## Seminar information archive

Seminar information archive ～08/21｜Today's seminar 08/22 | Future seminars 08/23～

#### 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.

#### 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.

### 2018/06/29

#### 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)

### 2018/06/27

#### Operator Algebra Seminars

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

TBA

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

### 2018/06/26

#### 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.)

The Cauchy problem of the drift-diffusion system in R^n (日本語)

**OGAWA Takayoshi**(Tohoku University)The Cauchy problem of the drift-diffusion system in R^n (日本語)

[ Abstract ]

We consider the Cauchy problem of the drift-diffusion system in the whole space. Introducing the scaling critical case, we consider the solvability of the drift-diffusion system in the whole space and give some large time behavior of solutions. This talk is based on a collaboration with Masaki Kurokiba and Hiroshi Wakui.

We consider the Cauchy problem of the drift-diffusion system in the whole space. Introducing the scaling critical case, we consider the solvability of the drift-diffusion system in the whole space and give some large time behavior of solutions. This talk is based on a collaboration with Masaki Kurokiba and Hiroshi Wakui.

### 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.

### 2018/06/22

#### 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.

### 2018/06/20

#### 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.

### 2018/06/19

#### 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.

### 2018/06/18

#### Tokyo Probability Seminar

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

(JAPANESE)

**Hideki TANEMURA**(Department of Mathematics, Keio University)(JAPANESE)

#### Operator Algebra Seminars

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

Equivariant index theorem (English)

**Ryszard Nest**(Copenhagen Univ.)Equivariant index theorem (English)

### 2018/06/13

#### Operator Algebra Seminars

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

Poisson boundary for the discrete affine group (English)

**Ryokichi Tanaka**(Tohoku Univ.)Poisson boundary for the discrete affine group (English)

### 2018/06/12

#### Algebraic Geometry Seminar

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

Ample canonical heights for endomorphisms on projective varieties (English or Japanese)

**Takahiro Shibata**(Kyoto)Ample canonical heights for endomorphisms on projective varieties (English or Japanese)

[ Abstract ]

Given a smooth projective variety on a number field and an

endomorphism on it, we would like to know how the height of a point

grows by iteration of the action of the endomorphism. When the

endomorphism is polarized, Call and Silverman construct the canonical

height, which is an important tool for the calculation of growth of

heights. In this talk, we will give a generalization of the Call-

Silverman canonical heights for not necessarily polarized endomorphisms,

ample canonical heights, and propose an analogue of the Northcott

finiteness theorem as a conjecture. We will see that the conjecture

holds when the variety is an abelian variety or a surface.

Given a smooth projective variety on a number field and an

endomorphism on it, we would like to know how the height of a point

grows by iteration of the action of the endomorphism. When the

endomorphism is polarized, Call and Silverman construct the canonical

height, which is an important tool for the calculation of growth of

heights. In this talk, we will give a generalization of the Call-

Silverman canonical heights for not necessarily polarized endomorphisms,

ample canonical heights, and propose an analogue of the Northcott

finiteness theorem as a conjecture. We will see that the conjecture

holds when the variety is an abelian variety or a surface.

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