## Seminar information archive

Seminar information archive ～02/23｜Today's seminar 02/24 | Future seminars 02/25～

#### Operator Algebra Seminars

16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Automorphisms of Compact Quantum Groups (ENGLISH)

**Issan Patri**(Inst. Math. Sci.)Automorphisms of Compact Quantum Groups (ENGLISH)

### 2013/11/12

#### PDE Real Analysis Seminar

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

Optimal initial values and regularity conditions of Besov space type for weak solutions to the Navier-Stokes system (ENGLISH)

**Reinhard Farwig**(Technische Universität Darmstadt)Optimal initial values and regularity conditions of Besov space type for weak solutions to the Navier-Stokes system (ENGLISH)

[ Abstract ]

In a joint work with H. Sohr (Paderborn) and W. Varnhorn (Kassel) we discuss the optimal condition on initial values for the instationary Navier-Stokes system in a bounded domain to get a locally regular solution in Serrin's class.

Then this result based on a description in Besov spaces will be used at all or almost all instants to prove new conditional regularity results for weak solutions.

In a joint work with H. Sohr (Paderborn) and W. Varnhorn (Kassel) we discuss the optimal condition on initial values for the instationary Navier-Stokes system in a bounded domain to get a locally regular solution in Serrin's class.

Then this result based on a description in Besov spaces will be used at all or almost all instants to prove new conditional regularity results for weak solutions.

#### Tuesday Seminar on Topology

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

The Batalin-Vilkovisky Formalism and Cohomology of Moduli Spaces (ENGLISH)

**Alexander Voronov**(University of Minnesota)The Batalin-Vilkovisky Formalism and Cohomology of Moduli Spaces (ENGLISH)

[ Abstract ]

We use the Batalin-Vilkovisky formalism to give a new proof of Costello's theorem on the existence and uniqueness of solution to the Quantum Master Equation. We also make a physically motivated conjecture on the rational homology of moduli spaces. This is a joint work with Domenico D'Alessandro.

We use the Batalin-Vilkovisky formalism to give a new proof of Costello's theorem on the existence and uniqueness of solution to the Quantum Master Equation. We also make a physically motivated conjecture on the rational homology of moduli spaces. This is a joint work with Domenico D'Alessandro.

#### Numerical Analysis Seminar

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

Numerical analysis of friction-type boundary value problems by "method of numerical integration" (JAPANESE)

[ Reference URL ]

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

**Takahito Kashiwabara**(The University of Tokyo)Numerical analysis of friction-type boundary value problems by "method of numerical integration" (JAPANESE)

[ Reference URL ]

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

### 2013/11/11

#### Seminar on Geometric Complex Analysis

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

Levi-flat real hypersurfaces with Takeuchi 1-complete complements (JAPANESE)

**Masanori Adachi**(Nagoya University)Levi-flat real hypersurfaces with Takeuchi 1-complete complements (JAPANESE)

[ Abstract ]

In this talk, we discuss compact Levi-flat real hypersurfaces with Takeuchi 1-complete complements from several viewpoints. Based on a Bochner-Hartogs type extension theorem for CR sections over these hypersurfaces, we give an example of a compact Levi-flat CR manifold with a positive CR line bundle whose Ohsawa-Sibony's projective embedding map cannot be transversely infinitely differentiable. We also give a geometrical expression of the Diederich-Fornaess exponents of Takeuchi 1-complete defining functions, and discuss a possible dynamical interpretation of them.

In this talk, we discuss compact Levi-flat real hypersurfaces with Takeuchi 1-complete complements from several viewpoints. Based on a Bochner-Hartogs type extension theorem for CR sections over these hypersurfaces, we give an example of a compact Levi-flat CR manifold with a positive CR line bundle whose Ohsawa-Sibony's projective embedding map cannot be transversely infinitely differentiable. We also give a geometrical expression of the Diederich-Fornaess exponents of Takeuchi 1-complete defining functions, and discuss a possible dynamical interpretation of them.

#### Algebraic Geometry Seminar

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

Geography via the base loci (ENGLISH)

**Sung Rak Choi**(POSTECH)Geography via the base loci (ENGLISH)

[ Abstract ]

The geography of log model refers to the decomposition of the set of effective adjoint divisors into the cells defined by the resulting models that are obtained by the log minimal model program.

We will describe the geography in terms of the asymptotic base loci and Zariski decompositions of divisors.

As an application, we give a partial answer to a question of B. Totaro concerning the structure of partially ample cones.

The geography of log model refers to the decomposition of the set of effective adjoint divisors into the cells defined by the resulting models that are obtained by the log minimal model program.

We will describe the geography in terms of the asymptotic base loci and Zariski decompositions of divisors.

As an application, we give a partial answer to a question of B. Totaro concerning the structure of partially ample cones.

#### Lie Groups and Representation Theory

16:30-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Alternating sign matrices, primed shifted tableaux and Tokuyama

factorisation theorems (ENGLISH)

**Ronald King**(the University of Southampton)Alternating sign matrices, primed shifted tableaux and Tokuyama

factorisation theorems (ENGLISH)

[ Abstract ]

Twenty years ago Okada established a remarkable set of identities relating weighted sums over half-turn alternating sign matrices (ASMs) to products taking the form of deformations of Weyl denominator formulae for Lie algebras B_n, C_n and D_n. Shortly afterwards Simpson added another such identity to the list. It will be shown that various classes of ASMs are in bijective correspondence with certain sets of shifted tableaux, and that statistics on these ASMs may be expressed in terms of the entries in corresponding compass point matrices (CPMs). This then enables the Okada and Simpson identities to be expressed in terms of weighted sums over primed shifted tableaux. This offers the possibility of extending each of these identities, that originally involved a single parameter and a single shifted tableau shape, to more general identities involving both sequences of parameters and shapes specified by arbitrary partitions. It is conjectured that in each case an appropriate multi-parameter weighted sum can be expressed as a product of a deformed Weyl denominator and group character of the type first proved in the A_n case by Tokuyma in 1988. The conjectured forms of the generalised Okada and Simpson identities will be given explicitly, along with an account of recent progress made in collaboration with Angèle Hamel in proving some of them.

Twenty years ago Okada established a remarkable set of identities relating weighted sums over half-turn alternating sign matrices (ASMs) to products taking the form of deformations of Weyl denominator formulae for Lie algebras B_n, C_n and D_n. Shortly afterwards Simpson added another such identity to the list. It will be shown that various classes of ASMs are in bijective correspondence with certain sets of shifted tableaux, and that statistics on these ASMs may be expressed in terms of the entries in corresponding compass point matrices (CPMs). This then enables the Okada and Simpson identities to be expressed in terms of weighted sums over primed shifted tableaux. This offers the possibility of extending each of these identities, that originally involved a single parameter and a single shifted tableau shape, to more general identities involving both sequences of parameters and shapes specified by arbitrary partitions. It is conjectured that in each case an appropriate multi-parameter weighted sum can be expressed as a product of a deformed Weyl denominator and group character of the type first proved in the A_n case by Tokuyma in 1988. The conjectured forms of the generalised Okada and Simpson identities will be given explicitly, along with an account of recent progress made in collaboration with Angèle Hamel in proving some of them.

#### Seminar on Probability and Statistics

14:50-16:00 Room #052 (Graduate School of Math. Sci. Bldg.)

LASSO に対する AIC タイプの情報量規準 (JAPANESE)

[ Reference URL ]

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/06.html

**NINOMIYA, Yoshiyuki**(Kyusyu University)LASSO に対する AIC タイプの情報量規準 (JAPANESE)

[ Reference URL ]

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/06.html

### 2013/11/08

#### Operator Algebra Seminars

10:00-12:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Introduction to the Ando-Haagerup theory IV (JAPANESE)

**Reiji Tomatsu**(Hokkaido Univ.)Introduction to the Ando-Haagerup theory IV (JAPANESE)

#### Colloquium

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

Ext Analogues of Branching laws (ENGLISH)

**Dipendra Prasad**(Tata Institute of Fundamental Research)Ext Analogues of Branching laws (ENGLISH)

[ Abstract ]

The decomposition of a representation of a group when restricted to a

subgroup is an important problem well-studied for finite and compact Lie

groups, and continues to be of much contemporary interest in the context

of real and $p$-adic groups. We will survey some of the questions that have

recently been considered, and look at a variation of these questions involving concepts in homological algebra which gives rise to interesting newer questions.

The decomposition of a representation of a group when restricted to a

subgroup is an important problem well-studied for finite and compact Lie

groups, and continues to be of much contemporary interest in the context

of real and $p$-adic groups. We will survey some of the questions that have

recently been considered, and look at a variation of these questions involving concepts in homological algebra which gives rise to interesting newer questions.

### 2013/11/07

#### Operator Algebra Seminars

15:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Introduction to the Ando-Haagerup theory III (JAPANESE)

**Reiji Tomatsu**(Hokkaido Univ.)Introduction to the Ando-Haagerup theory III (JAPANESE)

#### GCOE Seminars

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

Maximum Regularity Principle for Conservative Evolutionary Partial Dierential Equations (ENGLISH)

**Bingyu Zhang**(University of Cincinnati)Maximum Regularity Principle for Conservative Evolutionary Partial Dierential Equations (ENGLISH)

#### Lie Groups and Representation Theory

13:30-14:20 Room #000 (Graduate School of Math. Sci. Bldg.)

Global Geometry and Analysis on Locally Pseudo-Riemannian Homogeneous Spaces (ENGLISH)

**Toshiyuki Kobayashi**(the University of Tokyo)Global Geometry and Analysis on Locally Pseudo-Riemannian Homogeneous Spaces (ENGLISH)

[ Abstract ]

The local to global study of geometries was a major trend of 20th century geometry, with remarkable developments achieved particularly in Riemannian geometry. In contrast, in areas such as Lorentz geometry, familiar to us as the space-time of relativity theory, and more generally in pseudo-Riemannian geometry of general signature, surprising little is known about global properties of the geometry even if we impose a locally homogeneous structure.

Taking anti-de Sitter manifolds, which are locally modelled on AdS^n as an example, I plan to explain two programs:

1. (global shape) Exisitence problem of compact locally homogeneous spaces, and defomation theory.

2. (spectral analysis) Construction of the spectrum of the Laplacian, and its stability under the deformation of the geometric structure.

The local to global study of geometries was a major trend of 20th century geometry, with remarkable developments achieved particularly in Riemannian geometry. In contrast, in areas such as Lorentz geometry, familiar to us as the space-time of relativity theory, and more generally in pseudo-Riemannian geometry of general signature, surprising little is known about global properties of the geometry even if we impose a locally homogeneous structure.

Taking anti-de Sitter manifolds, which are locally modelled on AdS^n as an example, I plan to explain two programs:

1. (global shape) Exisitence problem of compact locally homogeneous spaces, and defomation theory.

2. (spectral analysis) Construction of the spectrum of the Laplacian, and its stability under the deformation of the geometric structure.

#### Lie Groups and Representation Theory

14:30-17:40 Room #000 (Graduate School of Math. Sci. Bldg.)

Weightless cohomology of algebraic varieties (ENGLISH)

Visible actions on generalized flag varieties

--- Geometry of multiplicity-free representations of $SO(N)$ (ENGLISH)

Holomorphic discrete series and Borel-de Siebenthal discrete series (ENGLISH)

Branching laws and the local Langlands correspondence (ENGLISH)

**Vaibhav Vaish**(the Institute of Mathematical Sciences) 14:30-15:20Weightless cohomology of algebraic varieties (ENGLISH)

[ Abstract ]

Using Morel's weight truncations in categories of mixed sheaves, we attach to any variety defined over complex numbers, over finite fields or even over a number field, a series of groups called the weightless cohomology groups. These lie between the usual cohomology and the intersection cohomology, have a natural ring structure, satisfy Kunneth, and are functorial for certain morphisms.

The construction is motivic and naturally arises in the context of Shimura Varieties where they capture the cohomology of Reductive Borel-Serre compactification. The construction also yields invariants of singularities associated with the combinatorics of the boundary divisors in any resolution.

Using Morel's weight truncations in categories of mixed sheaves, we attach to any variety defined over complex numbers, over finite fields or even over a number field, a series of groups called the weightless cohomology groups. These lie between the usual cohomology and the intersection cohomology, have a natural ring structure, satisfy Kunneth, and are functorial for certain morphisms.

The construction is motivic and naturally arises in the context of Shimura Varieties where they capture the cohomology of Reductive Borel-Serre compactification. The construction also yields invariants of singularities associated with the combinatorics of the boundary divisors in any resolution.

**Yuichiro Tanaka**(the University of Tokyo) 15:40-16:10Visible actions on generalized flag varieties

--- Geometry of multiplicity-free representations of $SO(N)$ (ENGLISH)

[ Abstract ]

The subject of study is tensor product representations of irreducible representations of the orthogonal group, which are multiplicity-free. Here we say a group representation is multiplicity-free if any irreducible representation occurs at most once in its irreducible decomposition.

The motivation is the theory of visible actions on complex manifolds, which was introduced by T. Kobayashi. In this theory, the main tool for proving the multiplicity-freeness property of group representations is the ``propagation theorem of the multiplicity-freeness property". By using this theorem and Stembridge's classification result, we obtain the following: All the multiplicity-free tensor product representations of $SO(N)$ and $Spin(N)$ can be obtained from character, alternating tensor product and spin representations combined with visible actions on orthogonal generalized flag varieties.

The subject of study is tensor product representations of irreducible representations of the orthogonal group, which are multiplicity-free. Here we say a group representation is multiplicity-free if any irreducible representation occurs at most once in its irreducible decomposition.

The motivation is the theory of visible actions on complex manifolds, which was introduced by T. Kobayashi. In this theory, the main tool for proving the multiplicity-freeness property of group representations is the ``propagation theorem of the multiplicity-freeness property". By using this theorem and Stembridge's classification result, we obtain the following: All the multiplicity-free tensor product representations of $SO(N)$ and $Spin(N)$ can be obtained from character, alternating tensor product and spin representations combined with visible actions on orthogonal generalized flag varieties.

**Pampa Paul**(Indian Statistical Institute, Kolkata) 16:10-16:40Holomorphic discrete series and Borel-de Siebenthal discrete series (ENGLISH)

[ Abstract ]

Let $G_0$ be a simply connected non-compact real simple Lie group with maximal compact subgroup $K_0$.

Let $T_0\\subset K_0$ be a Cartan subgroup of $K_0$ as well as of $G_0$. So $G_0$ has discrete series representations.

Denote by $\\frak{g}, \\frak{k},$ and $\\frak{t}$, the

complexifications of the Lie algebras $\\frak{g}_0, \\frak{k}_0$ and $\\frak{t}_0$ of $G_0, K_0$ and $T_0$ respectively.

There exists a positive root system $\\Delta^+$ of $\\frak{g}$ with respect to $\\frak{t}$, known as the Borel-de Siebenthal positive system for which there is exactly one non-compact simple root, denoted $\\nu$. Let $\\mu$ denote the highest root.

If $G_0/K_0$ is Hermitian symmetric, then $\\nu$ has coefficient $1$ in $\\mu$ and one can define holomorphic discrete series representation of $G_0$ using $\\Delta^+$.

If $G_0/K_0$ is not Hermitian symmetric, the coefficient of $\\nu$ in the highest root $\\mu$ is $2$.

In this case, Borel-de Siebenthal discrete series of $G_0$ is defined using $\\Delta^+$ in a manner analogous to the holomorphic discrete series.

Let $\\nu^*$ be the fundamental weight corresponding to $\\nu$ and $L_0$ be the centralizer in $K_0$ of the circle subgroup defined by $i\\nu^*$.

Note that $L_0 = K_0$, when $G_0/K_0$ is Hermitian symmetric. Otherwise, $L_0$ is a proper subgroup of $K_0$ and $K_0/L_0$ is an irreducible compact Hermitian symmetric space.

Let $G$ be the simply connected Lie group with Lie algebra $\\frak{g}$ and $K_0^* \\subset G$ be the dual of $K_0$ with respect to $L_0$ (or, the image of $L_0$ in $G$).

Then $K_0^*/L_0$ is an irreducible non-compact Hermitian symmetric space dual to $K_0/L_0$.

In this talk, to each Borel-de Siebenthal discrete series of $G_0$, a holomorphic discrete series of $K_0^*$ will be associated and occurrence of common $L_0$-types in both the series will be discussed.

Let $G_0$ be a simply connected non-compact real simple Lie group with maximal compact subgroup $K_0$.

Let $T_0\\subset K_0$ be a Cartan subgroup of $K_0$ as well as of $G_0$. So $G_0$ has discrete series representations.

Denote by $\\frak{g}, \\frak{k},$ and $\\frak{t}$, the

complexifications of the Lie algebras $\\frak{g}_0, \\frak{k}_0$ and $\\frak{t}_0$ of $G_0, K_0$ and $T_0$ respectively.

There exists a positive root system $\\Delta^+$ of $\\frak{g}$ with respect to $\\frak{t}$, known as the Borel-de Siebenthal positive system for which there is exactly one non-compact simple root, denoted $\\nu$. Let $\\mu$ denote the highest root.

If $G_0/K_0$ is Hermitian symmetric, then $\\nu$ has coefficient $1$ in $\\mu$ and one can define holomorphic discrete series representation of $G_0$ using $\\Delta^+$.

If $G_0/K_0$ is not Hermitian symmetric, the coefficient of $\\nu$ in the highest root $\\mu$ is $2$.

In this case, Borel-de Siebenthal discrete series of $G_0$ is defined using $\\Delta^+$ in a manner analogous to the holomorphic discrete series.

Let $\\nu^*$ be the fundamental weight corresponding to $\\nu$ and $L_0$ be the centralizer in $K_0$ of the circle subgroup defined by $i\\nu^*$.

Note that $L_0 = K_0$, when $G_0/K_0$ is Hermitian symmetric. Otherwise, $L_0$ is a proper subgroup of $K_0$ and $K_0/L_0$ is an irreducible compact Hermitian symmetric space.

Let $G$ be the simply connected Lie group with Lie algebra $\\frak{g}$ and $K_0^* \\subset G$ be the dual of $K_0$ with respect to $L_0$ (or, the image of $L_0$ in $G$).

Then $K_0^*/L_0$ is an irreducible non-compact Hermitian symmetric space dual to $K_0/L_0$.

In this talk, to each Borel-de Siebenthal discrete series of $G_0$, a holomorphic discrete series of $K_0^*$ will be associated and occurrence of common $L_0$-types in both the series will be discussed.

**Dipendra Prasad**(Tata Institute of Fundamental Research) 16:50-17:40Branching laws and the local Langlands correspondence (ENGLISH)

[ Abstract ]

The decomposition of a representation of a group when restricted to a subgroup is an important problem well-studied for finite and compact Lie groups, and continues to be of much contemporary interest in the context of real and $p$-adic groups. We will survey some of the questions that have recently been considered drawing analogy with Compact Lie groups, and what it suggests in the context of real and $p$-adic groups via what is called the local Langlands correspondence.

The decomposition of a representation of a group when restricted to a subgroup is an important problem well-studied for finite and compact Lie groups, and continues to be of much contemporary interest in the context of real and $p$-adic groups. We will survey some of the questions that have recently been considered drawing analogy with Compact Lie groups, and what it suggests in the context of real and $p$-adic groups via what is called the local Langlands correspondence.

### 2013/11/06

#### Operator Algebra Seminars

10:00-12:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Introduction to the Ando-Haagerup theory II (JAPANESE)

**Reiji Tomatsu**(Hokkaido Univ.)Introduction to the Ando-Haagerup theory II (JAPANESE)

### 2013/11/05

#### Tuesday Seminar on Topology

16:30-18:00 Room #123 (Graduate School of Math. Sci. Bldg.)

The isotopy problem of non-singular closed 1-forms. (ENGLISH)

**Carlos Moraga Ferrandiz**(The University of Tokyo, JSPS)The isotopy problem of non-singular closed 1-forms. (ENGLISH)

[ Abstract ]

Given alpha_0, alpha_1 two cohomologous non-singular closed 1-forms of a compact manifold M, are they always isotopic? We expect a negative answer to this question, at least in high dimensions by the work of Laudenbach, as well as an obstruction living in the algebraic K-theory of the Novikov ring associated to the underlying cohomology class.

A similar problem for functions N x [0,1] --> [0,1] without critical points was treated by Hatcher and Wagoner in the 70s.

The first goal of this talk is to explain how we can carry a part of the strategy of Hatcher and Wagoner into the context of closed 1-forms and to indicate the main difficulties that appear by doing so. The second goal is to show the techniques to treat this difficulties and the progress in defining the expected obstruction.

Given alpha_0, alpha_1 two cohomologous non-singular closed 1-forms of a compact manifold M, are they always isotopic? We expect a negative answer to this question, at least in high dimensions by the work of Laudenbach, as well as an obstruction living in the algebraic K-theory of the Novikov ring associated to the underlying cohomology class.

A similar problem for functions N x [0,1] --> [0,1] without critical points was treated by Hatcher and Wagoner in the 70s.

The first goal of this talk is to explain how we can carry a part of the strategy of Hatcher and Wagoner into the context of closed 1-forms and to indicate the main difficulties that appear by doing so. The second goal is to show the techniques to treat this difficulties and the progress in defining the expected obstruction.

#### Operator Algebra Seminars

15:30-17:30 Room #118 (Graduate School of Math. Sci. Bldg.)

Introduction to the Ando-Haagerup theory I (JAPANESE)

**Reiji Tomatsu**(Hokkaido Univ.)Introduction to the Ando-Haagerup theory I (JAPANESE)

### 2013/10/30

#### Operator Algebra Seminars

16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Amenable minimal Cantor systems of free groups arising from

diagonal actions (JAPANESE)

**Yuhei Suzuki**(Univ. Tokyo)Amenable minimal Cantor systems of free groups arising from

diagonal actions (JAPANESE)

#### Number Theory Seminar

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

Explicit integral cocycles on GLn and special values of p-adic partial zeta functions (ENGLISH)

**Pierre Charollois**(Université Paris 6)Explicit integral cocycles on GLn and special values of p-adic partial zeta functions (ENGLISH)

[ Abstract ]

Building on earlier work by Sczech, we contruct an explicit integral valued cocycle on GLn(Z).

It allows for the detailed analysis of the order of vanishing and of the special value at s=0 of the p-adic partial zeta functions introduced by Pi. Cassou-Noguès and Deligne-Ribet. In particular we recover a result of Wiles (1990) on Gross conjecture.

Another construction, now based on Shintani's method, is shown to lead to a cohomologous cocycle. This is joint work with S. Dasgupta and M. Greenberg.

Building on earlier work by Sczech, we contruct an explicit integral valued cocycle on GLn(Z).

It allows for the detailed analysis of the order of vanishing and of the special value at s=0 of the p-adic partial zeta functions introduced by Pi. Cassou-Noguès and Deligne-Ribet. In particular we recover a result of Wiles (1990) on Gross conjecture.

Another construction, now based on Shintani's method, is shown to lead to a cohomologous cocycle. This is joint work with S. Dasgupta and M. Greenberg.

#### Classical Analysis

16:00-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

The space of monodromy and Stokes data for q-difference equations (ENGLISH)

**Jacques Sauloy**(Institute de Mathematiques de Toulouse, Universite Paul Sabatier)The space of monodromy and Stokes data for q-difference equations (ENGLISH)

[ Abstract ]

Riemann-Hilbert correspondance for fuchsian q-difference equations has been obtained by Sauloy along the lines of Birkhoff and then, for irregular equations, by Ramis, Sauloy and Zhang in terms of q-Stokes operators.

However, these correspondances are not formulated in geometric terms, which makes them little suitable for the study of isomonodromy or "iso-Stokes" deformations. Recently, under the impulse of Ohyama, we started to construct such a geometric description in order to apply it to the famous work of Jimbo-Sakai and then to more recent extensions. I shall describe this work.

Riemann-Hilbert correspondance for fuchsian q-difference equations has been obtained by Sauloy along the lines of Birkhoff and then, for irregular equations, by Ramis, Sauloy and Zhang in terms of q-Stokes operators.

However, these correspondances are not formulated in geometric terms, which makes them little suitable for the study of isomonodromy or "iso-Stokes" deformations. Recently, under the impulse of Ohyama, we started to construct such a geometric description in order to apply it to the famous work of Jimbo-Sakai and then to more recent extensions. I shall describe this work.

### 2013/10/29

#### Tuesday Seminar on Topology

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

Fundamental groups of algebraic varieties (ENGLISH)

**Daniel Matei**(IMAR, Bucharest)Fundamental groups of algebraic varieties (ENGLISH)

[ Abstract ]

We discuss restrictions imposed by the complex

structure on fundamental groups of quasi-projective

algebraic varieties with mild singularities.

We investigate quasi-projectivity of various geometric

classes of finitely presented groups.

We discuss restrictions imposed by the complex

structure on fundamental groups of quasi-projective

algebraic varieties with mild singularities.

We investigate quasi-projectivity of various geometric

classes of finitely presented groups.

#### Numerical Analysis Seminar

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

Development of multi-dimensional compact difference formulas with the aid of formula manipulation software (JAPANESE)

[ Reference URL ]

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

**Sei-ichiro Nagoya**(ARK Information Systems)Development of multi-dimensional compact difference formulas with the aid of formula manipulation software (JAPANESE)

[ Reference URL ]

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

#### Lie Groups and Representation Theory

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

Geometry of multiplicity-free representations of SO(N) and visible actions (JAPANESE)

**Yuichiro Tanaka**(the University of Tokyo, Graduate School of Mathematical Sciences)Geometry of multiplicity-free representations of SO(N) and visible actions (JAPANESE)

[ Abstract ]

For a connected compact simple Lie group of type B or D,

we find pairs $(V_{1},V_{2})$ of irreducible representations of G such that the tensor product representation $V_{1}¥otimes V_{2}$ is multiplicity-free by a geometric consideration based on

a notion of visible actions on complex manifolds,

introduced by T. Kobayashi. The pairs we find exhaust

all the multiplicity-free pairs by an earlier

combinatorial classification due to Stembridge.

For a connected compact simple Lie group of type B or D,

we find pairs $(V_{1},V_{2})$ of irreducible representations of G such that the tensor product representation $V_{1}¥otimes V_{2}$ is multiplicity-free by a geometric consideration based on

a notion of visible actions on complex manifolds,

introduced by T. Kobayashi. The pairs we find exhaust

all the multiplicity-free pairs by an earlier

combinatorial classification due to Stembridge.

### 2013/10/28

#### Seminar on Geometric Complex Analysis

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

Minimal singular metrics of a line bundle admitting no Zariski decomposition (JAPANESE)

**Takayuki Koike**(The University of Tokyo)Minimal singular metrics of a line bundle admitting no Zariski decomposition (JAPANESE)

[ Abstract ]

We give a concrete expression of a minimal singular metric of a big line bundle on a compact Kähler manifold which is the total space of a toric bundle over a complex torus. In this class of manifolds, Nakayama constructed examples which have line bundles admitting no Zariski decomposition even after any proper modifications. As an application, we discuss the Zariski closedness of non-nef loci and the openness conjecture of Demailly and Kollar in this class.

We give a concrete expression of a minimal singular metric of a big line bundle on a compact Kähler manifold which is the total space of a toric bundle over a complex torus. In this class of manifolds, Nakayama constructed examples which have line bundles admitting no Zariski decomposition even after any proper modifications. As an application, we discuss the Zariski closedness of non-nef loci and the openness conjecture of Demailly and Kollar in this class.

#### Algebraic Geometry Seminar

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

Weak Borisov-Alexeev-Borisov conjecture for 3-fold Mori Fiber spaces (ENGLISH)

**Chen Jiang**(University of Tokyo)Weak Borisov-Alexeev-Borisov conjecture for 3-fold Mori Fiber spaces (ENGLISH)

[ Abstract ]

We investigate $\\epsilon$-klt log Fano 3-folds with some Mori fiber space structure, more precisely, with a del Pezzo fibration structure, or a conic bundle structure over projective plane. We give a bound for the log anti-canonical volume of such pair. The method is constructing non-klt centers and using connectedness lemma. This result is related to birational boundedness of log Fano varieties.

We investigate $\\epsilon$-klt log Fano 3-folds with some Mori fiber space structure, more precisely, with a del Pezzo fibration structure, or a conic bundle structure over projective plane. We give a bound for the log anti-canonical volume of such pair. The method is constructing non-klt centers and using connectedness lemma. This result is related to birational boundedness of log Fano varieties.

< Previous 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133 Next >