## Seminar information archive

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

### 2015/07/13

#### Seminar on Geometric Complex Analysis

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

$L^2$ cohomology and deformation of Einstein metrics on strictly pseudo convex domains

**Yoshihiko Matsumoto**(Tokyo Institute of Technology)$L^2$ cohomology and deformation of Einstein metrics on strictly pseudo convex domains

[ Abstract ]

Consider a bounded domain of a Stein manifold, with strictly pseudo convex smooth boundary, endowed with an ACH-Kähler metric (examples being domains of $\mathbb{C}^n$ with their Bergman metrics or Cheng-Yau’s Einstein metrics). We give a vanishing theorem on the $L^2$ $\overline{\partial}$-cohomology group with values in the holomorphic tangent bundle. As an application, Einstein perturbations of the Cheng-Yau metric are discussed.

Consider a bounded domain of a Stein manifold, with strictly pseudo convex smooth boundary, endowed with an ACH-Kähler metric (examples being domains of $\mathbb{C}^n$ with their Bergman metrics or Cheng-Yau’s Einstein metrics). We give a vanishing theorem on the $L^2$ $\overline{\partial}$-cohomology group with values in the holomorphic tangent bundle. As an application, Einstein perturbations of the Cheng-Yau metric are discussed.

#### Tokyo Probability Seminar

16:30-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)

On interacting particle systems in beta random matrix theory

Random field of gradients and elasticity

**Mykhaylo Shkolnikov**(Mathematics Department, Princeton University) 16:30-17:20On interacting particle systems in beta random matrix theory

[ Abstract ]

I will first introduce multilevel Dyson Brownian motions and review how those extend to the setting of beta random matrix theory. Then, I will describe a connection between multilevel Dyson Brownian motions and interacting particle systems on the real line with local interactions. This is the first connection of this kind for values of beta different from 1 and 2. Based on joint work with Vadim Gorin.

I will first introduce multilevel Dyson Brownian motions and review how those extend to the setting of beta random matrix theory. Then, I will describe a connection between multilevel Dyson Brownian motions and interacting particle systems on the real line with local interactions. This is the first connection of this kind for values of beta different from 1 and 2. Based on joint work with Vadim Gorin.

**Stefan Adams**(Mathematics Institute, Warwick University) 17:30-18:20Random field of gradients and elasticity

[ Abstract ]

Random fields of gradients are a class of model systems arising in the studies of random interfaces, random geometry, field theory, and elasticity theory. These random objects pose challenging problems for probabilists as even an a priori distribution involves strong correlations, and are likely to be an universal class of models combining probability, analysis and physics in the study of critical phenomena. They emerge in the following three areas, effective models for random interfaces, Gaussian Free Fields (scaling limits), and mathematical models for the Cauchy-Born rule of materials, i.e., a microscopic approach to nonlinear elasticity. The latter class of models requires that interaction energies are non-convex functions of the gradients. Open problems over the last decades include unicity of Gibbs measures, the scaling to GFF and strict convexity of the free energy. We present in the talk first results for the free energy and the scaling limit at low temperatures using Gaussian measures and rigorous renormalisation group techniques yielding an analysis in terms of dynamical systems. The key ingredient is a finite range decomposition for parameter dependent families of Gaussian measures. (partly joint work with S. Mueller & R. Kotecky)

Random fields of gradients are a class of model systems arising in the studies of random interfaces, random geometry, field theory, and elasticity theory. These random objects pose challenging problems for probabilists as even an a priori distribution involves strong correlations, and are likely to be an universal class of models combining probability, analysis and physics in the study of critical phenomena. They emerge in the following three areas, effective models for random interfaces, Gaussian Free Fields (scaling limits), and mathematical models for the Cauchy-Born rule of materials, i.e., a microscopic approach to nonlinear elasticity. The latter class of models requires that interaction energies are non-convex functions of the gradients. Open problems over the last decades include unicity of Gibbs measures, the scaling to GFF and strict convexity of the free energy. We present in the talk first results for the free energy and the scaling limit at low temperatures using Gaussian measures and rigorous renormalisation group techniques yielding an analysis in terms of dynamical systems. The key ingredient is a finite range decomposition for parameter dependent families of Gaussian measures. (partly joint work with S. Mueller & R. Kotecky)

### 2015/07/11

#### Harmonic Analysis Komaba Seminar

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

An intrinsic square function on weighted Herz spaces with variable exponent

(日本語)

Remarks on the strong maximum principle involving p-Laplacian

(日本語)

**Mitsuo Izuki**(Okayama University) 13:30 -15:00An intrinsic square function on weighted Herz spaces with variable exponent

(日本語)

**Toshio Horiuchi**(Ibaraki University) 15:30 -17:00Remarks on the strong maximum principle involving p-Laplacian

(日本語)

### 2015/07/10

#### thesis presentations

13:30-14:45 Room #128 (Graduate School of Math. Sci. Bldg.)

On stability of viscosity solutions under non-Euclidean metrics（非ユークリッド距離構造の下での粘性解の安定性） (JAPANESE)

**中安 淳**(東京大学大学院数理科学研究科)On stability of viscosity solutions under non-Euclidean metrics（非ユークリッド距離構造の下での粘性解の安定性） (JAPANESE)

### 2015/07/09

#### Infinite Analysis Seminar Tokyo

15:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

An extension of the LMO functor and formal Gaussian integrals (JAPANESE)

On the relative number of ends of higher dimensional Thompson groups (JAPANESE)

**Yuta Nozaki**(Graduate School of Mathematical Sciences, the University of Tokyo) 15:00-16:30An extension of the LMO functor and formal Gaussian integrals (JAPANESE)

[ Abstract ]

Cheptea, Habiro and Massuyeau introduced the LMO functor as an

extension of the LMO invariant of closed 3-manifolds.

The LMO functor is “the monoidal category of Lagrangian cobordisms

between surfaces with at most one boundary component” to “the monoidal

category of certain Jacobi diagrams”.

In this talk, we extend the LMO functor to the case of any number of

boundary components.

In particular, we focus on a formal Gaussian integral, that is an

essential tool to construct the LMO functor.

Cheptea, Habiro and Massuyeau introduced the LMO functor as an

extension of the LMO invariant of closed 3-manifolds.

The LMO functor is “the monoidal category of Lagrangian cobordisms

between surfaces with at most one boundary component” to “the monoidal

category of certain Jacobi diagrams”.

In this talk, we extend the LMO functor to the case of any number of

boundary components.

In particular, we focus on a formal Gaussian integral, that is an

essential tool to construct the LMO functor.

**Motoko Kato**(Graduate School of Mathematical Sciences, the University of Tokyo) 17:00-18:30On the relative number of ends of higher dimensional Thompson groups (JAPANESE)

[ Abstract ]

In 2004, Brin defined n−dimensional Thompson group nV for every natural number n ≥ 1. nV is a generalization of the Thompson group V . The Thompson group V can be described as a subgroup of the homeomorphism group of the Cantor set C. In this point of view, nV is a subgroup of the homeomorphism group of Cn. We prove that the number of ends of nV is equal to 1 and there is a subgroup of nV such that the relative number of ends is ∞. As a corollary of the second result, for each n, nV has Haagerup property and it can not be the fundamental group of a compact K ̈ahler manifold. These results are the generalizations of the corresponding results of Farley, who studied the Thompson group V .

In 2004, Brin defined n−dimensional Thompson group nV for every natural number n ≥ 1. nV is a generalization of the Thompson group V . The Thompson group V can be described as a subgroup of the homeomorphism group of the Cantor set C. In this point of view, nV is a subgroup of the homeomorphism group of Cn. We prove that the number of ends of nV is equal to 1 and there is a subgroup of nV such that the relative number of ends is ∞. As a corollary of the second result, for each n, nV has Haagerup property and it can not be the fundamental group of a compact K ̈ahler manifold. These results are the generalizations of the corresponding results of Farley, who studied the Thompson group V .

### 2015/07/08

#### Operator Algebra Seminars

16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)

Conformal field theory, subfactors and planar algebras

**Marcel Bischoff**(Vanderbilt Univ.)Conformal field theory, subfactors and planar algebras

#### FMSP Lectures

16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)

Conformal field theory, subfactors and planar algebras (ENGLISH)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

**Marcel Bischoff**(Vanderbilt Univ.)Conformal field theory, subfactors and planar algebras (ENGLISH)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

### 2015/07/07

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Representation varieties detect essential surfaces (JAPANESE)

**Takahiro Kitayama**(Tokyo Institute of Technology)Representation varieties detect essential surfaces (JAPANESE)

[ Abstract ]

Extending Culler-Shalen theory, Hara and I presented a way to construct

certain kinds of branched surfaces (possibly without any branch) in a 3-

manifold from an ideal point of a curve in the SL_n-character variety.

There exists an essential surface in some 3-manifold known to be not

detected in the classical SL_2-theory. We show that every essential

surface in a 3-manifold is given by the ideal point of a line in the SL_

n-character variety for some n. The talk is partially based on joint

works with Stefan Friedl and Matthias Nagel, and also with Takashi Hara.

Extending Culler-Shalen theory, Hara and I presented a way to construct

certain kinds of branched surfaces (possibly without any branch) in a 3-

manifold from an ideal point of a curve in the SL_n-character variety.

There exists an essential surface in some 3-manifold known to be not

detected in the classical SL_2-theory. We show that every essential

surface in a 3-manifold is given by the ideal point of a line in the SL_

n-character variety for some n. The talk is partially based on joint

works with Stefan Friedl and Matthias Nagel, and also with Takashi Hara.

### 2015/07/06

#### Seminar on Geometric Complex Analysis

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

On the structure of holomorphic automorphism groups of generalized complex ellipsoids and generalized Hartogs triangles (JAPANESE)

**Akio Kodama**On the structure of holomorphic automorphism groups of generalized complex ellipsoids and generalized Hartogs triangles (JAPANESE)

[ Abstract ]

In this talk, we first review the structure of holomorphic automorphism groups of generalized complex ellipsoids and, as an application of this, we clarify completely the structure of generalized Hartogs triangles. Finally, if possible, I will mention some known results on proper holomorphic self-mappings of generalized complex ellipsoids, generalized Hartogs triangles, and discuss a related question to these results.

In this talk, we first review the structure of holomorphic automorphism groups of generalized complex ellipsoids and, as an application of this, we clarify completely the structure of generalized Hartogs triangles. Finally, if possible, I will mention some known results on proper holomorphic self-mappings of generalized complex ellipsoids, generalized Hartogs triangles, and discuss a related question to these results.

### 2015/07/03

#### Geometry Colloquium

10:00-11:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Proper actions of reductive groups on pseudo-Riemannian symmetric spaces and its compact dual. (日本語)

**Takayuki OKUDA**(HIroshima University)Proper actions of reductive groups on pseudo-Riemannian symmetric spaces and its compact dual. (日本語)

[ Abstract ]

Let G be a non-compact semisimple Lie group. We take a pair of symmetric pairs (G,H) and (G,L) such that the diagonal action of G on G/H \times G/L is proper. In this talk, we show that by taking ``the compact dual of triple (G,H,L)'', we obtain a compact symmetric space M = U/K and its reflective submanifolds S_1 and S_2 satisfying that the intersection of S_1 and gS_2 is discrete in M for any g in U. In particular, we give a classification of such triples (G,H,L).

Let G be a non-compact semisimple Lie group. We take a pair of symmetric pairs (G,H) and (G,L) such that the diagonal action of G on G/H \times G/L is proper. In this talk, we show that by taking ``the compact dual of triple (G,H,L)'', we obtain a compact symmetric space M = U/K and its reflective submanifolds S_1 and S_2 satisfying that the intersection of S_1 and gS_2 is discrete in M for any g in U. In particular, we give a classification of such triples (G,H,L).

### 2015/07/01

#### Operator Algebra Seminars

16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)

Approximate unitary equivalence of finite index endomorphisms of the AFD

factors

**Koichi Shimada**(Univ. Tokyo)Approximate unitary equivalence of finite index endomorphisms of the AFD

factors

### 2015/06/30

#### Lie Groups and Representation Theory

17:00-18:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Random subgroups and representation theory

**Anatoly Vershik**(St. Petersburg Department of Steklov Institute of Mathematics)Random subgroups and representation theory

[ Abstract ]

The following problem had been appeared independently in different teams and various reason:

to describe the Borel measures on the lattice of all subgroups of given group, which are invariant with respect to the action of the group by conjugacy. The main interest of course represents nonatomic measures which exist not for any group.

I will explain how these measures connected with characters and representations of the group, and describe the complete list of such measures for infinite symmetric group.

The following problem had been appeared independently in different teams and various reason:

to describe the Borel measures on the lattice of all subgroups of given group, which are invariant with respect to the action of the group by conjugacy. The main interest of course represents nonatomic measures which exist not for any group.

I will explain how these measures connected with characters and representations of the group, and describe the complete list of such measures for infinite symmetric group.

#### Tuesday Seminar on Topology

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

The Cannon-Thurston maps and the canonical decompositions of punctured surface bundles over the circle (JAPANESE)

**Makoto Sakuma**(Hiroshima University)The Cannon-Thurston maps and the canonical decompositions of punctured surface bundles over the circle (JAPANESE)

[ Abstract ]

To each once-punctured-torus bundle over the circle with pseudo-Anosov monodromy,

there are associated two tessellations of the complex plane:

one is the triangulation of a horosphere induced by the canonical decomposition into ideal tetrahedra,

and the other is a fractal tessellation given by the Cannon-Thurston map of the fiber group.

In a joint work with Warren Dicks, I had described the relation between these two tessellations.

This result was recently generalized by Francois Gueritaud to punctured surface bundles

with pseudo-Anosov monodromy where all singuraities of the invariant foliations are at punctures.

In this talk, I will explain Gueritaud's work and related work by Naoki Sakata.

To each once-punctured-torus bundle over the circle with pseudo-Anosov monodromy,

there are associated two tessellations of the complex plane:

one is the triangulation of a horosphere induced by the canonical decomposition into ideal tetrahedra,

and the other is a fractal tessellation given by the Cannon-Thurston map of the fiber group.

In a joint work with Warren Dicks, I had described the relation between these two tessellations.

This result was recently generalized by Francois Gueritaud to punctured surface bundles

with pseudo-Anosov monodromy where all singuraities of the invariant foliations are at punctures.

In this talk, I will explain Gueritaud's work and related work by Naoki Sakata.

### 2015/06/29

#### Seminar on Geometric Complex Analysis

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

Cohomology Formula for Obstructions to Asymptotic Chow semistability (JAPANESE)

**Yuta Suzuki**(Univ. of Tokyo)Cohomology Formula for Obstructions to Asymptotic Chow semistability (JAPANESE)

[ Abstract ]

Odaka and Wang proved the intersection formula for the Donaldson-Futaki invariant. We generalize this result for the higher Futaki invariants which are obstructions to asymptotic Chow semistability.

Odaka and Wang proved the intersection formula for the Donaldson-Futaki invariant. We generalize this result for the higher Futaki invariants which are obstructions to asymptotic Chow semistability.

#### Algebraic Geometry Seminar

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

Twisted cubics and cubic fourfolds (English)

**Manfred Lehn**(Mainz/RIMS)Twisted cubics and cubic fourfolds (English)

[ Abstract ]

The moduli scheme of generalised twisted cubics on a smooth

cubic fourfold Y non containing a plane is smooth projective of

dimension 10 and admits a contraction to an 8-dimensional

holomorphic symplectic manifold Z(Y). The latter is shown to be

birational to the Hilbert scheme of four points on a K3 surface if

Y is of Pfaffian type. This is a report on joint work with C. Lehn,

C. Sorger and D. van Straten and with N. Addington.

The moduli scheme of generalised twisted cubics on a smooth

cubic fourfold Y non containing a plane is smooth projective of

dimension 10 and admits a contraction to an 8-dimensional

holomorphic symplectic manifold Z(Y). The latter is shown to be

birational to the Hilbert scheme of four points on a K3 surface if

Y is of Pfaffian type. This is a report on joint work with C. Lehn,

C. Sorger and D. van Straten and with N. Addington.

#### Tokyo Probability Seminar

16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)

**Kunio Nishioka**(Faculty of Commerce, Chuo University)#### Numerical Analysis Seminar

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

Stabilized Runge-Kutta methods for the weak approximation of solutions of stochastic differential equations (日本語)

**Yoshio Komori**(Kyushu Institute of Technology)Stabilized Runge-Kutta methods for the weak approximation of solutions of stochastic differential equations (日本語)

[ Abstract ]

We are concerned with numerical methods which give weak approximations for stiff It\^{o} stochastic differential equations (SDEs). Implicit methods are one of good candidates to deal with such SDEs. In fact, a well-designed implicit method has been recently proposed by Abdulle and his colleagues [Abdulle et al. 2013a]. On the other hand, it is well known that the numerical solution of stiff SDEs leads to a stepsize reduction when explicit methods are used. However, there are some classes of explicit methods that are well suited to solving some types of stiff SDEs. One such class is the class of stochastic orthogonal Runge-Kutta Chebyshev (SROCK) methods [Abdulle et al. 2013b]. SROCK methods reduce to Runge-Kutta Chebyshev methods when applied to ordinary differential equations (ODEs). Another promising class of methods is the class of explicit methods that reduce to explicit exponential Runge-Kutta (RK) methods [Hochbruck et al. 2005, 2010] when applied to semilinear ODEs.

In this talk, we will propose new exponential RK methods which achieve weak order two for multi-dimensional, non-commutative SDEs with a semilinear drift term. We will analytically investigate their stability properties in mean square, and will check their performance in numerical experiments.

(This is a joint work with D. Cohen and K. Burrage.)

We are concerned with numerical methods which give weak approximations for stiff It\^{o} stochastic differential equations (SDEs). Implicit methods are one of good candidates to deal with such SDEs. In fact, a well-designed implicit method has been recently proposed by Abdulle and his colleagues [Abdulle et al. 2013a]. On the other hand, it is well known that the numerical solution of stiff SDEs leads to a stepsize reduction when explicit methods are used. However, there are some classes of explicit methods that are well suited to solving some types of stiff SDEs. One such class is the class of stochastic orthogonal Runge-Kutta Chebyshev (SROCK) methods [Abdulle et al. 2013b]. SROCK methods reduce to Runge-Kutta Chebyshev methods when applied to ordinary differential equations (ODEs). Another promising class of methods is the class of explicit methods that reduce to explicit exponential Runge-Kutta (RK) methods [Hochbruck et al. 2005, 2010] when applied to semilinear ODEs.

In this talk, we will propose new exponential RK methods which achieve weak order two for multi-dimensional, non-commutative SDEs with a semilinear drift term. We will analytically investigate their stability properties in mean square, and will check their performance in numerical experiments.

(This is a joint work with D. Cohen and K. Burrage.)

#### Operator Algebra Seminars

16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)

Block spin renormalization and R. Thompson's groups F and T

**Vaughan F. R. Jones**(Vanderbilt University)Block spin renormalization and R. Thompson's groups F and T

### 2015/06/26

#### Colloquium

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

Dimer models and mirror symmetry (JAPANESE)

**Kazushi Ueda**(Graduate School of Mathematical Sciences, University of Tokyo)Dimer models and mirror symmetry (JAPANESE)

### 2015/06/25

#### Infinite Analysis Seminar Tokyo

17:00-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Autonomous limit of the 4-dimensional Painlev¥.FN"e-type equations and degeneration of curves of genus two (JAPANESE)

**Akane Nakamura**(Tokyo University, Graduate School of Mathematical Sciences)Autonomous limit of the 4-dimensional Painlev¥.FN"e-type equations and degeneration of curves of genus two (JAPANESE)

[ Abstract ]

The Painlev¥.FN"e equations have been generalized from various aspects. Recently, the 4-dimensional Painlev¥N"e-type equations were classified by corresponding linear equations(Sakai, Kawakami-N.-Sakai, Kawakami). In this talk, I explain an attempt to characterize the 40 types of integrable systems obtained as the autonomous limit of the 4-dimensional Painlev¥N"e-type equations, by inspecting the degenerations of their spectral curves, which are curves of genus two.

The Painlev¥.FN"e equations have been generalized from various aspects. Recently, the 4-dimensional Painlev¥N"e-type equations were classified by corresponding linear equations(Sakai, Kawakami-N.-Sakai, Kawakami). In this talk, I explain an attempt to characterize the 40 types of integrable systems obtained as the autonomous limit of the 4-dimensional Painlev¥N"e-type equations, by inspecting the degenerations of their spectral curves, which are curves of genus two.

### 2015/06/24

#### Operator Algebra Seminars

16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)

Gapped ground state phases, topological order and anyons

**Matthew Cha**(UC Davis)Gapped ground state phases, topological order and anyons

### 2015/06/23

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Box complexes and model structures on the category of graphs (JAPANESE)

**Takahiro Matsushita**(The University of Tokyo)Box complexes and model structures on the category of graphs (JAPANESE)

[ Abstract ]

To determine the chromatic numbers of graphs, so-called the graph

coloring problem, is one of the most classical problems in graph theory.

Box complex is a Z_2-space associated to a graph, and it is known that

its equivariant homotopy invariant is related to the chromatic number.

Csorba showed that for each finite Z_2-CW-complex X, there is a graph

whose box complex is Z_2-homotopy equivalent to X. From this result, I

expect that the usual model category of Z_2-topological spaces is

Quillen equivalent to a certain model structure on the category of

graphs, whose weak equivalences are graph homomorphisms inducing Z_2-

homotopy equivalences between their box complexes.

In this talk, we introduce model structures on the category of graphs

whose weak equivalences are described as above. We also compare our

model categories of graphs with the category of Z_2-topological spaces.

To determine the chromatic numbers of graphs, so-called the graph

coloring problem, is one of the most classical problems in graph theory.

Box complex is a Z_2-space associated to a graph, and it is known that

its equivariant homotopy invariant is related to the chromatic number.

Csorba showed that for each finite Z_2-CW-complex X, there is a graph

whose box complex is Z_2-homotopy equivalent to X. From this result, I

expect that the usual model category of Z_2-topological spaces is

Quillen equivalent to a certain model structure on the category of

graphs, whose weak equivalences are graph homomorphisms inducing Z_2-

homotopy equivalences between their box complexes.

In this talk, we introduce model structures on the category of graphs

whose weak equivalences are described as above. We also compare our

model categories of graphs with the category of Z_2-topological spaces.

### 2015/06/22

#### Algebraic Geometry Seminar

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

Rational cohomology tori

(English)

http://webusers.imj-prg.fr/~marti.lahoz/

**Martí Lahoz**(Institut de Mathématiques de Jussieu )Rational cohomology tori

(English)

[ Abstract ]

Complex tori can be topologically characterised among compact Kähler

manifolds by their integral cohomology ring. I will discuss the

structure of compact Kähler manifolds whose rational cohomology ring is

isomorphic to the rational cohomology ring of a torus and give some

examples. This is joint work with Olivier Debarre and Zhi Jiang.

[ Reference URL ]Complex tori can be topologically characterised among compact Kähler

manifolds by their integral cohomology ring. I will discuss the

structure of compact Kähler manifolds whose rational cohomology ring is

isomorphic to the rational cohomology ring of a torus and give some

examples. This is joint work with Olivier Debarre and Zhi Jiang.

http://webusers.imj-prg.fr/~marti.lahoz/

#### Seminar on Geometric Complex Analysis

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

Amoebas and Horn hypergeometric functions

**Susumu Tanabé**(Université Galatasaray)Amoebas and Horn hypergeometric functions

[ Abstract ]

Since 10 years, the utility of the Horn hypergeometric functions in Algebraic Geometry has been recognized in a small circle of specialists. The main reason for this interest lies in the fact that every period integral of an affine non-degenerate complete intersection variety can be described as a Horn hypergeometric function (HGF). Therefore the monodromy of the middle dimensional homology can be calculated as the monodromy of an Horn HGF’s.

There is a slight difference between the Gel’fand-Kapranov-Zelevinski HGF’s and the Horn HGF’s. The latter may contain so called “persistent polynomial solutions” that cannot be mapped to GKZ HGF’s via a natural isomorphism between two spaces of HGF’s. In this talk, I will review basic facts on the Horn HGF’s. As a main tool to study the topology of the discriminant loci together with the

analytic aspects of the story, amoebas – image by the log map of the discriminant- will be highlighted.

As an application of this theory the following theorem can be established. For a bivariate Horn HGF system, its monodromy invariant space is always one dimensional if and only if its Ore-Sato polygon is either a zonotope or a Minkowski sum of a triangle and some segments.

This is a collaboration with Timur Sadykov.

Since 10 years, the utility of the Horn hypergeometric functions in Algebraic Geometry has been recognized in a small circle of specialists. The main reason for this interest lies in the fact that every period integral of an affine non-degenerate complete intersection variety can be described as a Horn hypergeometric function (HGF). Therefore the monodromy of the middle dimensional homology can be calculated as the monodromy of an Horn HGF’s.

There is a slight difference between the Gel’fand-Kapranov-Zelevinski HGF’s and the Horn HGF’s. The latter may contain so called “persistent polynomial solutions” that cannot be mapped to GKZ HGF’s via a natural isomorphism between two spaces of HGF’s. In this talk, I will review basic facts on the Horn HGF’s. As a main tool to study the topology of the discriminant loci together with the

analytic aspects of the story, amoebas – image by the log map of the discriminant- will be highlighted.

As an application of this theory the following theorem can be established. For a bivariate Horn HGF system, its monodromy invariant space is always one dimensional if and only if its Ore-Sato polygon is either a zonotope or a Minkowski sum of a triangle and some segments.

This is a collaboration with Timur Sadykov.

#### Tokyo Probability Seminar

16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)

Lamplighter random walks on fractals

**Chikara Nakamura**(Research Institute for Mathematical Sciences, Kyoto University)Lamplighter random walks on fractals

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