## Seminar information archive

#### Geometry Colloquium

10:00-11:30   Room #126 (Graduate School of Math. Sci. Bldg.)
MASAI, Hideyoshi (The University of Tokyo)
Closed random mapping tori are asymmetric
(Japanese)
[ Abstract ]
We consider random walks on the mapping class group of closed surfaces and mapping tori of such random mapping classes. It has been shown that such random mapping tori admit hyperbolic structure, and hence their symmetry groups are finite groups. In this talk we prove that the symmetry group of random mapping tori are trivial.

### 2015/11/10

#### Tuesday Seminar on Topology

17:30-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Kiyonori Gomi (Shinshu University)
Topological T-duality for "Real" circle bundle (JAPANESE)
[ Abstract ]
Topological T-duality originates from T-duality in superstring theory,
and is first studied by Bouwkneght, Evslin and Mathai. The duality
basically consists of two parts: The first part is that, for any pair
of a principal circle bundle with H-flux', there is another T-dual'
pair on the same base space. The second part states that the twisted
K-groups of the total spaces of principal circle bundles in duality
are isomorphic under degree shift. This is the most simple topological
T-duality following Bunke and Schick, and there are a number of
generalizations. The generalization I will talk about is a topological
T-duality for "Real" circle bundles, motivated by T-duality in type II
orbifold string theory. In this duality, a variant of Z_2-equivariant
K-theory appears.

### 2015/11/09

#### Algebraic Geometry Seminar

15:30-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Yukari Ito (Nagoya University)
3-dimensional McKay correspondence (English)
[ Abstract ]
The original McKay correspondence is a relation between group theory of a finite subgroup G of SL(2,C) and geometry of the minimal resolution of the quotient singularity by G, and was generalized several ways. In particular, 3-dimensional generalization was extended to derived categorical eqivalence and the G-Hilbert scheme was useful to explain the correspondence. However, most results hold only for abelian subgroups. In this talk, I would like to introduce an iterated G-Hilbert scheme and show more geometrical McKay correspondence for non-abelian subgroups.

### 2015/11/05

#### Algebraic Geometry Seminar

15:30-17:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Shinnosuke Okawa (Osaka University)
Compact moduli of marked noncommutative del Pezzo surfaces via quivers (English)
[ Abstract ]
I will introduce certain GIT construction via quivers of compactified moduli spaces of marked noncommutative del Pezzo surfaces. For projective plane, quadric surface, and those of degree 3, 2, 1, we obtain projective toric varieties of dimension 2, 3, 8, 9, 10, respectively. Then I will discuss relations with deformation theory of abelian categories, blow-up of noncommutative projective planes, and three-block exceptional collections due to Karpov and Nogin. This talk is based on joint works in progress with Tarig Abdelgadir and Kazushi Ueda.

#### Applied Analysis

16:00-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)
Henri Berestycki (EHESS)
The effect of a line with fast diffusion on Fisher-KPP propagation (ENGLISH)
[ Abstract ]
I will present a system of equations describing the effect of inclusion of a line (the "road") with fast diffusion on biological invasions in the plane. Outside of the road, the propagation is of the classical Fisher-KPP type. We find that past a certain precise threshold for the ratio of diffusivity coefficients, the presence of the road enhances the speed of global propagation. I will discuss several further effects such as transport or reaction on the road. I will also discuss the influence of various parameters on the asymptotic behaviour of the invasion speed and shape. I report here on results from a series of joint works with Jean-Michel Roquejoffre and Luca Rossi.

### 2015/11/02

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Shimobe Hirokazu (Osaka Univ.)
A class of non-Kahler manifolds (Japanese)
[ Abstract ]
We consider a special case of compact complex manifolds which are said to be super strongly Gauduchon manifolds. A super strongly Gauduchon manifold is a complex manifold with a super strongly Gauduchon metric. We mainly consider non-Kähler super strongly Gauduchon manifolds. We give a cohomological condition for a compact complex manifold to have a super strongly Gauduchon metric, and give examples of non-trivial super strongly Gauduchon manifolds from nil-manifolds. We also consider its stability under small deformations and proper modifications of super strongly Gauduchon manifolds.

#### Tokyo Probability Seminar

16:50-18:20   Room #128 (Graduate School of Math. Sci. Bldg.)
Naoki Kubota (College of Science and Tenology, Nihon University)
Concentrations for the travel cost of the simple random walk in random potentials

### 2015/10/30

#### FMSP Lectures

15:00-16:15   Room #128 (Graduate School of Math. Sci. Bldg.)
Arnaud Ducrot (University of Bordeaux)
Asymptotic behaviour of a nonlocal logistic equation (ENGLISH)
[ Abstract ]
In this talk we consider a nonlocal logistic equation endowed with periodic boundary conditions modelling the motion of cells. This equation takes into account birth and death process using a simple logistic effect while the motion of particles follows a nonlocal Darcy law with a smooth kernel.
We first investigate the well-posedness of the problem before investigating the long time behaviour of the solutions. The lack of asymptotic compactness of the semiflow is overcome by using a Young measure framework. Using a suitable energy functional, we
establish the convergence of the solutions with respect to the Young measure topology.
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ducrot.pdf

#### FMSP Lectures

16:30-17:45   Room #128 (Graduate School of Math. Sci. Bldg.)
Peter Bates (Michigan State University)
How should a drop of liquid on a smooth curved surface move in zero gravity? (ENGLISH)
[ Abstract ]
Questions such as this may be formulated as questions regarding solutions to nonlinear evolutionary partial differential equations having a small coefficient on the leading order derivative term. Evolutionary partial differential equations may be regarded as (semi-) dynamical systems in an infinite-dimensional space. An abstract theorem is proved giving the existence of an invariant manifold for a semi-dynamical system when an approximately invariant manifold exists with a certain topological nondegeneracy condition in a neighborhood. This is then used to prove the existence of eternal solutions to the nonlinear PDE and answer the question about the motion of a droplet on a curved manifold. The abstract theorem extends fundamental work of Hirsch-Pugh-Shub and Fenichel on the perturbation of invariant manifolds from the 1970's to infinite-dimensional semi-dynamical systems.
This represents joint work with Kening Lu and Chongchun Zeng.
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bates.pdf

### 2015/10/28

#### Mathematical Biology Seminar

14:55-16:40   Room #128演習室 (Graduate School of Math. Sci. Bldg.)
Ryo Oizumi (Ministry of Health, Labour and Welfare)
Application of stochastic control theory to r/K selection theory affiliation (JAPANESE)

#### Operator Algebra Seminars

16:45-18:15   Room #118 (Graduate School of Math. Sci. Bldg.)
Hiroki Sako (Niigata University)
Uniformly locally finite metric spaces and Folner type conditions

### 2015/10/27

#### Number Theory Seminar

18:00-19:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Masanori Asakura (Hokkaido University)
On the period conjecture of Gross-Deligne for fibrations (English)
[ Abstract ]
The period conjecture of Gross-Deligne asserts that the periods of algebraic varieties with complex multiplication are products of values of the gamma function at rational numbers. This is proved for CM elliptic curves by Lerch-Chowla-Selberg, and for abelian varieties by Shimura-Deligne-Anderson. However the question in the general case is still open. In this talk, we verify an alternating variant of the period conjecture for the cohomology of fibrations with relative multiplication. The proof relies on the Saito-Terasoma product formula for epsilon factors of integrable regular singular connections and the Riemann-Roch-Hirzebruch theorem. This is a joint work with Javier Fresan.

#### Tuesday Seminar on Topology

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Yuanyuan Bao (The University of Tokyo)
Heegaard Floer homology for graphs (JAPANESE)
[ Abstract ]
Ozsváth and Szabó defined the Heegaard Floer homology (HF) for a closed oriented 3-manifold. The definition was then generalized to links embedded in a 3-manifold and the manifolds with boundary (sutured and bordered manifolds). In the case of links, there is a beautiful combinatorial way to rewrite the original definition of HF, which was defined on a Heegaard diagram of the given link, by using grid diagram. For a balanced bipartite graph, we defined its Heegaard diagram and the HF for it. Around the same time, Harvey and O’Donnol defined the combinatorial HF for transverse graphs (see the definition in [arXiv:1506.04785v1]). In this talk, we compare these two methods.

#### Tuesday Seminar on Topology

15:00-16:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Jianfeng Lin (UCLA)
The unfolded Seiberg-Witten-Floer spectrum and its applications
(ENGLISH)
[ Abstract ]
Following Furuta's idea of finite dimensional approximation in
the Seiberg-Witten theory, Manolescu defined the Seiberg-Witten-Floer
stable homotopy type for rational homology three-spheres in 2003. In
this talk, I will explain how to construct similar invariants for a
general three-manifold and discuss some applications of these new
invariants. This is a joint work with Tirasan Khandhawit and Hirofumi
Sasahira.

### 2015/10/26

#### Algebraic Geometry Seminar

15:30-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Lawrence Ein (University of Illinois at Chicago)
Asymptotic syzygies and the gonality conjecture (English)
[ Abstract ]
We'll discuss my joint work with Lazarsfeld on the gonality conjecture about the syzygies of a smooth projective curve when it is embedded into the projective space by the complete linear system of a sufficiently very ample line bundles. We'll also discuss some results about the asymptotic syzygies f higher dimensional varieties.

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Kazuko Matsumoto (Tokyo Univ. of Science)
The Fubini-distance functions to pseudoconvex domains in $\mathbb{C}\mathbb{P}^2$ (Japanese)
[ Abstract ]
In this talk, we would like to present two explicit formulas for the Levi forms of the Fubini-Study distance functions to complex or real hypersurfaces in $\mathbb{C}\mathbb{P}^2$. This is the first step for us to approach the non-existence conjecture of Levi-flat real hypersurfaces in $\mathbb{C}\mathbb{P}^2$. We would like to also discuss a certain important quantity found in the formulas.

#### Numerical Analysis Seminar

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Fredrik Lindgren (Osaka University)
Numerical approximation of spinodal decomposition in the presence of noise (English)
[ Abstract ]
Numerical approximations of stochastic partial differential equations (SPDE) has evolved to a vivid subfield of computational mathematics in the last decades. It poses new challenges both for numerical analysis and the theory of SPDE.

In this talk we will discuss the strength and weaknesses of the \emph{semigroup approach} to SPDE when it is combined with the idea of viewing a single-step method in time as a \emph{rational approximation of a semigroup}. We shall apply this framework to the stochastic Allen-Cahn equation, a parabolic semi-linear SPDE where the non-linearity is non-globally Lipschitz continuous, but has a \emph{one-sided Lipschitz condition}, and the deterministic equation has a Lyapunov functional.

We focus on semi-discretisation in time, the first step in Rothe's method, and show how the semigroup approach allows for convergence proofs under the assumption that the numerical solution admits moment bounds. However, this assumption turns out to be difficult to verify in the semi-group framework, and the rates achieved are not sharp. This is due to the fact that the one-sided Lipschitz condition, being a variational inequality, can't be utilised. We thus turn to variational methods to solve this issue.

If time admits we shall also comment on the stochastic Cahn-Hilliard equation where the non-linearity has a one-sided Lipschitz condition in a lower norm, only. However, the fact of convergence can still be proved.

This is joint work with Daisuke Furihata (Osaka University), Mih\'aly Kov\'acs (University of Otago, New Zealand), Stig Larsson (Chalmers University of Technology, Sweden) and Shuji Yoshikawa (Ehime University).

### 2015/10/23

#### Geometry Colloquium

10:00-11:30   Room #126 (Graduate School of Math. Sci. Bldg.)
Nobuhiko Otoba (Keio University)
Metrics of constant scalar curvature on sphere bundles (Japanese)
[ Abstract ]
This talk is based on joint work with Jimmy Petean (CIMAT).
I'd like to talk about our attempt to study the Yamabe PDE on Riemannian twisted product manifolds, more precisely, the total spaces of Riemannian submersions with totally geodesic fibers. To demonstrate how the argument works,
I construct metrics of constant scalar curvature on unit sphere bundles for real vector bundles of the type $E \oplus L$,
the Whitney sum of a vector bundle $E$ and a line bundle $L$ with respective inner products, and then estimate the number of solutions to the corresponding Yamabe PDE.

### 2015/10/22

#### FMSP Lectures

16:00-16:50   Room #002 (Graduate School of Math. Sci. Bldg.)
Hans-Otto Walther (University of Giessen)
The semiflow of a delay differential equation on its solution manifold (ENGLISH)
[ Abstract ]
The lecture surveys work after the turn of the millenium on well-posedness of initial value problems for di_erential equations with variable delay. The focus is on results which provide continuously di_erentiable solution operators, so that in case studies ingredients of dynamical systems theory, such as local invariant manifolds or Poincar_e return maps, become available. We explain why the familar theory of retarded functional di_erential equations [1,2,4] fails for equations with variable delay, discuss what has been achieved for the latter, for autonomous and for nonautonomous equations, with delays bounded or unbounded, and address open problems.
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-1.pdf

#### FMSP Lectures

17:00-17:50   Room #002 (Graduate School of Math. Sci. Bldg.)
Hans-Otto Walther (University of Giessen)
Shilnikov chaos due to state-dependent delay, by means of the fixed point index (ENGLISH)
[ Abstract ]
What can variability of a delay in a delay differential equation do to the dynamics? We find a bounded delay functional d(¥phi), with d(¥phi)=1 on a neighborhood of ¥phi=0, such that the equation x'(t)=-a x(t-d(x_t)) has a solution which is homoclinic to 0, with shift dynamics in its vicinity, whereas the linear equation x'(t)=-a x(t-1) with constant time lag, for small solutions, is hyperbolic with 2-dimensional unstable space.
The proof involves regularity properties of the semiflow close to the homoclinic loop in the solution manifold and a generalization of a method due to Piotr Zgliczynsky which uses the fixed point index and a closing argument in order to establish shift dynamics when certain covering relations hold. (Joint work with Bernhard Lani-Wayda)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-2.pdf

#### Applied Analysis

16:00-17:50   Room #002 (Graduate School of Math. Sci. Bldg.)
Hans-Otto Walther (University of Giessen)
(Part I) The semiflow of a delay differential equation on its solution manifold
(Part II) Shilnikov chaos due to state-dependent delay, by means of the fixed point index
(ENGLISH)
[ Abstract ]
(Part I) 16:00 - 16:50
The semiflow of a delay differential equation on its solution manifold
(Part II) 17:00 - 17:50
Shilnikov chaos due to state-dependent delay, by means of the fixed point index

(Part I)
The lecture surveys recent work on initial value problems for differential equations with variable delay. The focus is on differentiable solution operators.

The lecture explains why the theory for retarded functional differential equations which is familiar from monographs before the turn of the millenium fails in case of variable delay, discusses what has been achieved in this case, for autonomous and non-autonomous equations, with delays bounded and unbounded, and addresses open problems.

[detailed abstract]
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-1.pdf

(Part II)
What can variability of a delay in a delay differential equation do to the dynamics? We find a bounded delay functional $d(\phi)$, with $d(\phi)=1$ on a neighborhood of $\phi=0$, such that the equation $x'(t)=-a x(t-d(x_t))$ has a solution which is homoclinic to $0$, with shift dynamics in its vicinity, whereas the linear equation $x'(t)=-a x(t-1)$ with constant time lag, for small solutions, is hyperbolic with 2-dimensional unstable space.

The proof involves regularity properties of the semiflow close to the homoclinic loop in the solution manifold and a generalization of a method due to Piotr Zgliczynsky which uses the fixed point index and a closing argument in order to establish shift dynamics when certain covering relations hold. (Joint work with Bernhard Lani-Wayda)

[detailed abstract]
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-2.pdf

[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-1.pdf

### 2015/10/21

#### Mathematical Biology Seminar

14:55-16:40   Room #128演習室 (Graduate School of Math. Sci. Bldg.)
Ryosuke Omori (Research Center for Zoonosis Control, Hokkaido University, Japan)
The distribution of the duration of immunity determines the periodicity of Mycoplasma pneumoniae incidence. (JAPANESE)
[ Abstract ]
Estimating the periodicity of outbreaks is sometimes equivalent to the
prediction of future outbreaks. However, the periodicity may change
over time so understanding the mechanism of outbreak periodicity is
important. So far, mathematical modeling studies suggest several
drivers for outbreak periodicity including, 1) environmental factors
(e.g. temperature) and 2) host behavior (contact patterns between host
individuals). Among many diseases, multiple determinants can be
considered to cause the outbreak periodicity and it is difficult to
understand the periodicity quantitatively. Here we introduce our case
study of Mycoplasma pneumoniae (MP) which shows three to five year
periodic outbreaks, with multiple candidates for determinants for the
outbreak periodicity being narrowed down to the last one, the variance
of the length of the immunity duration. To our knowledge this is the
first study showing that the variance in the length of the immunity
duration is essential for the periodicity of the outbreaks.
[ Reference URL ]
http://researchers.general.hokudai.ac.jp/profile/ja.e3OkdvtshzEabOVZ2w5OYw==.html

### 2015/10/20

#### FMSP Lectures

16:50-18:20   Room #128 (Graduate School of Math. Sci. Bldg.)
Danielle Hilhorst (CNRS / University of Paris-Sud)
Existence of an entropy solution in the sense of Young measures for a first order conservation law with a stochastic source term (ENGLISH)
[ Abstract ]
We consider a finite volume scheme for a first order conservation law with a monotone flux function and a multiplicative source term involving a Q-Wiener process. We define a stochastic entropy solution in the sense of Young measures. We present some a priori estimates for the discrete solution including a weak BV estimate. After performing a time interpolation, we prove two entropy inequalities and show that the discrete solution converges along a subsequence to an entropy solution in the sense of Young measures.
This is joint work with T. Funaki, Y. Gao and H. Weber.
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Hilhorst151020.pdf

#### Tuesday Seminar of Analysis

16:50-18:20   Room #128 (Graduate School of Math. Sci. Bldg.)
Danielle Hilhorst (CNRS / University of Paris-Sud)
Existence of an entropy solution in the sense of Young measures for a first order conservation law with a stochastic source term (ENGLISH)
[ Abstract ]
We consider a finite volume scheme for a first order conservation law with a monotone flux function and a multiplicative source term involving a Q-Wiener process. We define a stochastic entropy solution in the sense of Young measures. We present some a priori estimates for the discrete solution including a weak BV estimate. After performing a time interpolation, we prove two entropy inequalities and show that the discrete solution converges along a subsequence to an entropy solution in the sense of Young measures.
This is joint work with T. Funaki, Y. Gao and H. Weber.
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Hilhorst151020.pdf

#### Tuesday Seminar on Topology

17:30-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Bruno Scardua (Universidade Federal do Rio de Janeiro)
On the existence of stable compact leaves for
transversely holomorphic foliations (ENGLISH)
[ Abstract ]
One of the most important results in the theory of foliations is
the celebrated Local stability theorem of Reeb :
A compact leaf of a foliation having finite holonomy group is
stable, indeed, it admits a fundamental system of invariant
neighborhoods where each leaf is compact with finite holonomy
group. This result, together with the Global stability theorem of Reeb
(for codimension one real foliations), has many important consequences
and motivates several questions in the theory of foliations. In this talk
we show how to prove:

A transversely holomorphic foliation on a compact complex manifold, exhibits a compact stable
leaf if and only if the set of compact leaves is not a zero measure subset of the manifold.

This is a joint work with Cesar Camacho.