## Future seminars

Seminar information archive ～06/17｜Today's seminar 06/18 | Future seminars 06/19～

### 2018/06/19

#### Algebraic Geometry Seminar

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

Dormant Miura opers and Tango structures (Japanese (writing in English))

**Yasuhiro Wakabayashi**(TIT)Dormant Miura opers and Tango structures (Japanese (writing in English))

[ Abstract ]

Only Japanese abstract is available.

Only Japanese abstract is available.

#### Tuesday Seminar of Analysis

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

KdV is wellposed in $H^{-1}$ (English)

**Rowan Killip**(UCLA)KdV is wellposed in $H^{-1}$ (English)

#### Numerical Analysis Seminar

16:50-18:20 Room #002 (Graduate School of Math. Sci. Bldg.)

Small data global existence for the semi-discrete scheme of a model system of hyperbolic balance laws (Japanese)

**Shuji Yoshikawa**(Oita University)Small data global existence for the semi-discrete scheme of a model system of hyperbolic balance laws (Japanese)

#### Tuesday Seminar on Topology

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

Characteristic classes via 4-dimensional gauge theory (JAPANESE)

**Hokuto Konno**(The University of Tokyo)Characteristic classes via 4-dimensional gauge theory (JAPANESE)

[ Abstract ]

Using gauge theory, more precisely SO(3)-Yang-Mills theory and Seiberg-Witten theory, I will construct characteristic classes of 4-manifold bundles. These characteristic classes are extensions of the SO(3)-Donaldson invariant and the Seiberg-Witten invariant to families of 4-manifolds, and can detect non-triviality of smooth 4-manifold bundles. The basic idea of the construction of these characteristic classes is to consider an infinite dimensional analogue of classical characteristic classes of manifold bundles, typified by the Mumford-Morita-Miller classes for surface bundles.

Using gauge theory, more precisely SO(3)-Yang-Mills theory and Seiberg-Witten theory, I will construct characteristic classes of 4-manifold bundles. These characteristic classes are extensions of the SO(3)-Donaldson invariant and the Seiberg-Witten invariant to families of 4-manifolds, and can detect non-triviality of smooth 4-manifold bundles. The basic idea of the construction of these characteristic classes is to consider an infinite dimensional analogue of classical characteristic classes of manifold bundles, typified by the Mumford-Morita-Miller classes for surface bundles.

#### Tuesday Seminar on Topology

14:30-16:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Relative and equivariant Lagrangian Floer homology and Atiyah-Floer conjecture (JAPANESE)

**Kenji Fukaya**(Simons center, SUNY)Relative and equivariant Lagrangian Floer homology and Atiyah-Floer conjecture (JAPANESE)

[ Abstract ]

Atiyah-Floer conjecture concerns a relationship between Floer homology in Gauge theory and Lagrangian Floer homology. One of its difficulty is that the symplectic manifold on wich we consider Lagrangian Floer homology is in general singular. In this talk I will explain that, by using relative and equivariant version of Lagrangian Floer homology, we can resolve this problem and can at least state the conjecture as rigorous mathematical conjecture.

Atiyah-Floer conjecture concerns a relationship between Floer homology in Gauge theory and Lagrangian Floer homology. One of its difficulty is that the symplectic manifold on wich we consider Lagrangian Floer homology is in general singular. In this talk I will explain that, by using relative and equivariant version of Lagrangian Floer homology, we can resolve this problem and can at least state the conjecture as rigorous mathematical conjecture.

### 2018/06/20

#### Number Theory Seminar

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

Criteria for good reduction of hyperbolic polycurves (JAPANESE)

**Ippei Nagamachi**(University of Tokyo)Criteria for good reduction of hyperbolic polycurves (JAPANESE)

[ Abstract ]

We give good reduction criteria for hyperbolic polycurves, i.e., successive extensions of families of curves, under mild assumption. These criteria are higher dimensional versions of the good reduction criterion for hyperbolic curves given by Oda and Tamagawa. In this talk, we construct homotopy exact sequences by using intermediate quotient groups of geometric etale fundamental groups of hyperbolic polycurves.

We give good reduction criteria for hyperbolic polycurves, i.e., successive extensions of families of curves, under mild assumption. These criteria are higher dimensional versions of the good reduction criterion for hyperbolic curves given by Oda and Tamagawa. In this talk, we construct homotopy exact sequences by using intermediate quotient groups of geometric etale fundamental groups of hyperbolic polycurves.

### 2018/06/22

#### Lectures

16:00-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Fibrations of R^3 by oriented lines

**Michael Harrison**(Lehigh University)Fibrations of R^3 by oriented lines

[ Abstract ]

Is it possible to cover 3-dimensional space by a collection of lines, such that no two lines intersect and no two lines are parallel? More precisely, does there exist a fibration of R^3 by pairwise skew lines? We give some examples and provide a complete topological classification of such objects, by exhibiting a deformation retract from the space of skew fibrations of R^3 to its subspace of Hopf fibrations. As a corollary of the proof we obtain Gluck and Warner's classification of great circle fibrations of S^3. We continue with some recent results regarding contact structures on R^3 which are naturally induced by skew fibrations. Finally, we discuss fibrations of R^3 which may contain parallel fibers, and discuss when such objects induce contact structures.

Is it possible to cover 3-dimensional space by a collection of lines, such that no two lines intersect and no two lines are parallel? More precisely, does there exist a fibration of R^3 by pairwise skew lines? We give some examples and provide a complete topological classification of such objects, by exhibiting a deformation retract from the space of skew fibrations of R^3 to its subspace of Hopf fibrations. As a corollary of the proof we obtain Gluck and Warner's classification of great circle fibrations of S^3. We continue with some recent results regarding contact structures on R^3 which are naturally induced by skew fibrations. Finally, we discuss fibrations of R^3 which may contain parallel fibers, and discuss when such objects induce contact structures.

### 2018/06/25

#### Tokyo Probability Seminar

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

BSDEs driven by cylindrical martingales with application to approximate hedging in bond markets (JAPANESE)

**Yushi HAMAGUCHI**(Graduate School of Science, Kyoto University)BSDEs driven by cylindrical martingales with application to approximate hedging in bond markets (JAPANESE)

#### Discrete mathematical modelling seminar

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

Gap Probabilities and discrete Painlevé equations

**Anton Dzhamay**(University of Northern Colorado)Gap Probabilities and discrete Painlevé equations

[ Abstract ]

It is well-known that important statistical quantities, such as gap probabilities, in various discrete probabilistic models of random matrix type satisfy the so-called discrete Painlevé equations, which provides an effective way to computing them. In this talk we discuss this correspondence for a particular class of models, known as boxed plane partitions (equivalently, lozenge tilings of a hexagon). For uniform probability distribution, this is one of the most studied models of random surfaces. Borodin, Gorin, and Rains showed that it is possible to assign a very general elliptic weight to the distribution, with various degenerations of this weight corresponding to the degeneration cascade of discrete polynomial ensembles, such as Racah and Hahn ensembles and their q-analogues. This also correspond to the degeneration scheme of discrete Painlevé equations, due to Sakai. In this talk we consider the q-Hahn and q-Racah ensembles and corresponding discrete Painlevé equations of types q-P(A_{2}^{(1)}) and q-P(A_{1}^{(1)}).

This is joint work with Alisa Knizel (Columbia University)

It is well-known that important statistical quantities, such as gap probabilities, in various discrete probabilistic models of random matrix type satisfy the so-called discrete Painlevé equations, which provides an effective way to computing them. In this talk we discuss this correspondence for a particular class of models, known as boxed plane partitions (equivalently, lozenge tilings of a hexagon). For uniform probability distribution, this is one of the most studied models of random surfaces. Borodin, Gorin, and Rains showed that it is possible to assign a very general elliptic weight to the distribution, with various degenerations of this weight corresponding to the degeneration cascade of discrete polynomial ensembles, such as Racah and Hahn ensembles and their q-analogues. This also correspond to the degeneration scheme of discrete Painlevé equations, due to Sakai. In this talk we consider the q-Hahn and q-Racah ensembles and corresponding discrete Painlevé equations of types q-P(A_{2}^{(1)}) and q-P(A_{1}^{(1)}).

This is joint work with Alisa Knizel (Columbia University)

#### Seminar on Geometric Complex Analysis

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

Cornered Asymptotically Hyperbolic Spaces

**Stephen McKeown**(Princeton University)Cornered Asymptotically Hyperbolic Spaces

[ Abstract ]

This talk will concern cornered asymptotically hyperbolic spaces, which have a finite boundary in addition to the usual infinite boundary. I will first describe the construction a normal form near the corner for these spaces. Then I will discuss formal existence and uniqueness, near the corner, of asymptotically hyperbolic Einstein metrics, with a CMC-umbilic condition imposed on the finite boundary. This is analogous to the Fefferman-Graham construction for the ordinary, non-cornered setting. Finally, I will present work in progress regarding scattering on such spaces.

This talk will concern cornered asymptotically hyperbolic spaces, which have a finite boundary in addition to the usual infinite boundary. I will first describe the construction a normal form near the corner for these spaces. Then I will discuss formal existence and uniqueness, near the corner, of asymptotically hyperbolic Einstein metrics, with a CMC-umbilic condition imposed on the finite boundary. This is analogous to the Fefferman-Graham construction for the ordinary, non-cornered setting. Finally, I will present work in progress regarding scattering on such spaces.

### 2018/06/26

#### Algebraic Geometry Seminar

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

Varieties with nef diagonal (English)

**Kiwamu Watanabe**(Saitama)Varieties with nef diagonal (English)

[ Abstract ]

For a smooth projective variety $X$, we consider when the diagonal $Δ _X$ is nef as a

cycle on $X \times X$. In particular, we give a classication of complete intersections and smooth

del Pezzo varieties where the diagonal is nef. We also study the nefness of the diagonal for

spherical varieties. This is a joint work with Taku Suzuki.

For a smooth projective variety $X$, we consider when the diagonal $Δ _X$ is nef as a

cycle on $X \times X$. In particular, we give a classication of complete intersections and smooth

del Pezzo varieties where the diagonal is nef. We also study the nefness of the diagonal for

spherical varieties. This is a joint work with Taku Suzuki.

#### Tuesday Seminar of Analysis

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

TBA (日本語)

**OGAWA Takayoshi**(Tohoku University)TBA (日本語)

### 2018/06/27

#### Operator Algebra Seminars

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

TBA

**Seung-Hyeok Kye**(Seoul National Univ.)TBA

### 2018/06/29

#### Colloquium

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

Power concavity for parabolic equations (日本語)

**Kazuhiro Ishige**(The University of Tokyo)Power concavity for parabolic equations (日本語)

### 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.)

(JAPANESE)

**Katsuhiko Matsuzaki**(Waseda University)(JAPANESE)

#### PDE Real Analysis Seminar

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

Convex integration in fluid dynamics (English)

**László Székelyhidi Jr.**(Universität Leipzig)Convex integration in fluid dynamics (English)

[ Abstract ]

In the talk we present the technique of convex integration for constructing weak solutions to various equations in fluid mechanics.

We will focus on the recent resolution of Onsagers conjecture, but also discuss further directions and in particular the applicability to dissipative systems.

In the talk we present the technique of convex integration for constructing weak solutions to various equations in fluid mechanics.

We will focus on the recent resolution of Onsagers conjecture, but also discuss further directions and in particular the applicability to dissipative systems.

### 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.

### 2018/07/09

#### Seminar on Geometric Complex Analysis

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

(ENGLISH)

**Casey Kelleher**(Princeton University)(ENGLISH)

### 2018/07/10

#### Algebraic Geometry Seminar

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

TBA (English)

**Ching-Jui Lai**(NCKU)TBA (English)

[ Abstract ]

TBA

TBA

#### 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.

### 2018/07/11

#### Operator Algebra Seminars

16:45-18:15 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)

### 2018/07/13

#### 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.

### 2018/07/17

#### 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).