## Seminar information archive

Seminar information archive ～05/25｜Today's seminar 05/26 | Future seminars 05/27～

#### thesis presentations

10:30-11:45 Room #122 (Graduate School of Math. Sci. Bldg.)

Special Lagrangian submanifolds and mean curvature flows（特殊ラグランジュ部分多様体と平均曲率流について） (JAPANESE)

**山本 光**(東京大学大学院数理科学研究科)Special Lagrangian submanifolds and mean curvature flows（特殊ラグランジュ部分多様体と平均曲率流について） (JAPANESE)

#### FMSP Lectures

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

Selected topics in fractional partial differential equations (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Luchko.pdf

**Yuri Luchko**(University of Applied Sciences, Berlin)Selected topics in fractional partial differential equations (ENGLISH)

[ Abstract ]

In this talk, some remarkable mathematical and physical properties of solutions to the fractional diffusion equation, the alpha-fractional diffusion and alpha-fractional wave equations, the fractional reaction-diffusion equation, and the fractional Schrödinger equation are revisited. From the mathematical viewpoint, the maximum principle for the initial-boundary-value problems for the fractional diffusion equation, the scaling properties of the solutions to the alpha-fractional diffusion and alpha-fractional wave equations and the role of the Mellin integral transform technique for their analytical treatment, as well as the eigenvalue problem for the fractional Schrödinger equation are considered. Physical aspects include a discussion of a probabilistic interpretation of the fundamental solutions to the Cauchy problem for the alpha-fractional diffusion equation, their entropy and the entropy production rates, and some different concepts of the propagation velocities of the fractional wave processes.

[ Reference URL ]In this talk, some remarkable mathematical and physical properties of solutions to the fractional diffusion equation, the alpha-fractional diffusion and alpha-fractional wave equations, the fractional reaction-diffusion equation, and the fractional Schrödinger equation are revisited. From the mathematical viewpoint, the maximum principle for the initial-boundary-value problems for the fractional diffusion equation, the scaling properties of the solutions to the alpha-fractional diffusion and alpha-fractional wave equations and the role of the Mellin integral transform technique for their analytical treatment, as well as the eigenvalue problem for the fractional Schrödinger equation are considered. Physical aspects include a discussion of a probabilistic interpretation of the fundamental solutions to the Cauchy problem for the alpha-fractional diffusion equation, their entropy and the entropy production rates, and some different concepts of the propagation velocities of the fractional wave processes.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Luchko.pdf

### 2015/12/15

#### Tuesday Seminar on Topology

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

The Curved Cartan Complex (ENGLISH)

**Constantin Teleman**(University of California, Berkeley)The Curved Cartan Complex (ENGLISH)

[ Abstract ]

The Cartan model computes the equivariant cohomology of a smooth manifold X with

differentiable action of a compact Lie group G, from the invariant polynomial

functions on the Lie algebra with values in differential forms and a deformation

of the de Rham differential. Before extracting invariants, the Cartan differential

does not square to zero and is apparently meaningless. Unrecognised was the fact

that the full complex is a curved algebra, computing the quotient by G of the

algebra of differential forms on X. This generates, for example, a gauged version of

string topology. Another instance of the construction, applied to deformation

quantisation of symplectic manifolds, gives the BRST construction of the symplectic

quotient. Finally, the theory for a X point with an additional quadratic curving

computes the representation category of the compact group G, and this generalises

to the loop group of G and even to real semi-simple groups.

The Cartan model computes the equivariant cohomology of a smooth manifold X with

differentiable action of a compact Lie group G, from the invariant polynomial

functions on the Lie algebra with values in differential forms and a deformation

of the de Rham differential. Before extracting invariants, the Cartan differential

does not square to zero and is apparently meaningless. Unrecognised was the fact

that the full complex is a curved algebra, computing the quotient by G of the

algebra of differential forms on X. This generates, for example, a gauged version of

string topology. Another instance of the construction, applied to deformation

quantisation of symplectic manifolds, gives the BRST construction of the symplectic

quotient. Finally, the theory for a X point with an additional quadratic curving

computes the representation category of the compact group G, and this generalises

to the loop group of G and even to real semi-simple groups.

### 2015/12/14

#### Seminar on Geometric Complex Analysis

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

Twistor correspondence for associative Grassmanniann

**Fuminori Nakata**(Fukushima Univ.)Twistor correspondence for associative Grassmanniann

[ Abstract ]

It is well known that the 6-dimensional sphere has a non-integrable almost complex structure which is introduced from the (right) multiplication of imaginary octonians. On this 6-sphere, there is a family of psuedo-holomorphic $\mathbb{C}\mathbb{P}^1$ parameterised by the associative Grassmannian, where the associative Grassmaniann is an 8-dimensional quaternion Kaehler manifold defined as the set of associative 3-planes in the 7-dimensional real vector space of the imaginary octonians. In the talk, we show that this story is quite analogous to the Penrose's twistor correspondence and that the geometric structures on the associative Grassmaniann nicely fit to this construction. This is a joint work with H. Hashimoto, K. Mashimo and M. Ohashi.

It is well known that the 6-dimensional sphere has a non-integrable almost complex structure which is introduced from the (right) multiplication of imaginary octonians. On this 6-sphere, there is a family of psuedo-holomorphic $\mathbb{C}\mathbb{P}^1$ parameterised by the associative Grassmannian, where the associative Grassmaniann is an 8-dimensional quaternion Kaehler manifold defined as the set of associative 3-planes in the 7-dimensional real vector space of the imaginary octonians. In the talk, we show that this story is quite analogous to the Penrose's twistor correspondence and that the geometric structures on the associative Grassmaniann nicely fit to this construction. This is a joint work with H. Hashimoto, K. Mashimo and M. Ohashi.

#### Algebraic Geometry Seminar

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

Extending Hori-Vafa toric mirror symmetry via SYZ and modular forms (English)

**Atsushi Kanazawa**(Harvard)Extending Hori-Vafa toric mirror symmetry via SYZ and modular forms (English)

[ Abstract ]

In this talk, I will introduce partial compactification for a class of toric Calabi-Yau manifolds. A fundamental question is how the Hori-Vafa toric mirror symmetry extends to this new class of Calabi-Yau manifolds. The answer leads us to a new connection between SYZ mirror symmetry and modular forms. If time permits, I will also discuss higher dimensional analogues of the Yau-Zaslow formula (for an elliptic K3 surface) in terms of Siegel modular forms. This talk is based on a joint work with Siu-Cheong Lau.

In this talk, I will introduce partial compactification for a class of toric Calabi-Yau manifolds. A fundamental question is how the Hori-Vafa toric mirror symmetry extends to this new class of Calabi-Yau manifolds. The answer leads us to a new connection between SYZ mirror symmetry and modular forms. If time permits, I will also discuss higher dimensional analogues of the Yau-Zaslow formula (for an elliptic K3 surface) in terms of Siegel modular forms. This talk is based on a joint work with Siu-Cheong Lau.

### 2015/12/09

#### Operator Algebra Seminars

16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)

K-theory in subfactors and conformal field theory

**David E. Evans**(Cardiff Univ.)K-theory in subfactors and conformal field theory

#### Number Theory Seminar

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

Chern classes in Iwasawa theory (English)

**Ted Chinburg**(University of Pennsylvania & IHES)Chern classes in Iwasawa theory (English)

[ Abstract ]

Many of the main conjectures in Iwasawa theory can be phrased as saying that the first Chern class of an Iwasawa module is generated by a p-adic L-series. In this talk I will describe how higher Chern classes pertain to the higher codimension behavior of Iwasawa modules. I'll then describe a template for conjectures which would link such higher Chern classes to elements in the K-theory of Iwasawa algebras which are constructed from tuples of Katz p-adic L-series. I will finally describe an instance in which a result of this kind, for the second Chern class of an unramified Iwasawa module, can be proved over an imaginary quadratic field. This is joint work with F. Bleher, R. Greenberg, M. Kakde, G. Pappas, R. Sharifi and M. J. Taylor.

Many of the main conjectures in Iwasawa theory can be phrased as saying that the first Chern class of an Iwasawa module is generated by a p-adic L-series. In this talk I will describe how higher Chern classes pertain to the higher codimension behavior of Iwasawa modules. I'll then describe a template for conjectures which would link such higher Chern classes to elements in the K-theory of Iwasawa algebras which are constructed from tuples of Katz p-adic L-series. I will finally describe an instance in which a result of this kind, for the second Chern class of an unramified Iwasawa module, can be proved over an imaginary quadratic field. This is joint work with F. Bleher, R. Greenberg, M. Kakde, G. Pappas, R. Sharifi and M. J. Taylor.

### 2015/12/08

#### Tuesday Seminar on Topology

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

Lens space surgery and Kirby calculus of 4-manifolds (JAPANESE)

**Yuichi Yamada**(The Univ. of Electro-Comm.)Lens space surgery and Kirby calculus of 4-manifolds (JAPANESE)

[ Abstract ]

The problem asking "Which knot yields a lens space by Dehn surgery" is

called "lens space surgery". Berge's list ('90) is believed to be the

complete list, but it is still unproved, even after some progress by

Heegaard Floer Homology.

This problem seems to enter a new aspect: study using 4-manifolds, lens

space surgery from lens spaces, checking hyperbolicity by computer.

In the talk, we review the structure of Berge's list and talk on our

study on pairs of distinct knots but yield same lens spaces, and

4-maniolds constructed from such pairs. This is joint work with Motoo

Tange (Tsukuba University).

The problem asking "Which knot yields a lens space by Dehn surgery" is

called "lens space surgery". Berge's list ('90) is believed to be the

complete list, but it is still unproved, even after some progress by

Heegaard Floer Homology.

This problem seems to enter a new aspect: study using 4-manifolds, lens

space surgery from lens spaces, checking hyperbolicity by computer.

In the talk, we review the structure of Berge's list and talk on our

study on pairs of distinct knots but yield same lens spaces, and

4-maniolds constructed from such pairs. This is joint work with Motoo

Tange (Tsukuba University).

### 2015/12/07

#### Tokyo Probability Seminar

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

Quenched invariance principle for random walks in time-dependent balanced random environment

**Jean-Dominique Deuschel**(TU Berlin)Quenched invariance principle for random walks in time-dependent balanced random environment

[ Abstract ]

We prove an almost sure functional limit theorem for a random walk in an space-time ergodic balanced environment under certain moment conditions. The proof is based on the maximal principle for parabolic difference operators. We also deal with the non-elliptic case, where the corresponding limiting diffusion matrix can be random in higher dimensions. This is a joint work with N. Berger, X. Guo and A. Ramirez.

We prove an almost sure functional limit theorem for a random walk in an space-time ergodic balanced environment under certain moment conditions. The proof is based on the maximal principle for parabolic difference operators. We also deal with the non-elliptic case, where the corresponding limiting diffusion matrix can be random in higher dimensions. This is a joint work with N. Berger, X. Guo and A. Ramirez.

#### Seminar on Geometric Complex Analysis

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

Cycle connectivity and pseudoconcavity of flag domains (Japanese)

**Tatsuki Hayama**(Senshu Univ.)Cycle connectivity and pseudoconcavity of flag domains (Japanese)

[ Abstract ]

We consider an open real group orbit in a complex flag variety which has no non-constant function. We introduce Huckleberry's results on cycle connectivity and show that it is pseudoconcave if it satisfies a certain condition on the root system of the Lie algebra. In Hodge theory, we are mainly interested in the case where it is a Mumford-Tate domain. We also discuss Hodge theoretical meanings of this work.

We consider an open real group orbit in a complex flag variety which has no non-constant function. We introduce Huckleberry's results on cycle connectivity and show that it is pseudoconcave if it satisfies a certain condition on the root system of the Lie algebra. In Hodge theory, we are mainly interested in the case where it is a Mumford-Tate domain. We also discuss Hodge theoretical meanings of this work.

#### Algebraic Geometry Seminar

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

Flops and spherical functors (English)

**Alexey Bondal**(IPMU)Flops and spherical functors (English)

[ Abstract ]

I will describe various functors on derived categories of coherent sheaves

related to flops and relations between these functors. A categorical

version of deformation theory of systems of objects in abelian categories

will be outlined and its relation to flop spherical functors will be

presented.

I will describe various functors on derived categories of coherent sheaves

related to flops and relations between these functors. A categorical

version of deformation theory of systems of objects in abelian categories

will be outlined and its relation to flop spherical functors will be

presented.

### 2015/12/04

#### Colloquium

16:50-17:50 Room #123 (Graduate School of Math. Sci. Bldg.)

Exact forms and closed forms on some infinite product spaces appearing in the study of probability theory

(JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/teacher/sasada.html

**Makiko Sasada**(Graduate School of Mathematical Sciences, University of Tokyo)Exact forms and closed forms on some infinite product spaces appearing in the study of probability theory

(JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/teacher/sasada.html

#### Geometry Colloquium

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

The q-Boson system and a deformation of the affine Hecke algebra (Japanese)

**Yoshihiro Takeyama**(Graduate School of Pure and Applied Sciences, University of Tsukuba)The q-Boson system and a deformation of the affine Hecke algebra (Japanese)

[ Abstract ]

The q-Boson system due to Sasamoto and Wadati is a one-dimensional "integrable" stochastic particle model. Its Q-matrix is constructed in the framework of the quantum inverse scattering method and we obtain the eigenvectors by means of the algebraic Bethe ansatz method. Recently it is found that the q-Boson model can be derived also from a representation of a deformation of the affine Hecke algebra and its representation. In this formulation we get the eigenvectors of the transpose of the Q-matrix which were constructed by the technique called the coordinate Bethe ansatz. In this talk I review the above results and discuss the relationship between the two methods.

The q-Boson system due to Sasamoto and Wadati is a one-dimensional "integrable" stochastic particle model. Its Q-matrix is constructed in the framework of the quantum inverse scattering method and we obtain the eigenvectors by means of the algebraic Bethe ansatz method. Recently it is found that the q-Boson model can be derived also from a representation of a deformation of the affine Hecke algebra and its representation. In this formulation we get the eigenvectors of the transpose of the Q-matrix which were constructed by the technique called the coordinate Bethe ansatz. In this talk I review the above results and discuss the relationship between the two methods.

### 2015/12/03

#### Seminar on Probability and Statistics

16:40-18:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Learning theory and sparsity ～ Sparsity and low rank matrix learning ～

**Arnak Dalalyan**(ENSAE ParisTech)Learning theory and sparsity ～ Sparsity and low rank matrix learning ～

[ Abstract ]

In this third lecture, we will present extensions of the previously introduced sparse recovery techniques to the problems of machine learning and statistics in which a large matrix should be learned from data. The analogue of the sparsity, in this context, is the low-rankness of the matrix. We will show that such matrices can be effectively learned by minimizing the empirical risk penalized by the nuclear norm. The resulting problem is a problem of semi-definite programming and can be solved efficiently even when the dimension is large. Theoretical guarantees for this method will be established in the case of matrix completion with known sampling distribution.

In this third lecture, we will present extensions of the previously introduced sparse recovery techniques to the problems of machine learning and statistics in which a large matrix should be learned from data. The analogue of the sparsity, in this context, is the low-rankness of the matrix. We will show that such matrices can be effectively learned by minimizing the empirical risk penalized by the nuclear norm. The resulting problem is a problem of semi-definite programming and can be solved efficiently even when the dimension is large. Theoretical guarantees for this method will be established in the case of matrix completion with known sampling distribution.

#### FMSP Lectures

16:40-18:00 Room #123 (Graduate School of Math. Sci. Bldg.)

(3)Sparsity and low rank matrix learning. (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dalalyan.pdf

**Arnak Dalalyan**(ENSAE ParisTech)(3)Sparsity and low rank matrix learning. (ENGLISH)

[ Abstract ]

In this third lecture, we will present extensions of the previously introduced sparse recovery techniques to the problems of machine learning and statistics in which a large matrix should be learned from data. The analogue of the sparsity, in this context, is the low-rankness of the matrix. We will show that such matrices can be effectively learned by minimizing the empirical risk penalized by the nuclear norm. The resulting problem is a problem of semi-definite programming and can be solved efficiently even when the dimension is large. Theoretical guarantees for this method will be established in the case of matrix completion with known sampling distribution.

[ Reference URL ]In this third lecture, we will present extensions of the previously introduced sparse recovery techniques to the problems of machine learning and statistics in which a large matrix should be learned from data. The analogue of the sparsity, in this context, is the low-rankness of the matrix. We will show that such matrices can be effectively learned by minimizing the empirical risk penalized by the nuclear norm. The resulting problem is a problem of semi-definite programming and can be solved efficiently even when the dimension is large. Theoretical guarantees for this method will be established in the case of matrix completion with known sampling distribution.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dalalyan.pdf

### 2015/12/02

#### Operator Algebra Seminars

16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Drinfeld center and representation theory for monoidal categories

**Makoto Yamashita**(Ochanomizu Univ.)Drinfeld center and representation theory for monoidal categories

#### Seminar on Probability and Statistics

14:55-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Learning theory and sparsity ～ Lasso, Dantzig selector and their statistical properties ～

**Arnak Dalalyan**(ENSAE ParisTech)Learning theory and sparsity ～ Lasso, Dantzig selector and their statistical properties ～

[ Abstract ]

In this second lecture, we will focus on the problem of high dimensional linear regression under the sparsity assumption and discuss the three main statistical problems: denoising, prediction and model selection. We will prove that convex programming based predictors such as the lasso and the Dantzig selector are provably consistent as soon as the dictionary elements are normalized and an appropriate upper bound on the noise-level is available. We will also show that under additional assumptions on the dictionary elements, the aforementioned methods are rate-optimal and model-selection consistent.

In this second lecture, we will focus on the problem of high dimensional linear regression under the sparsity assumption and discuss the three main statistical problems: denoising, prediction and model selection. We will prove that convex programming based predictors such as the lasso and the Dantzig selector are provably consistent as soon as the dictionary elements are normalized and an appropriate upper bound on the noise-level is available. We will also show that under additional assumptions on the dictionary elements, the aforementioned methods are rate-optimal and model-selection consistent.

#### FMSP Lectures

14:55-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

(2)Lasso, Dantzig selector and their statistical properties. (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dalalyan.pdf

**Arnak Dalalyan**(ENSAE ParisTech)(2)Lasso, Dantzig selector and their statistical properties. (ENGLISH)

[ Abstract ]

In this second lecture, we will focus on the problem of high dimensional linear regression under the sparsity assumption and discuss the three main statistical problems: denoising, prediction and model selection. We will prove that convex programming based predictors such as the lasso and the Dantzig selector are provably consistent as soon as the dictionary elements are normalized and an appropriate upper bound on the noise-level is available. We will also show that under additional assumptions on the dictionary elements, the aforementioned methods are rate-optimal and model-selection consistent.

[ Reference URL ]In this second lecture, we will focus on the problem of high dimensional linear regression under the sparsity assumption and discuss the three main statistical problems: denoising, prediction and model selection. We will prove that convex programming based predictors such as the lasso and the Dantzig selector are provably consistent as soon as the dictionary elements are normalized and an appropriate upper bound on the noise-level is available. We will also show that under additional assumptions on the dictionary elements, the aforementioned methods are rate-optimal and model-selection consistent.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dalalyan.pdf

#### Mathematical Biology Seminar

14:55-16:40 Room #128 (Graduate School of Math. Sci. Bldg.)

Network centrality measure based on sensitivity analysis of the basic reproductive ratio

[ Reference URL ]

http://www.soken.ac.jp/

**Kenta Yajima**( The Graduate University for Advanced Studies (Sokendai), School of Advanced Sciences)Network centrality measure based on sensitivity analysis of the basic reproductive ratio

[ Reference URL ]

http://www.soken.ac.jp/

### 2015/12/01

#### Tuesday Seminar of Analysis

16:50-18:20 Room #126 (Graduate School of Math. Sci. Bldg.)

On complex singularity analysis for some linear partial differential equations

**Stéphane Malek**(Université de Lille, France)On complex singularity analysis for some linear partial differential equations

[ Abstract ]

We investigate the existence of local holomorphic solutions Y of linear partial differential equations in three complex variables whose coefficients are holomorphic on some polydisc outside some singular set S. The coefficients are written as linear combinations of powers of a solution X of some first order nonlinear partial differential equation following an idea :we have initiated in a previous joint work with C. Stenger. The solutions Y are shown to develop singularities along the singular set S with estimates of exponential type depending on the growth's rate of X near the singular set. We construct these solutions with the help of series of functions with infinitely many variables which involve derivatives of all orders of X in one variable. Convergence and bounds estimates of these series are studied using a majorant series method which leads to an auxiliary functional equation that contains differential operators in infinitely many variables. Using a fixed point argument, we show that these functional equations actually have solutions in some Banach spaces of formal power series. (Joint work with A. Lastra and C. Stenger).

We investigate the existence of local holomorphic solutions Y of linear partial differential equations in three complex variables whose coefficients are holomorphic on some polydisc outside some singular set S. The coefficients are written as linear combinations of powers of a solution X of some first order nonlinear partial differential equation following an idea :we have initiated in a previous joint work with C. Stenger. The solutions Y are shown to develop singularities along the singular set S with estimates of exponential type depending on the growth's rate of X near the singular set. We construct these solutions with the help of series of functions with infinitely many variables which involve derivatives of all orders of X in one variable. Convergence and bounds estimates of these series are studied using a majorant series method which leads to an auxiliary functional equation that contains differential operators in infinitely many variables. Using a fixed point argument, we show that these functional equations actually have solutions in some Banach spaces of formal power series. (Joint work with A. Lastra and C. Stenger).

#### Tuesday Seminar on Topology

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

Monodromies of splitting families for singular fibers (JAPANESE)

**Takayuki Okuda**(The University of Tokyo)Monodromies of splitting families for singular fibers (JAPANESE)

[ Abstract ]

A degeneration of Riemann surfaces is a family of complex curves

over a disk allowed to have a singular fiber.

A singular fiber may split into several simpler singular fibers

under a deformation family of such families,

which is called a splitting family for the singular fiber.

We are interested in the topology of splitting families.

For the topological types of degenerations of Riemann surfaces,

it is known that there is a good relationship with

the surface mapping classes, via topological monodromy.

In this talk,

we introduce the "topological monodromies of splitting families",

and give a description of those of certain splitting families.

A degeneration of Riemann surfaces is a family of complex curves

over a disk allowed to have a singular fiber.

A singular fiber may split into several simpler singular fibers

under a deformation family of such families,

which is called a splitting family for the singular fiber.

We are interested in the topology of splitting families.

For the topological types of degenerations of Riemann surfaces,

it is known that there is a good relationship with

the surface mapping classes, via topological monodromy.

In this talk,

we introduce the "topological monodromies of splitting families",

and give a description of those of certain splitting families.

### 2015/11/30

#### Seminar on Geometric Complex Analysis

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

Extension of holomorphic functions defined on non reduced analytic subvarieties (English)

**Jean-Pierre Demailly**(Univ. de Grenoble I)Extension of holomorphic functions defined on non reduced analytic subvarieties (English)

[ Abstract ]

The goal of this talk will be to discuss $L^2$ extension properties of holomorphic sections of vector bundles satisfying weak semi-positivity properties. Using techniques borrowed from recent proofs of the Ohsawa-Takegoshi extension theorem, we obtain several new surjectivity results for the restriction morphism to a non necessarily reduced subvariety, provided the latter is defined as the zero variety of a multiplier ideal sheaf. These extension results are derived from $L^2$ approximation techniques, and they hold under (probably) optimal curvature conditions.

The goal of this talk will be to discuss $L^2$ extension properties of holomorphic sections of vector bundles satisfying weak semi-positivity properties. Using techniques borrowed from recent proofs of the Ohsawa-Takegoshi extension theorem, we obtain several new surjectivity results for the restriction morphism to a non necessarily reduced subvariety, provided the latter is defined as the zero variety of a multiplier ideal sheaf. These extension results are derived from $L^2$ approximation techniques, and they hold under (probably) optimal curvature conditions.

#### Algebraic Geometry Seminar

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

Interesting surfaces which are coverings of a rational surface branched over few lines (English)

**Fabrizio Catanese**(Universität Bayreuth)Interesting surfaces which are coverings of a rational surface branched over few lines (English)

[ Abstract ]

Surfaces which are covers of the plane branched over 5 or 6 lines have provided answers to long standing questions, for instance the BCD surfaces for Fujita's question on semiampleness of VHS (Dettweiler-Cat); and examples of ball quotients (Hirzebruch), automorphisms acting trivially on integral cohomology (Cat-Gromadtzki), canonical maps with high degree or image-degree (Pardini, Bauer-Cat). I shall speak especially about the above Abelian coverings of the plane, the geometry of the del Pezzo surface of degree 5, the rigidity of BCD surfaces, and a criterion for a fibred surface to be a projective classifying space.

Surfaces which are covers of the plane branched over 5 or 6 lines have provided answers to long standing questions, for instance the BCD surfaces for Fujita's question on semiampleness of VHS (Dettweiler-Cat); and examples of ball quotients (Hirzebruch), automorphisms acting trivially on integral cohomology (Cat-Gromadtzki), canonical maps with high degree or image-degree (Pardini, Bauer-Cat). I shall speak especially about the above Abelian coverings of the plane, the geometry of the del Pezzo surface of degree 5, the rigidity of BCD surfaces, and a criterion for a fibred surface to be a projective classifying space.

#### Tokyo Probability Seminar

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

Self-organized criticality in a discrete model of limited aggregation

**Raoul Normand**(Institute of Mathematics, Academia Sinica)Self-organized criticality in a discrete model of limited aggregation

[ Abstract ]

We consider a discrete model of coagulation, where a large number of particles are initially given a prescribed number of arms. We successively choose arms uniformly at random and bind them two by two, unless they belong to "large" clusters. In that sense, the large clusters are frozen and become inactive. We study the graph structure obtained, and describe what a typical cluster looks like. We show that there is a fixed time T such that, before time T, a typical cluster is a subcritical Galton-Watson tree, whereas after time T, a typical cluster is a critical Galton-Watson tree. In that sense, we observe a phenomenon called self-organized criticality.

We consider a discrete model of coagulation, where a large number of particles are initially given a prescribed number of arms. We successively choose arms uniformly at random and bind them two by two, unless they belong to "large" clusters. In that sense, the large clusters are frozen and become inactive. We study the graph structure obtained, and describe what a typical cluster looks like. We show that there is a fixed time T such that, before time T, a typical cluster is a subcritical Galton-Watson tree, whereas after time T, a typical cluster is a critical Galton-Watson tree. In that sense, we observe a phenomenon called self-organized criticality.

### 2015/11/27

#### Colloquium

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

Recent development in amenable groups (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~kida/

**Yoshikata Kida**(Graduate School of Mathematical Sciences, University of Tokyo)Recent development in amenable groups (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~kida/

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