野康平**(京都大学大学院理学研究科)Weighted Green functions of polynomial skew products on C^2

#### Algebraic Geometry Seminar

16:40-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)

Rationality of the Brauer-Severi Varieties of Skylanin algebras

**Colin Ingalls**(University of New Brunswick and RIMS)Rationality of the Brauer-Severi Varieties of Skylanin algebras

[ Abstract ]

Iskovskih's conjecture states that a conic bundle over

a surface is rational if and only if the surface has a pencil of

rational curves which meet the discriminant in 3 or fewer points,

(with one exceptional case). We generalize Iskovskih's proof that

such conic bundles are rational, to the case of projective space

bundles of higher dimension. The proof involves maximal orders

and toric geometry. As a corollary we show that the Brauer-Severi

variety of a Sklyanin algebra is rational.

Iskovskih's conjecture states that a conic bundle over

a surface is rational if and only if the surface has a pencil of

rational curves which meet the discriminant in 3 or fewer points,

(with one exceptional case). We generalize Iskovskih's proof that

such conic bundles are rational, to the case of projective space

bundles of higher dimension. The proof involves maximal orders

and toric geometry. As a corollary we show that the Brauer-Severi

variety of a Sklyanin algebra is rational.

### 2009/11/14

#### Monthly Seminar on Arithmetic of Automorphic Forms

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

On weak endoscopic lift (117号室)

Derivations and Automorphisms on the noncommutative algebra of power series.

**岡崎武生**(京都大学) 13:30-14:30On weak endoscopic lift (117号室)

[ Abstract ]

rank 2のsymplectic 群の保型表現$\\pi$の spinor L-関数(4次)が殆どの素点で楕円保型形式のL-関数の積になっているものをweak ndoscopic liftと呼びます. $\\pi$がtemperedならば, 全てのweak endoscopic liftはrank 4のtheta関数(theta lift)でかける事がBrooks Roberts氏により知られています.

本公演では, このtheta liftの明示的な構成法やその周辺に関する話題(Siegel 三次多様体など)についてお話したいと思います.

rank 2のsymplectic 群の保型表現$\\pi$の spinor L-関数(4次)が殆どの素点で楕円保型形式のL-関数の積になっているものをweak ndoscopic liftと呼びます. $\\pi$がtemperedならば, 全てのweak endoscopic liftはrank 4のtheta関数(theta lift)でかける事がBrooks Roberts氏により知られています.

本公演では, このtheta liftの明示的な構成法やその周辺に関する話題(Siegel 三次多様体など)についてお話したいと思います.

**井原健太郎**(POSTEC) 15:00-16:00Derivations and Automorphisms on the noncommutative algebra of power series.

[ Abstract ]

We discuss a relationship between a class of derivations and a class of automorphisms on the noncommutative algebra of formal power series in two variables. Each class relates bijectively by exponential and logarithm maps. In this talk we define a specific class of derivations, which generates a noncommutaive Lie algebra whose defining relations are related to a classical Witt algebra. The main claim is the explicit description of the

automorphisms which are corresponding to the derivations via exponential map.

We discuss a relationship between a class of derivations and a class of automorphisms on the noncommutative algebra of formal power series in two variables. Each class relates bijectively by exponential and logarithm maps. In this talk we define a specific class of derivations, which generates a noncommutaive Lie algebra whose defining relations are related to a classical Witt algebra. The main claim is the explicit description of the

automorphisms which are corresponding to the derivations via exponential map.

### 2009/11/12

#### Lectures

10:40-12:10 Room #128 (Graduate School of Math. Sci. Bldg.)

冨田竹崎理論とその応用 (6)

**竹崎正道**(UCLA)冨田竹崎理論とその応用 (6)

#### Operator Algebra Seminars

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

Recent results for amalgamated free products of type II$_1$ factors

**酒匂宏樹**(東大数理)Recent results for amalgamated free products of type II$_1$ factors

### 2009/11/11

#### Lectures

14:40-16:10 Room #128 (Graduate School of Math. Sci. Bldg.)

冨田竹崎理論とその応用 (5)

**竹崎正道**(UCLA)冨田竹崎理論とその応用 (5)

### 2009/11/10

#### Lectures

14:40-16:10 Room #128 (Graduate School of Math. Sci. Bldg.)

冨田竹崎理論とその応用 (4)

**竹崎正道**(UCLA)冨田竹崎理論とその応用 (4)

#### Tuesday Seminar on Topology

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

Resurgent analysis of the Witten Laplacian in one dimension

**Alexander Getmanenko**(IPMU)Resurgent analysis of the Witten Laplacian in one dimension

[ Abstract ]

I will recall Witten's approach to the Morse theory through properties of a certain differential operator. Then I will introduce resurgent analysis -- an asymptotic method used, in particular, for studying quantum-mechanical tunneling. In conclusion I will discuss how the methods of resurgent analysis can help us "see" pseudoholomorphic discs in the eigenfunctions of the Witten Laplacian.

I will recall Witten's approach to the Morse theory through properties of a certain differential operator. Then I will introduce resurgent analysis -- an asymptotic method used, in particular, for studying quantum-mechanical tunneling. In conclusion I will discuss how the methods of resurgent analysis can help us "see" pseudoholomorphic discs in the eigenfunctions of the Witten Laplacian.

### 2009/11/09

#### Kavli IPMU Komaba Seminar

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

Differential Graded Categories and heterotic string theory

**Makoto Sakurai**(東京大学大学院数理科学研究科)Differential Graded Categories and heterotic string theory

[ Abstract ]

The saying "category theory is an abstract nonsense" is even physically not true.

The schematic language of triangulated category presents a new stage of string theory.

To illuminate this idea, I will draw your attention to the blow-up minimal model

of complex algebraic surfaces. This is done under the hypothetical assumptions

of "generalized complex structure" of cotangent bundle due to Hitchin school.

The coordinate transformation Jacobian matrices of the measure of sigma model

with spin structures cause one part of the gravitational "anomaly cancellation"

of smooth Kahler manifold $X$ and Weyl anomaly of compact Riemann surface $\\Sigma$.

$Anom = c_1 (X) c_1 (\\Sigma) \\oplus ch_2 (X)$,

in terms of 1st and 2nd Chern characters. Note that when $\\Sigma$ is a puctured disk

with flat metric, the chiral algebra is nothing but the ordinary vertex algebra.

Note that I do not explain the complex differential geometry,

but essentially more recent works with the category of DGA (Diffenreial Graded Algebra),

which is behind the super conformal field theory of chiral algebras.

My result of "vanishing tachyon" (nil-radical part of vertex algebras)

and "causality resortation" in compactified non-critical heterotic sigma model

is physically a promising idea of new solution to unitary representation of operator algebras.

This idea is realized in the formalism of BRST cohomology and its generalization

in $\\mathcal{N} = (0,2)$ supersymmetry, that is, non-commutative geometry

with non-linear constraint condition of pure spinors for covariant quantization.

The saying "category theory is an abstract nonsense" is even physically not true.

The schematic language of triangulated category presents a new stage of string theory.

To illuminate this idea, I will draw your attention to the blow-up minimal model

of complex algebraic surfaces. This is done under the hypothetical assumptions

of "generalized complex structure" of cotangent bundle due to Hitchin school.

The coordinate transformation Jacobian matrices of the measure of sigma model

with spin structures cause one part of the gravitational "anomaly cancellation"

of smooth Kahler manifold $X$ and Weyl anomaly of compact Riemann surface $\\Sigma$.

$Anom = c_1 (X) c_1 (\\Sigma) \\oplus ch_2 (X)$,

in terms of 1st and 2nd Chern characters. Note that when $\\Sigma$ is a puctured disk

with flat metric, the chiral algebra is nothing but the ordinary vertex algebra.

Note that I do not explain the complex differential geometry,

but essentially more recent works with the category of DGA (Diffenreial Graded Algebra),

which is behind the super conformal field theory of chiral algebras.

My result of "vanishing tachyon" (nil-radical part of vertex algebras)

and "causality resortation" in compactified non-critical heterotic sigma model

is physically a promising idea of new solution to unitary representation of operator algebras.

This idea is realized in the formalism of BRST cohomology and its generalization

in $\\mathcal{N} = (0,2)$ supersymmetry, that is, non-commutative geometry

with non-linear constraint condition of pure spinors for covariant quantization.

### 2009/11/07

#### Infinite Analysis Seminar Tokyo

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

Tau-functions of Toda theories, partitions and conformal blocks

TBA

**Andrei Marshakov**(Lebedev Physical Institute) 13:30-14:30Tau-functions of Toda theories, partitions and conformal blocks

[ Abstract ]

I discuss the class of tau-functions,

corresponding to special solutions of integrable systems,

related to Hurwitz numbers and supersymmetric Yang-Mills

theories. Their natural generalization turn to coincide with

the conformal blocks of two-dimensional conformal

field theories. In special case these conformal

blocks turn into the scalar products of certain ``coherent

states'' in the highest-weight module of the Virasoro

algebra, generalizing the matrix elements

for the well-known coherent states in Fock spaces.

I discuss the class of tau-functions,

corresponding to special solutions of integrable systems,

related to Hurwitz numbers and supersymmetric Yang-Mills

theories. Their natural generalization turn to coincide with

the conformal blocks of two-dimensional conformal

field theories. In special case these conformal

blocks turn into the scalar products of certain ``coherent

states'' in the highest-weight module of the Virasoro

algebra, generalizing the matrix elements

for the well-known coherent states in Fock spaces.

**TBA**(TBA) 15:00-16:00TBA

[ Abstract ]

TBA

TBA

### 2009/11/05

#### Lecture Series on Mathematical Sciences in Soceity

16:20-17:50 Room #056 (Graduate School of Math. Sci. Bldg.)

社会における学位取得者の役割Ⅱ

**藤原 洋**(インターネット総合研究所代表取締役所長)社会における学位取得者の役割Ⅱ

#### Applied Analysis

16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

A Mathematical Aspect of the One-Dimensional Keller and Rubinow Model for Liesegang Bands

**大西 勇**(広島大学大学院理学研究科)A Mathematical Aspect of the One-Dimensional Keller and Rubinow Model for Liesegang Bands

[ Abstract ]

In 1896, colloid-chemist R.E. Liesegang [4] observed strikingly

regular patterns in precipitation-reaction processes, which are referred to as Liesegang bands or rings, according to their shape. In this talk I introduce an attempt to understand from a mathematical viewpoint the experiments in which regularized structures with spatially distinct bands of precipitated material are exhibited, with clearly visible scaling properties. This study is a result [1] of a collaboration with Professors D. Hilhorst, R. van der Hout, and M. Mimura.

References:

[1] Hilhorst, D., van der Hout, R., Mimura, M., and Ohnishi, I.: A Mathematical Study of the One-Dimensional Keller and Rubinow Model for Liesegang Bands. J. Stat Phys 135: 107-132 (2009)

[2] Kai, S., Muller, S.C.: Spatial and temporal macroscopic structures in chemical reaction system: precipitation patterns and interfacial motion. Sci. Form 1, 8-38 (1985)

[3] Keller, J.B., Rubinow, S.I.: Recurrent precipitation and Liesegang rings. J. Chem. Phys. 74, 5000-5007 (1981)

[4] Liesegang, R.E.: Chemische Fernwirkung. Photo. Archiv 800, 305-309 (1896)

[5] Mimura, M., Ohnishi, I., Ueyama, D.: A mathematical aspect of Liesegang phenomena in two space dimensions. Res. Rep. Res. Inst. Math. Sci. 1499, 185-201 (2006)

[6] Ohnishi, I.,Mimura, M.: A mathematical aspect of Liesegang phenomena. In: Proceedings of Equadiff-11, pp. 343-352 (2005).

In 1896, colloid-chemist R.E. Liesegang [4] observed strikingly

regular patterns in precipitation-reaction processes, which are referred to as Liesegang bands or rings, according to their shape. In this talk I introduce an attempt to understand from a mathematical viewpoint the experiments in which regularized structures with spatially distinct bands of precipitated material are exhibited, with clearly visible scaling properties. This study is a result [1] of a collaboration with Professors D. Hilhorst, R. van der Hout, and M. Mimura.

References:

[1] Hilhorst, D., van der Hout, R., Mimura, M., and Ohnishi, I.: A Mathematical Study of the One-Dimensional Keller and Rubinow Model for Liesegang Bands. J. Stat Phys 135: 107-132 (2009)

[2] Kai, S., Muller, S.C.: Spatial and temporal macroscopic structures in chemical reaction system: precipitation patterns and interfacial motion. Sci. Form 1, 8-38 (1985)

[3] Keller, J.B., Rubinow, S.I.: Recurrent precipitation and Liesegang rings. J. Chem. Phys. 74, 5000-5007 (1981)

[4] Liesegang, R.E.: Chemische Fernwirkung. Photo. Archiv 800, 305-309 (1896)

[5] Mimura, M., Ohnishi, I., Ueyama, D.: A mathematical aspect of Liesegang phenomena in two space dimensions. Res. Rep. Res. Inst. Math. Sci. 1499, 185-201 (2006)

[6] Ohnishi, I.,Mimura, M.: A mathematical aspect of Liesegang phenomena. In: Proceedings of Equadiff-11, pp. 343-352 (2005).

### 2009/11/04

#### Lie Groups and Representation Theory

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

Birational Hyperbolic Geometry

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

**Gert Heckman**(IMAPP, Faculty of Science, Radboud University Nijmegen)Birational Hyperbolic Geometry

[ Abstract ]

We study compactifications for complex ball quotients.

We first recall the Satake-Bailey-Borel compactification and the Mumford resolution.

Then we discuss compactifications of ball quotients minus a totally geodesic divisor.

These compactifications turn up for a suitable class of period maps.

[ Reference URL ]We study compactifications for complex ball quotients.

We first recall the Satake-Bailey-Borel compactification and the Mumford resolution.

Then we discuss compactifications of ball quotients minus a totally geodesic divisor.

These compactifications turn up for a suitable class of period maps.

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2009/11/02

#### Algebraic Geometry Seminar

16:40-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)

Cohomology of moduli spaces of curves and modular forms

**Gerard van der Geer**(Universiteit van Amsterdam)Cohomology of moduli spaces of curves and modular forms

[ Abstract ]

The Eichler-Shimura theorem expresses cohomology of local systems

on the moduli of elliptic curves in terms of modular forms. The

cohomology of local systems can be succesfully explored by counting

points over finite fields. We show how this can be applied to

obtain a lot of information about the cohomology of other moduli spaces

of low genera and also about Siegel modular forms of genus 2 and 3.

This is joint work with Jonas Bergstroem and Carel Faber.

The Eichler-Shimura theorem expresses cohomology of local systems

on the moduli of elliptic curves in terms of modular forms. The

cohomology of local systems can be succesfully explored by counting

points over finite fields. We show how this can be applied to

obtain a lot of information about the cohomology of other moduli spaces

of low genera and also about Siegel modular forms of genus 2 and 3.

This is joint work with Jonas Bergstroem and Carel Faber.

### 2009/10/30

#### Lecture Series on Mathematical Sciences in Soceity

16:20-17:50 Room #117 (Graduate School of Math. Sci. Bldg.)

アクチュアリーの役割Ⅱ

**辻 芳彦**((社)日本アクチュアリー会事務局事務局長)アクチュアリーの役割Ⅱ

#### GCOE Seminars

15:00-16:00 Room #370 (Graduate School of Math. Sci. Bldg.)

Regularized total least squares: computational aspects and error bounds

**Shuai Lu**(Johann Radon Institute)Regularized total least squares: computational aspects and error bounds

[ Abstract ]

For solving linear ill-posed problems, regularization methods are required when the right hand side and/or the operator are corrupted by some noise. In the present talk, regularized solutions are constructed using regularized total least squares and dual regularized total least squares. We discuss computational aspects and provide order optimal error bounds that characterize the accuracy of the regularized solutions. The results extend earlier results where the operator is exactly given. We also present some numerical experiments, which shed light on the relationship between RTLS, dual RTLS and the standard Tikhonov regularization.

For solving linear ill-posed problems, regularization methods are required when the right hand side and/or the operator are corrupted by some noise. In the present talk, regularized solutions are constructed using regularized total least squares and dual regularized total least squares. We discuss computational aspects and provide order optimal error bounds that characterize the accuracy of the regularized solutions. The results extend earlier results where the operator is exactly given. We also present some numerical experiments, which shed light on the relationship between RTLS, dual RTLS and the standard Tikhonov regularization.

### 2009/10/29

#### Operator Algebra Seminars

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

Fusion graphs for Lie groups at level k and quantum symmetries

**Robert Coquereaux**(CNRS/CPT, Marseille)Fusion graphs for Lie groups at level k and quantum symmetries

#### Lectures

16:30-17:30 Room #270 (Graduate School of Math. Sci. Bldg.)

Spectral properties of Nikolaevskiy chaos

**Michael I. Tribelsky**(MIREA (Technical University), Moscow, Russia)Spectral properties of Nikolaevskiy chaos

### 2009/10/28

#### Lectures

16:30-17:30 Room #370 (Graduate School of Math. Sci. Bldg.)

Dispersive and Strichartz estimates for hyperbolic equations of general form

**Michael Ruzhansky**(Imperial College, London)Dispersive and Strichartz estimates for hyperbolic equations of general form

### 2009/10/27

#### Tuesday Seminar on Topology

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

A new appearance of the Morita-Penner cocycle

**Alex Bene**(IPMU)A new appearance of the Morita-Penner cocycle

[ Abstract ]

In this talk, I will recall the Morita-Penner cocycle on the dual fatgraph complex for a surface with one boundary component. This cocycle, when restricted to paths representing elements of the mapping class group, represents the extended first Johnson homomorphism \\tau_1, thus can be viewed as a (in some specific sense canonical) "groupoid extension" of \\tau_1. There are now several different contexts in which this cocycle can be constructed, and in this talk I will briefly review several of them, including one discovered in the context of finite type invariants of homology cylinders in joint work with J.E. Andersen, J-B. Meilhan, and R.C. Penner.

In this talk, I will recall the Morita-Penner cocycle on the dual fatgraph complex for a surface with one boundary component. This cocycle, when restricted to paths representing elements of the mapping class group, represents the extended first Johnson homomorphism \\tau_1, thus can be viewed as a (in some specific sense canonical) "groupoid extension" of \\tau_1. There are now several different contexts in which this cocycle can be constructed, and in this talk I will briefly review several of them, including one discovered in the context of finite type invariants of homology cylinders in joint work with J.E. Andersen, J-B. Meilhan, and R.C. Penner.

### 2009/10/26

#### Seminar on Geometric Complex Analysis

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

On Vojta's conjecture in the split function field case

**Pietro Corvaja**(Università di Udine)On Vojta's conjecture in the split function field case

### 2009/10/23

#### Lecture Series on Mathematical Sciences in Soceity

16:20-17:50 Room #117 (Graduate School of Math. Sci. Bldg.)

アクチュアリーの役割Ⅰ

**辻 芳彦**((社)日本アクチュアリー会事務局事務局長)アクチュアリーの役割Ⅰ

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