## Seminar information archive

Seminar information archive ～09/22｜Today's seminar 09/23 | Future seminars 09/24～

#### thesis presentations

13:00-14:15 Room #128 (Graduate School of Math. Sci. Bldg.)

### 2018/07/25

#### FMSP Lectures

10:15-12:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)

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

**Christian Schnell**(Stony Book University)Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)

[ Abstract ]

Consider a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). After reviewing what is known about the pushforward of the canonical bundle under such a morphism, we will try to extend these results to the case of pluricanonical bundles (= the tensor powers of the canonical bundle). Along the way, we will learn about three important tools: generic vanishing theory; Viehweg's cyclic covering trick; and some new results from complex analysis about metrics with singularities. As an application, we will discuss the proof of Iitaka's conjecture (about the subadditivity of the Kodaira dimension in algebraic fiber spaces) over abelian varieties, following Cao and Paun.

[ Reference URL ]Consider a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). After reviewing what is known about the pushforward of the canonical bundle under such a morphism, we will try to extend these results to the case of pluricanonical bundles (= the tensor powers of the canonical bundle). Along the way, we will learn about three important tools: generic vanishing theory; Viehweg's cyclic covering trick; and some new results from complex analysis about metrics with singularities. As an application, we will discuss the proof of Iitaka's conjecture (about the subadditivity of the Kodaira dimension in algebraic fiber spaces) over abelian varieties, following Cao and Paun.

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

### 2018/07/24

#### FMSP Lectures

10:15-12:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)

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

**Christian Schnell**(Stony Book University)Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)

[ Abstract ]

Consider a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). After reviewing what is known about the pushforward of the canonical bundle under such a morphism, we will try to extend these results to the case of pluricanonical bundles (= the tensor powers of the canonical bundle). Along the way, we will learn about three important tools: generic vanishing theory; Viehweg's cyclic covering trick; and some new results from complex analysis about metrics with singularities. As an application, we will discuss the proof of Iitaka's conjecture (about the subadditivity of the Kodaira dimension in algebraic fiber spaces) over abelian varieties, following Cao and Paun.

[ Reference URL ]Consider a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). After reviewing what is known about the pushforward of the canonical bundle under such a morphism, we will try to extend these results to the case of pluricanonical bundles (= the tensor powers of the canonical bundle). Along the way, we will learn about three important tools: generic vanishing theory; Viehweg's cyclic covering trick; and some new results from complex analysis about metrics with singularities. As an application, we will discuss the proof of Iitaka's conjecture (about the subadditivity of the Kodaira dimension in algebraic fiber spaces) over abelian varieties, following Cao and Paun.

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

### 2018/07/23

#### Seminar on Geometric Complex Analysis

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

Strange Fatou components of automorphisms of $\mathbb{C}^2$ and Runge embedding of $\mathbb{C} \times \mathbb{C}^*$ into $\mathbb{C}^2$. (ENGLISH)

**Filippo Bracci**(University of Rome Tor Vergata)Strange Fatou components of automorphisms of $\mathbb{C}^2$ and Runge embedding of $\mathbb{C} \times \mathbb{C}^*$ into $\mathbb{C}^2$. (ENGLISH)

[ Abstract ]

The classification of Fatou components for automorphisms of the complex space of dimension greater than $1$ is an interesting and difficult task. Recent deep results prove that the one-dimensional setting is deeply different from the higher dimensional one. Given an automorphism F of $\mathbb{C}^k$, the first bricks in the theory that one would like to understand are invariant Fatou components, namely, those connected open sets $U$, completely invariant under $F$, where the dynamics of $F$ is not chaotic. Among those, we consider “attracting” Fatou components, that is, those components on which the iterates of $F$ converge to a single point. Attracting Fatou components can be recurrent, if the limit point is inside the component or non-recurrent. Recurrent attracting Fatou components are always biholomorphic to $\mathbb{C}^k$, since it was proved by H. Peters, L. Vivas and E. F. Wold that in such a case the point is an attracting (hyperbolic) fixed point, and the Fatou component coincides with the global basin of attraction. Also, as a consequence of works of Ueda and Peters-Lyubich, it is know that all attracting non-recurrent Fatou components of polynomial automorphisms of $\mathbb{C}^2$ are biholomorphic to $\mathbb{C}^2$. One can quite easily find non-simply connected non-recurrent attracting Fatou components in $\mathbb{C}^3$ (mixing a two- dimensional dynamics with a dynamics with non-isolated fixed points in one- variable). In this talk I will explain how to construct a non-recurrent attracting Fatou component in $\mathbb{C}^2$ which is biholomorphic to $\mathbb{C}\times\mathbb{C}^*$. This“fantastic beast” is obtained by globalizing, using a result of F. Forstneric, a local construction due to the speaker and Zaitsev, which allows to create a global basin of attraction for an automorphism, and a Fatou coordinate on it. The Fatou coordinate turns out to be a fiber bundle map on $\mathbb{C}$, whose fiber is $\mathbb{C}^*$, then the global basin is biholomorphic to $\mathbb{C}\times\mathbb{C}^*$. The most subtle point is to show that such a basin is indeed a Fatou component. This is done exploiting Poschel's results about existence of local Siegel discs and suitable estimates for the Kobayashi distance.

Since attracting Fatou components are Runge, it turns out that this construction gives also an example of a Runge embedding of $\mathbb{C}\times\mathbb{C}^*$ into $\mathbb{C}^2$. Moreover, this example shows an automorphism of $\mathbb{C}^2$ leaving invariant two analytic discs intersecting transversally at the origin.

The talk is based on a joint work with J. Raissy and B. Stensones.

The classification of Fatou components for automorphisms of the complex space of dimension greater than $1$ is an interesting and difficult task. Recent deep results prove that the one-dimensional setting is deeply different from the higher dimensional one. Given an automorphism F of $\mathbb{C}^k$, the first bricks in the theory that one would like to understand are invariant Fatou components, namely, those connected open sets $U$, completely invariant under $F$, where the dynamics of $F$ is not chaotic. Among those, we consider “attracting” Fatou components, that is, those components on which the iterates of $F$ converge to a single point. Attracting Fatou components can be recurrent, if the limit point is inside the component or non-recurrent. Recurrent attracting Fatou components are always biholomorphic to $\mathbb{C}^k$, since it was proved by H. Peters, L. Vivas and E. F. Wold that in such a case the point is an attracting (hyperbolic) fixed point, and the Fatou component coincides with the global basin of attraction. Also, as a consequence of works of Ueda and Peters-Lyubich, it is know that all attracting non-recurrent Fatou components of polynomial automorphisms of $\mathbb{C}^2$ are biholomorphic to $\mathbb{C}^2$. One can quite easily find non-simply connected non-recurrent attracting Fatou components in $\mathbb{C}^3$ (mixing a two- dimensional dynamics with a dynamics with non-isolated fixed points in one- variable). In this talk I will explain how to construct a non-recurrent attracting Fatou component in $\mathbb{C}^2$ which is biholomorphic to $\mathbb{C}\times\mathbb{C}^*$. This“fantastic beast” is obtained by globalizing, using a result of F. Forstneric, a local construction due to the speaker and Zaitsev, which allows to create a global basin of attraction for an automorphism, and a Fatou coordinate on it. The Fatou coordinate turns out to be a fiber bundle map on $\mathbb{C}$, whose fiber is $\mathbb{C}^*$, then the global basin is biholomorphic to $\mathbb{C}\times\mathbb{C}^*$. The most subtle point is to show that such a basin is indeed a Fatou component. This is done exploiting Poschel's results about existence of local Siegel discs and suitable estimates for the Kobayashi distance.

Since attracting Fatou components are Runge, it turns out that this construction gives also an example of a Runge embedding of $\mathbb{C}\times\mathbb{C}^*$ into $\mathbb{C}^2$. Moreover, this example shows an automorphism of $\mathbb{C}^2$ leaving invariant two analytic discs intersecting transversally at the origin.

The talk is based on a joint work with J. Raissy and B. Stensones.

#### FMSP Lectures

10:15-12:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)

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

**Christian Schnell**(Stony Book University)Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)

[ Abstract ]

Consider a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). After reviewing what is known about the pushforward of the canonical bundle under such a morphism, we will try to extend these results to the case of pluricanonical bundles (= the tensor powers of the canonical bundle). Along the way, we will learn about three important tools: generic vanishing theory; Viehweg's cyclic covering trick; and some new results from complex analysis about metrics with singularities. As an application, we will discuss the proof of Iitaka's conjecture (about the subadditivity of the Kodaira dimension in algebraic fiber spaces) over abelian varieties, following Cao and Paun.

[ Reference URL ]Consider a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). After reviewing what is known about the pushforward of the canonical bundle under such a morphism, we will try to extend these results to the case of pluricanonical bundles (= the tensor powers of the canonical bundle). Along the way, we will learn about three important tools: generic vanishing theory; Viehweg's cyclic covering trick; and some new results from complex analysis about metrics with singularities. As an application, we will discuss the proof of Iitaka's conjecture (about the subadditivity of the Kodaira dimension in algebraic fiber spaces) over abelian varieties, following Cao and Paun.

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

### 2018/07/20

#### FMSP Lectures

**Christian Schnell**(Stony Book University)

Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)

Consider a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). After reviewing what is known about the pushforward of the canonical bundle under such a morphism, we will try to extend these results to the case of pluricanonical bundles (= the tensor powers of the canonical bundle). Along the way, we will learn about three important tools: generic vanishing theory; Viehweg's cyclic covering trick; and some new results from complex analysis about metrics with singularities. As an application, we will discuss the proof of Iitaka's conjecture (about the subadditivity of the Kodaira dimension in algebraic fiber spaces) over abelian varieties, following Cao and Paun.

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

### 2018/07/19

#### Applied Analysis

16:00-17:30 Room #118 (Graduate School of Math. Sci. Bldg.)

Uniqueness and nondegeneracy of ground states to scalar field equation involving critical Sobolev exponent

(Japanese)

**Norihisa Ikoma**(Keio University)Uniqueness and nondegeneracy of ground states to scalar field equation involving critical Sobolev exponent

(Japanese)

[ Abstract ]

This talk is devoted to studying the uniqueness and nondegeneracy of ground states to a nonlinear scalar field equation on the whole space. The nonlinearity consists of two power functions, and their growths are subcritical and critical in the Sobolev sense respectively. Under some assumptions, it is known that the equation admits a positive radial ground state and other ground states are made from the positive radial one. We show that if the dimensions are greater than or equal to 5 and the frequency is sufficiently large, then the positive radial ground state is unique and nondegenerate. This is based on joint work with Takafumi Akahori (Shizuoka Univ.), Slim Ibrahim (Univ. of Victoria), Hiroaki Kikuchi (Tsuda Univ.) and Hayato Nawa (Meiji Univ.).

This talk is devoted to studying the uniqueness and nondegeneracy of ground states to a nonlinear scalar field equation on the whole space. The nonlinearity consists of two power functions, and their growths are subcritical and critical in the Sobolev sense respectively. Under some assumptions, it is known that the equation admits a positive radial ground state and other ground states are made from the positive radial one. We show that if the dimensions are greater than or equal to 5 and the frequency is sufficiently large, then the positive radial ground state is unique and nondegenerate. This is based on joint work with Takafumi Akahori (Shizuoka Univ.), Slim Ibrahim (Univ. of Victoria), Hiroaki Kikuchi (Tsuda Univ.) and Hayato Nawa (Meiji Univ.).

### 2018/07/18

#### Algebraic Geometry Seminar

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

Normal Legendrian singularities (English)

**Jun-Muk Hwang**(KIAS)Normal Legendrian singularities (English)

[ Abstract ]

A germ of a Legendrian subvariety in a holomorphic contact manifold

is called a Legendrian singularity. Legendrian singularities are usually not normal.

We look at some examples of normal Legendrian singularities and discuss their rigidity under deformation.

A germ of a Legendrian subvariety in a holomorphic contact manifold

is called a Legendrian singularity. Legendrian singularities are usually not normal.

We look at some examples of normal Legendrian singularities and discuss their rigidity under deformation.

#### Mathematical Biology Seminar

15:00-16:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Effect of demographic stochasticity on large amplitude oscillation

**Malay Banerjee**(Department of Mathematics & Statistics, IIT Kanpur)Effect of demographic stochasticity on large amplitude oscillation

[ Abstract ]

Classical Rosenzweig-MacArthur model exhibits two types of stable coexistence, steady-state and oscillatory coexistence. The oscillatory coexistence is the result of super-critical Hopf-bifurcation and the Hopf-bifurcating limit cycle remains stable for parameter values beyond the bifurcation threshold. The size of the limit cycle grows with the increase in carrying capacity of prey and finally both the populations show high amplitude oscillations. Time evolution of prey and predator population densities exhibit large amplitude peaks separated by low density lengthy valleys. Persistence of both the populations at low population density over a longer time period is more prominent in case of fast growth of prey and comparatively slow growth of predator species due to slow-fast dynamics. In this situation, small amount of demographic stochasticity can cause the extinction of one or both the species. Main aim of this talk is to explain the effect of demographic stochasticity on the high amplitude oscillations produced by two and higher dimensional interacting population models.

Classical Rosenzweig-MacArthur model exhibits two types of stable coexistence, steady-state and oscillatory coexistence. The oscillatory coexistence is the result of super-critical Hopf-bifurcation and the Hopf-bifurcating limit cycle remains stable for parameter values beyond the bifurcation threshold. The size of the limit cycle grows with the increase in carrying capacity of prey and finally both the populations show high amplitude oscillations. Time evolution of prey and predator population densities exhibit large amplitude peaks separated by low density lengthy valleys. Persistence of both the populations at low population density over a longer time period is more prominent in case of fast growth of prey and comparatively slow growth of predator species due to slow-fast dynamics. In this situation, small amount of demographic stochasticity can cause the extinction of one or both the species. Main aim of this talk is to explain the effect of demographic stochasticity on the high amplitude oscillations produced by two and higher dimensional interacting population models.

#### thesis presentations

15:30-16:45 Room #128 (Graduate School of Math. Sci. Bldg.)

#### FMSP Lectures

**Christian Schnell**(Stony Book University)

Singular hermitian metrics and morphisms to abelian varieties (ENGLISH)

Consider a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). After reviewing what is known about the pushforward of the canonical bundle under such a morphism, we will try to extend these results to the case of pluricanonical bundles (= the tensor powers of the canonical bundle). Along the way, we will learn about three important tools: generic vanishing theory; Viehweg's cyclic covering trick; and some new results from complex analysis about metrics with singularities. As an application, we will discuss the proof of Iitaka's conjecture (about the subadditivity of the Kodaira dimension in algebraic fiber spaces) over abelian varieties, following Cao and Paun.

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

### 2018/07/17

#### Tuesday Seminar on Topology

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

Positive flow-spines and contact 3-manifolds (JAPANESE)

**Masaharu Ishikawa**(Keio University)Positive flow-spines and contact 3-manifolds (JAPANESE)

[ Abstract ]

A contact structure is a smooth distribution of hyperplanes on an odd-dimensional manifold that is non-integrable everywhere. In the case of dimension 3, there is a nice relationship between open book decompositions of 3-manifolds and contact structures up to contactomorphisms, called Giroux correspondence. A flow-spine is a spine of a 3-manifold admitting a flow such that it is transverse to the spine and the flow in the complement of the spine is diffeomorphic to a constant flow in an open ball. In this talk, we introduce some results in progress that give a correspondence between contact structures and positive flow-spines by regarding Reeb vector fields as flows of spines. This is a joint work with Y. Koda (Hiroshima) and H. Naoe (Tohoku).

A contact structure is a smooth distribution of hyperplanes on an odd-dimensional manifold that is non-integrable everywhere. In the case of dimension 3, there is a nice relationship between open book decompositions of 3-manifolds and contact structures up to contactomorphisms, called Giroux correspondence. A flow-spine is a spine of a 3-manifold admitting a flow such that it is transverse to the spine and the flow in the complement of the spine is diffeomorphic to a constant flow in an open ball. In this talk, we introduce some results in progress that give a correspondence between contact structures and positive flow-spines by regarding Reeb vector fields as flows of spines. This is a joint work with Y. Koda (Hiroshima) and H. Naoe (Tohoku).

#### thesis presentations

15:30-16:45 Room #128 (Graduate School of Math. Sci. Bldg.)

#### Infinite Analysis Seminar Tokyo

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

Operator algebra for statistical model of square ladder (ENGLISH)

**Valerii Sopin:**(Higher School of Economics (Moscow))Operator algebra for statistical model of square ladder (ENGLISH)

[ Abstract ]

In this talk we will define operator algebra for square ladder on the basis

of semi-infinite forms.

Keywords: hard-square model, square ladder, operator algebra, semi-infinite

forms, fermions, quadratic algebra, cohomology, Demazure modules,

Heisenberg algebra.

In this talk we will define operator algebra for square ladder on the basis

of semi-infinite forms.

Keywords: hard-square model, square ladder, operator algebra, semi-infinite

forms, fermions, quadratic algebra, cohomology, Demazure modules,

Heisenberg algebra.

### 2018/07/13

#### Colloquium

15:30-16:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Pluripotential theory and complex dynamics in higher dimension

**DINH Tien Cuong**(National University of Singapore )Pluripotential theory and complex dynamics in higher dimension

[ Abstract ]

Positive closed currents, the analytic counterpart of effective cycles in algebraic geometry, are central objects in pluripotential theory. They were introduced in complex dynamics in the 1990s and become now a powerful tool in the field. Challenging dynamical problems involve currents of any dimension. We will report recent developments on positive closed currents of arbitrary dimension, including the solutions to the regularization problem, the theory of super-potentials and the theory of densities. Applications to dynamics such as properties of dynamical invariants (e.g. dynamical degrees, entropies, currents, measures), solutions to equidistribution problems, and properties of periodic points will be discussed.

Positive closed currents, the analytic counterpart of effective cycles in algebraic geometry, are central objects in pluripotential theory. They were introduced in complex dynamics in the 1990s and become now a powerful tool in the field. Challenging dynamical problems involve currents of any dimension. We will report recent developments on positive closed currents of arbitrary dimension, including the solutions to the regularization problem, the theory of super-potentials and the theory of densities. Applications to dynamics such as properties of dynamical invariants (e.g. dynamical degrees, entropies, currents, measures), solutions to equidistribution problems, and properties of periodic points will be discussed.

### 2018/07/11

#### Operator Algebra Seminars

17:15-18:45 Room #126 (Graduate School of Math. Sci. Bldg.)

Recent progress in the classification of amenable C*-algebras (cont'd)

**George Elliott**(Univ. Toronto)Recent progress in the classification of amenable C*-algebras (cont'd)

### 2018/07/10

#### Algebraic Geometry Seminar

15:30-17:00 Room #002 (Graduate School of Math. Sci. Bldg.)

The effective bound of anticanonical volume of Fano threefolds (English)

**Ching-Jui Lai**(NCKU)The effective bound of anticanonical volume of Fano threefolds (English)

[ Abstract ]

According to Mori's program, varieties covered by rational curves are

built up from anti-canonically polarized varieties, aka Fano varieties. After fixed the

dimension and singularity type, Fano varieties form a bounded family by Birkar's proof (2016)

of Borisov-Alexeev-Borisov conjecture, which In particular implies that the anticanonical

volume -K^\dim is bounded. In this talk, we focus on canonical Fano threefolds,

where boundedness was established by Koll\'ar-Miyaoka-Mori-Takagi (2000).

Our aim is to find an effective bound of the anticanonical volume -K^3, which is

not explicit either from the work of Koll\'ar-Miyaoka-Mori-Takagi or Birkar. We will discuss

some effectiveness results related to this problem and prove that -K_X^3\leq 72 if \rho(X)\leq 2.

This partially extends early work of Mori, Mukai, Y. Prokhorov, et al.

According to Mori's program, varieties covered by rational curves are

built up from anti-canonically polarized varieties, aka Fano varieties. After fixed the

dimension and singularity type, Fano varieties form a bounded family by Birkar's proof (2016)

of Borisov-Alexeev-Borisov conjecture, which In particular implies that the anticanonical

volume -K^\dim is bounded. In this talk, we focus on canonical Fano threefolds,

where boundedness was established by Koll\'ar-Miyaoka-Mori-Takagi (2000).

Our aim is to find an effective bound of the anticanonical volume -K^3, which is

not explicit either from the work of Koll\'ar-Miyaoka-Mori-Takagi or Birkar. We will discuss

some effectiveness results related to this problem and prove that -K_X^3\leq 72 if \rho(X)\leq 2.

This partially extends early work of Mori, Mukai, Y. Prokhorov, et al.

#### Lectures

15:00-16:00 Room #128 (Graduate School of Math. Sci. Bldg.)

On the moduli space of flat symplectic surface bundles

**Sam Nariman**(Northwestern University)On the moduli space of flat symplectic surface bundles

[ Abstract ]

There are at least three different approaches to construct characteristic invariants of flat symplectic bundles. Reznikov generalized Chern-Weil theory for finite dimension Lie groups to the infinite dimensional group of symplectomorphisms. He constructed nontrivial invariants of symplectic bundles whose fibers are diffeomorphic to complex projective spaces. Kontsevich used formal symplectic geometry to build interesting classes that are not yet known to be nontrivial. Also for surface bundles whose holonomy groups preserve the symplectic form, Kotschick and Morita used the flux homomorphism to construct many nontrivial stable classes.

In this talk, we introduce infinite loop spaces whose cohomolgy groups describe the stable characteristic invariants of symplectic flat surface bundles. As an application, we give a homotopy theoretic description of

Kotschick and Morita's classes and prove a result about codimension 2 foliations that implies the nontriviality of KM classes.

There are at least three different approaches to construct characteristic invariants of flat symplectic bundles. Reznikov generalized Chern-Weil theory for finite dimension Lie groups to the infinite dimensional group of symplectomorphisms. He constructed nontrivial invariants of symplectic bundles whose fibers are diffeomorphic to complex projective spaces. Kontsevich used formal symplectic geometry to build interesting classes that are not yet known to be nontrivial. Also for surface bundles whose holonomy groups preserve the symplectic form, Kotschick and Morita used the flux homomorphism to construct many nontrivial stable classes.

In this talk, we introduce infinite loop spaces whose cohomolgy groups describe the stable characteristic invariants of symplectic flat surface bundles. As an application, we give a homotopy theoretic description of

Kotschick and Morita's classes and prove a result about codimension 2 foliations that implies the nontriviality of KM classes.

#### Tuesday Seminar on Topology

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

Loose Legendrians and arboreal singularities (ENGLISH)

**Emmy Murphy**(Northwestern University)Loose Legendrians and arboreal singularities (ENGLISH)

[ Abstract ]

Given a Stein manifold X, under what conditions can we ensure that X is symplectomorphic to C^n? For n>2 the condition of X being diffeomorphic to C^n does not suffice, and many counterexamples have been constructed which are detected by symplectic cohomology and the Fukaya category. One might conjecture that the diffeomorphism type together with a vanishing Fukaya category characterizes C^n. While this question is currently well of of reach, we present some new partial results. The main tools we'll discuss are arboreal singularities, constructable sheaf theory, and loose Legendrians -- and how they fit together to approach this question.

Given a Stein manifold X, under what conditions can we ensure that X is symplectomorphic to C^n? For n>2 the condition of X being diffeomorphic to C^n does not suffice, and many counterexamples have been constructed which are detected by symplectic cohomology and the Fukaya category. One might conjecture that the diffeomorphism type together with a vanishing Fukaya category characterizes C^n. While this question is currently well of of reach, we present some new partial results. The main tools we'll discuss are arboreal singularities, constructable sheaf theory, and loose Legendrians -- and how they fit together to approach this question.

#### Numerical Analysis Seminar

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

Free surface flow using orthogonal basis bubble function finite element method (Japanese)

**Junichi Matsumoto**(AIST)Free surface flow using orthogonal basis bubble function finite element method (Japanese)

### 2018/07/09

#### Seminar on Geometric Complex Analysis

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

Rigidity results for symplectic curvature flow (ENGLISH)

**Casey Kelleher**(Princeton University)Rigidity results for symplectic curvature flow (ENGLISH)

[ Abstract ]

We continue studying a parabolic flow of almost Kähler structure introduced by Streets and Tian which naturally extends Kähler-Ricci flow onto symplectic manifolds. In a system consisting primarily of quantities related to the Chern connection we establish clean formulas for the evolutions of canonical objects. Using this we give an extended characterization of fixed points of the flow.

We continue studying a parabolic flow of almost Kähler structure introduced by Streets and Tian which naturally extends Kähler-Ricci flow onto symplectic manifolds. In a system consisting primarily of quantities related to the Chern connection we establish clean formulas for the evolutions of canonical objects. Using this we give an extended characterization of fixed points of the flow.

### 2018/07/03

#### Tuesday Seminar on Topology

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

Symmetries on algebras and Hochschild homology in view of categories of operators (JAPANESE)

**Jun Yoshida**(The University of Tokyo)Symmetries on algebras and Hochschild homology in view of categories of operators (JAPANESE)

[ Abstract ]

The categorical construction of Hochschild homology by Connes reveals that the symmetric structure on the tensor product of abelian groups is essential. It means that the categorical meaning of ad-hoc generalizations of Hochschild homology in less symmetric monoidal abelian categories remains unclear. In this talk, I will propose formulation of this problem in terms of group operads introduced by Zhang. Moreover, for each group operad G, G-symmetric versions of categories of operators will be discussed. The notion plays a key role in defining Hochschild homology for homotopy algebras; such as topological Hochschild homology.

The categorical construction of Hochschild homology by Connes reveals that the symmetric structure on the tensor product of abelian groups is essential. It means that the categorical meaning of ad-hoc generalizations of Hochschild homology in less symmetric monoidal abelian categories remains unclear. In this talk, I will propose formulation of this problem in terms of group operads introduced by Zhang. Moreover, for each group operad G, G-symmetric versions of categories of operators will be discussed. The notion plays a key role in defining Hochschild homology for homotopy algebras; such as topological Hochschild homology.

#### Algebraic Geometry Seminar

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

Surface automorphisms and Salem numbers (English)

**Xun Yu**(Tianjin University)Surface automorphisms and Salem numbers (English)

[ Abstract ]

The entropy of a surface automorphism is either zero or the

logarithm of a Salem number.

In this talk, we will discuss which Salem numbers arise in this way. We

will show that any

supersingular K3 surface in odd characteristic has an automorphism the

entropy of which is

the logarithm of a Salem number of degree 22. In particular, such

automorphisms are

not geometrically liftable to characteristic 0.

The entropy of a surface automorphism is either zero or the

logarithm of a Salem number.

In this talk, we will discuss which Salem numbers arise in this way. We

will show that any

supersingular K3 surface in odd characteristic has an automorphism the

entropy of which is

the logarithm of a Salem number of degree 22. In particular, such

automorphisms are

not geometrically liftable to characteristic 0.

### 2018/07/02

#### Tokyo Probability Seminar

16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Distributional limit theorems for intermittent maps (JAPANESE)

**Toru SERA**(Graduate School of Science, Kyoto University)Distributional limit theorems for intermittent maps (JAPANESE)

#### Seminar on Geometric Complex Analysis

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

Rigidity of certain groups of circle homeomorphisms and Teichmueller spaces (JAPANESE)

**Katsuhiko Matsuzaki**(Waseda University)Rigidity of certain groups of circle homeomorphisms and Teichmueller spaces (JAPANESE)

[ Abstract ]

In this talk, I explain a complex analytic method and its applications

for the study of quasisymmetric homeomorphisms of the circle by extending them to the unit disk quasiconformally.

In RIMS conference "Open Problems in Complex Geometry'' held in 2010,

I gave a talk entitled "Problems on infinite dimensional Teichmueller spaces", and

mentioned several problems on the fixed points of group actions on

the universal Teichmueller space and its subspaces, and the rigidity of conjugation of

certain groups of circle homeomorphisms.

I will report on the development of these problems since then.

In this talk, I explain a complex analytic method and its applications

for the study of quasisymmetric homeomorphisms of the circle by extending them to the unit disk quasiconformally.

In RIMS conference "Open Problems in Complex Geometry'' held in 2010,

I gave a talk entitled "Problems on infinite dimensional Teichmueller spaces", and

mentioned several problems on the fixed points of group actions on

the universal Teichmueller space and its subspaces, and the rigidity of conjugation of

certain groups of circle homeomorphisms.

I will report on the development of these problems since then.

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