## Seminar information archive

Seminar information archive ～02/01｜Today's seminar 02/02 | Future seminars 02/03～

#### Seminar on Probability and Statistics

16:10-17:10 Room #002 (Graduate School of Math. Sci. Bldg.)

Asymptotic expansion and estimation of volatility

**Nakahiro Yoshida**(University of Tokyo, Institute of Statistical Mathematics, JST CREST)Asymptotic expansion and estimation of volatility

[ Abstract ]

Parametric estimation of volatility of an Ito process in a finite time horizon is discussed. Asymptotic expansion of the error distribution will be presented for the quasi likelihood estimators, i.e., quasi MLE, quasi Bayesian estimator and one-step quasi MLE. Statistics becomes non-ergodic, where the limit distribution is mixed normal. Asymptotic expansion is a basic tool in various areas in the traditional ergodic statistics such as higher order asymptotic decision theory, bootstrap and resampling plans, prediction theory, information criterion for model selection, information geometry, etc. Then a natural question is to obtain asymptotic expansion in the non-ergodic statistics. However, due to randomness of the characteristics of the limit, the classical martingale expansion or the mixing method cannot not apply. Recently a new martingale expansion was developed and applied to a quadratic form of the Ito process. The higher order terms are characterized by the adaptive random symbol and the anticipative random symbol. The Malliavin calculus is used for the description of the anticipative random symbols as well as for obtaining a decay of the characteristic functions. In this talk, the martingale expansion method and the quasi likelihood analysis with a polynomial type large deviation estimate of the quasi likelihood random field collaborate to derive expansions for the quasi likelihood estimators. Expansions of the realized volatility under microstructure noise, the power variation and the error of Euler-Maruyama scheme are recent applications. Further, some extension of martingale expansion to general martingales will be mentioned. References: SPA2013, arXiv:1212.5845, AISM2011, arXiv:1309.2071 (to appear in AAP), arXiv:1512.04716.

Parametric estimation of volatility of an Ito process in a finite time horizon is discussed. Asymptotic expansion of the error distribution will be presented for the quasi likelihood estimators, i.e., quasi MLE, quasi Bayesian estimator and one-step quasi MLE. Statistics becomes non-ergodic, where the limit distribution is mixed normal. Asymptotic expansion is a basic tool in various areas in the traditional ergodic statistics such as higher order asymptotic decision theory, bootstrap and resampling plans, prediction theory, information criterion for model selection, information geometry, etc. Then a natural question is to obtain asymptotic expansion in the non-ergodic statistics. However, due to randomness of the characteristics of the limit, the classical martingale expansion or the mixing method cannot not apply. Recently a new martingale expansion was developed and applied to a quadratic form of the Ito process. The higher order terms are characterized by the adaptive random symbol and the anticipative random symbol. The Malliavin calculus is used for the description of the anticipative random symbols as well as for obtaining a decay of the characteristic functions. In this talk, the martingale expansion method and the quasi likelihood analysis with a polynomial type large deviation estimate of the quasi likelihood random field collaborate to derive expansions for the quasi likelihood estimators. Expansions of the realized volatility under microstructure noise, the power variation and the error of Euler-Maruyama scheme are recent applications. Further, some extension of martingale expansion to general martingales will be mentioned. References: SPA2013, arXiv:1212.5845, AISM2011, arXiv:1309.2071 (to appear in AAP), arXiv:1512.04716.

### 2016/04/21

#### Geometry Colloquium

17:00-18:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Spectral convergence under bounded Ricci curvature (Japanese)

**Shouhei Honda**(Tohoku University)Spectral convergence under bounded Ricci curvature (Japanese)

[ Abstract ]

For a noncollapsed Gromov-Hausdorff convergent sequence of Riemannian manifolds with a uniform bound of Ricci curvature, we establish two spectral convergence. One of them is on the Hodge Laplacian acting on differential one-forms. The other is on the connection Laplacian acting on tensor fields of every type, which include all differential forms. These are sharp generalizations of Cheeger-Colding's spectral convergence of the Laplacian acting on functions to the cases of tensor fields and differential forms. These spectral convergence have two direct corollaries. One of them is to give new bounds on such eigenvalues, in terms of bounds on volume, diameter and the Ricci curvature. The other is that we show the upper semicontinuity of the first Betti numbers with respect to the Gromov-Hausdorff topology, and give the equivalence between the continuity of them and the existence of a uniform spectral gap. On the other hand we also define measurable curvature tensors of the noncollapsed Gromov-Hausdorff limit space of a sequence of Riemannian manifolds with a uniform bound of Ricci curvature, which include Riemannian curvature tensor, the Ricci curvature, and the scalar curvature. As fundamental properties of our Ricci curvature, we show that the Ricci curvature coincides with the difference between the Hodge Laplacian and the connection Laplacian, and is compatible with Gigli's one and Lott's Ricci measure. Moreover we prove a lower bound of the Ricci curvature is compatible with a reduced Riemannian curvature dimension condition. We also give a positive answer to Lott's question on the behavior of the scalar curvature with respect to the Gromov-Hausdorff topology by using our scalar curvature. This talk is based on arXiv:1510.05349.

For a noncollapsed Gromov-Hausdorff convergent sequence of Riemannian manifolds with a uniform bound of Ricci curvature, we establish two spectral convergence. One of them is on the Hodge Laplacian acting on differential one-forms. The other is on the connection Laplacian acting on tensor fields of every type, which include all differential forms. These are sharp generalizations of Cheeger-Colding's spectral convergence of the Laplacian acting on functions to the cases of tensor fields and differential forms. These spectral convergence have two direct corollaries. One of them is to give new bounds on such eigenvalues, in terms of bounds on volume, diameter and the Ricci curvature. The other is that we show the upper semicontinuity of the first Betti numbers with respect to the Gromov-Hausdorff topology, and give the equivalence between the continuity of them and the existence of a uniform spectral gap. On the other hand we also define measurable curvature tensors of the noncollapsed Gromov-Hausdorff limit space of a sequence of Riemannian manifolds with a uniform bound of Ricci curvature, which include Riemannian curvature tensor, the Ricci curvature, and the scalar curvature. As fundamental properties of our Ricci curvature, we show that the Ricci curvature coincides with the difference between the Hodge Laplacian and the connection Laplacian, and is compatible with Gigli's one and Lott's Ricci measure. Moreover we prove a lower bound of the Ricci curvature is compatible with a reduced Riemannian curvature dimension condition. We also give a positive answer to Lott's question on the behavior of the scalar curvature with respect to the Gromov-Hausdorff topology by using our scalar curvature. This talk is based on arXiv:1510.05349.

#### FMSP Lectures

15:00-16:00, 16:10-17:10 Room #002 (Graduate School of Math. Sci. Bldg.)

Rational homotopy theory : Quillen and Sullivan approach.(2) (ENGLISH)

[ Reference URL ]

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

**Aniceto Murillo et al**(Universidad de Malaga)Rational homotopy theory : Quillen and Sullivan approach.(2) (ENGLISH)

[ Reference URL ]

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

### 2016/04/20

#### FMSP Lectures

15:00-16:00, 16:10-17:10 Room #002 (Graduate School of Math. Sci. Bldg.)

Rational homotopy theory : Quillen and Sullivan approach.(1) (ENGLISH)

[ Reference URL ]

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

**Aniceto Murillo et al**(Universidad de Malaga)Rational homotopy theory : Quillen and Sullivan approach.(1) (ENGLISH)

[ Reference URL ]

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

#### Number Theory Seminar

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

On periodicity of geodesic continued fractions (Japanese)

**Hoto Bekki**(University of Tokyo)On periodicity of geodesic continued fractions (Japanese)

### 2016/04/19

#### Algebraic Geometry Seminar

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

Isomorphic quartic K3 surfaces and Cremona transformations (JAPANESE)

**Keiji Oguiso**(University of Tokyo)Isomorphic quartic K3 surfaces and Cremona transformations (JAPANESE)

[ Abstract ]

We show that

(i) there is a pair of smooth complex quartic K3 surfaces such that they are isomorphic as abstract varieties but not Cremona equivalent.

(ii) there is a pair of smooth complex quartic K3 surfaces such that they are Cemona equivalent but not projectively equivalent.

These two results are much inspired by e-mails from Professors Tuyen Truong and J\'anos Koll\'ar.

We show that

(i) there is a pair of smooth complex quartic K3 surfaces such that they are isomorphic as abstract varieties but not Cremona equivalent.

(ii) there is a pair of smooth complex quartic K3 surfaces such that they are Cemona equivalent but not projectively equivalent.

These two results are much inspired by e-mails from Professors Tuyen Truong and J\'anos Koll\'ar.

#### Tuesday Seminar on Topology

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

Topological rigidity of finite cyclic group actions on compact surfaces (ENGLISH)

**Błażej Szepietowski**(Gdansk University)Topological rigidity of finite cyclic group actions on compact surfaces (ENGLISH)

[ Abstract ]

Two actions of a group on a surface are called topologically equivalent if they are conjugate by a homeomorphism of the surface. I will describe a method of enumeration (and classification) of topological equivalence classes of actions of a finite group on a compact surface, based on the combinatorial theory of noneuclidean crystallographic groups (NEC groups in short) and a relationship between the outer automorphism group of an NEC group and certain mapping class group. By this method we study topological equivalence of actions of a finite cyclic group on a compact surface, in the situation where the order of the group is large relative to the genus of the surface.

Two actions of a group on a surface are called topologically equivalent if they are conjugate by a homeomorphism of the surface. I will describe a method of enumeration (and classification) of topological equivalence classes of actions of a finite group on a compact surface, based on the combinatorial theory of noneuclidean crystallographic groups (NEC groups in short) and a relationship between the outer automorphism group of an NEC group and certain mapping class group. By this method we study topological equivalence of actions of a finite cyclic group on a compact surface, in the situation where the order of the group is large relative to the genus of the surface.

### 2016/04/18

#### Operator Algebra Seminars

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

On the functoriality of Haagerup's $L^2$-space construction: Verticalizing decorated 2-categories

**Juan Orendain**(UNAM/Univ. Tokyo)On the functoriality of Haagerup's $L^2$-space construction: Verticalizing decorated 2-categories

#### Seminar on Geometric Complex Analysis

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

(JAPANESE)

**Kunio Obitsu**(Kagoshima University)(JAPANESE)

#### Numerical Analysis Seminar

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Error estimate for the finite element method in a smooth domain (日本語)

**Takahito Kashiwabara**(University of Tokyo)Error estimate for the finite element method in a smooth domain (日本語)

#### Tokyo Probability Seminar

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

Sharp interface limit for one-dimensional stochastic Allen-Cahn equation with Dirichlet boundary condition

**Kai Lee**(Graduate School of Mathematical Sciences, the university of Tokyo)Sharp interface limit for one-dimensional stochastic Allen-Cahn equation with Dirichlet boundary condition

### 2016/04/14

#### FMSP Lectures

15:30-17:00 Room #Lecture Hall, Kavli IPMU (Graduate School of Math. Sci. Bldg.)

Lecture 2: Geometric and algebraic Poisson modules (ENGLISH)

[ Reference URL ]

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

**Alan Weinstein**(University of California, Berkeley)Lecture 2: Geometric and algebraic Poisson modules (ENGLISH)

[ Reference URL ]

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

### 2016/04/13

#### Number Theory Seminar

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

Semisimplicity of geometric monodromy on etale cohomology (joint work with Anna Cadoret and Chun Yin Hui)

(English)

**Akio Tamagawa**(RIMS, Kyoto University)Semisimplicity of geometric monodromy on etale cohomology (joint work with Anna Cadoret and Chun Yin Hui)

(English)

[ Abstract ]

Let K be a function field over an algebraically closed field of characteritic p \geq 0, X a proper smooth K-scheme, and l a prime distinct from p. Deligne proved that the Q_l-coefficient etale cohomology groups of the geometric fiber of X --> K are always semisimple as G_K-modules. In this talk, we consider a similar problem for the F_l-coefficient etale cohomology groups. Among other things, we show that if p=0 (resp. in general), they are semisimple for all but finitely many l's (resp. for all l's in a set of density 1).

Let K be a function field over an algebraically closed field of characteritic p \geq 0, X a proper smooth K-scheme, and l a prime distinct from p. Deligne proved that the Q_l-coefficient etale cohomology groups of the geometric fiber of X --> K are always semisimple as G_K-modules. In this talk, we consider a similar problem for the F_l-coefficient etale cohomology groups. Among other things, we show that if p=0 (resp. in general), they are semisimple for all but finitely many l's (resp. for all l's in a set of density 1).

#### FMSP Lectures

13:30-14:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Determination of time-dependent coefficients for wave equations from partial data (ENGLISH)

[ Reference URL ]

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

**Yavar Kian**(Aix-Marseille Univ.)Determination of time-dependent coefficients for wave equations from partial data (ENGLISH)

[ Reference URL ]

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

### 2016/04/12

#### Lie Groups and Representation Theory

17:00-18:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Universal Gysin formulas for flag bundles

**Piotr Pragacz**(Institute of Mathematics, Polish Academy of Sciences)Universal Gysin formulas for flag bundles

[ Abstract ]

We give generalizations of the formula for the push-forward of a power of the hyperplane class in a projective bundle to flag bundles of type A, B, C, D. The formulas (and also the proofs) involve only the Segre classes of the original vector bundles and characteristic classes of universal bundles. This is a joint work with Lionel Darondeau.

We give generalizations of the formula for the push-forward of a power of the hyperplane class in a projective bundle to flag bundles of type A, B, C, D. The formulas (and also the proofs) involve only the Segre classes of the original vector bundles and characteristic classes of universal bundles. This is a joint work with Lionel Darondeau.

#### Tuesday Seminar on Topology

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

Homotopy theory of differential graded Lie algebras (ENGLISH)

**Aniceto Murillo**(Universidad de Malaga)Homotopy theory of differential graded Lie algebras (ENGLISH)

[ Abstract ]

Having as motivation the Deligne's principle by which every deformation functor is governed by a differential graded Lie algebra, we build a homotopy theory for these algebras which extend the classical Quillen approach and let us model any (non necessarily 1-connected nor path connected) complex. This is joint work with Urtzi Buijs, Yves Félix and Daniel Tanré.

Having as motivation the Deligne's principle by which every deformation functor is governed by a differential graded Lie algebra, we build a homotopy theory for these algebras which extend the classical Quillen approach and let us model any (non necessarily 1-connected nor path connected) complex. This is joint work with Urtzi Buijs, Yves Félix and Daniel Tanré.

#### Tuesday Seminar of Analysis

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

Scattering matrices and Dirichlet-to-Neumann maps (English)

**Jussi Behrndt**(Graz University of Technology)Scattering matrices and Dirichlet-to-Neumann maps (English)

[ Abstract ]

In this talk we discuss a recent result on the representation of the scattering matrix in terms of an abstract Titchmarsh-Weyl m-function. The general result can be applied to scattering problems for Schrödinger operators with $\delta$-type interactions on curves and hypersurfaces, and scattering problems involving Neumann and Robin realizations of Schrödinger operators on unbounded domains. In both applications we obtain formulas for the corresponding scattering matrices in terms of Dirichlet-to-Neumann maps. This talk is based on joint work with Mark Malamud and Hagen Neidhardt.

In this talk we discuss a recent result on the representation of the scattering matrix in terms of an abstract Titchmarsh-Weyl m-function. The general result can be applied to scattering problems for Schrödinger operators with $\delta$-type interactions on curves and hypersurfaces, and scattering problems involving Neumann and Robin realizations of Schrödinger operators on unbounded domains. In both applications we obtain formulas for the corresponding scattering matrices in terms of Dirichlet-to-Neumann maps. This talk is based on joint work with Mark Malamud and Hagen Neidhardt.

### 2016/04/11

#### Algebraic Geometry Seminar

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

Gysin maps, duality and Schubert classes (English)

https://www.impan.pl/~pragacz/main.htm

**Piotr Pragacz**(Institute of Mathematics, Polish Academy of Sciences )Gysin maps, duality and Schubert classes (English)

[ Abstract ]

We establish a Gysin formula for Schubert bundles

and a strong version of the duality theorem in Schubert calculus

on Grassmann bundles. We then combine them to compute the fundamental

classes of Schubert bundles in Grassmann bundles, which yields a new

proof of the Giambelli formula for vector bundles. This is a joint

work with Lionel Darondeau.

[ Reference URL ]We establish a Gysin formula for Schubert bundles

and a strong version of the duality theorem in Schubert calculus

on Grassmann bundles. We then combine them to compute the fundamental

classes of Schubert bundles in Grassmann bundles, which yields a new

proof of the Giambelli formula for vector bundles. This is a joint

work with Lionel Darondeau.

https://www.impan.pl/~pragacz/main.htm

#### Operator Algebra Seminars

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

On analytic construction of the group three-cocycles (English)

**Ryszard Nest**(Univ. Copenhagen)On analytic construction of the group three-cocycles (English)

#### FMSP Lectures

15:30-17:00 Room #Lecture Hall, Kavli IPMU (Graduate School of Math. Sci. Bldg.)

Lecture 1: Special subspaces in symplectic vector spaces (ENGLISH)

[ Reference URL ]

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

**Alan Weinstein**(University of California, Berkeley)Lecture 1: Special subspaces in symplectic vector spaces (ENGLISH)

[ Reference URL ]

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

#### Seminar on Geometric Complex Analysis

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

Defining the Julia sets on CP^2 (JAPANESE)

**Taro Asuke**(The University of Tokyo)Defining the Julia sets on CP^2 (JAPANESE)

[ Abstract ]

The Julia sets play a central role in the study of complex dynamical systems as well as Kleinian groups where they appear as limit sets. They are also known to be meaningful for complex foliations without singularities, however still not defined for singular ones. In this talk, I will discuss some expected properties of the Julia sets for singular foliations and difficulties for defining them.

The Julia sets play a central role in the study of complex dynamical systems as well as Kleinian groups where they appear as limit sets. They are also known to be meaningful for complex foliations without singularities, however still not defined for singular ones. In this talk, I will discuss some expected properties of the Julia sets for singular foliations and difficulties for defining them.

### 2016/04/08

#### Colloquium

15:30-16:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Using mathematical objects (ENGLISH)

**François Apery**(l'IRMA à Strasbourg)Using mathematical objects (ENGLISH)

[ Abstract ]

Mathematical models are not only teaching tools or pieces of museum but can also have inspiring influence to discovering new truths in mathematics. Through some examples including the Boy surface we will show how models have played a major role in the emergence of new results.

Mathematical models are not only teaching tools or pieces of museum but can also have inspiring influence to discovering new truths in mathematics. Through some examples including the Boy surface we will show how models have played a major role in the emergence of new results.

### 2016/04/05

#### Tuesday Seminar on Topology

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

Torsion invariants and representation varieties for non-positively curved cube complexes (JAPANESE)

**Takahiro Kitayama**(The University of Tokyo)Torsion invariants and representation varieties for non-positively curved cube complexes (JAPANESE)

[ Abstract ]

Applications of torsion invariants and representation varieties have been extensively studied for 3-manifolds. Twisted Alexander polynomials are known to detect the Thurston norm and fiberedness of a 3-manifold. Ideal points of character varieties are known to detect essential surfaces in a 3-manifold in a certain extension of Culler-Shalen theory. In view of cubulation of 3-manifolds one can expect that these results naturally extend to a wider framework and, in particular, the case of virtually special cube complexes. We formulate and discuss such analogous questions for non-positively curved cube complexes.

Applications of torsion invariants and representation varieties have been extensively studied for 3-manifolds. Twisted Alexander polynomials are known to detect the Thurston norm and fiberedness of a 3-manifold. Ideal points of character varieties are known to detect essential surfaces in a 3-manifold in a certain extension of Culler-Shalen theory. In view of cubulation of 3-manifolds one can expect that these results naturally extend to a wider framework and, in particular, the case of virtually special cube complexes. We formulate and discuss such analogous questions for non-positively curved cube complexes.

### 2016/04/04

#### Numerical Analysis Seminar

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Staggered discontinuous Galerkin methods for the incompressible Navier-Stokes equations (English)

**Eric Chung**(Chinese University of Hong Kong)Staggered discontinuous Galerkin methods for the incompressible Navier-Stokes equations (English)

[ Abstract ]

In this talk, we present a staggered discontinuous Galerkin method for the approximation of the incompressible Navier-Stokes equations. Our new method combines the advantages of discontinuous Galerkin methods and staggered meshes, and results in many good properties, namely local and global conservations, optimal convergence and superconvergence through the use of a local postprocessing technique. Another key feature is that our method provides a skew-symmetric discretization of the convection term, with the aim of giving a better conservation property compared with existing discretizations. We also analyze the stability and convergence of the method. In addition, we will present some numerical results to show the performance of the proposed method.

In this talk, we present a staggered discontinuous Galerkin method for the approximation of the incompressible Navier-Stokes equations. Our new method combines the advantages of discontinuous Galerkin methods and staggered meshes, and results in many good properties, namely local and global conservations, optimal convergence and superconvergence through the use of a local postprocessing technique. Another key feature is that our method provides a skew-symmetric discretization of the convection term, with the aim of giving a better conservation property compared with existing discretizations. We also analyze the stability and convergence of the method. In addition, we will present some numerical results to show the performance of the proposed method.

### 2016/03/29

#### Number Theory Seminar

17:30-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Motivic cohomology of formal schemes in characteristic p

(English)

**Matthew Morrow**(Universität Bonn)Motivic cohomology of formal schemes in characteristic p

(English)

[ Abstract ]

The logarithmic Hodge-Witt sheaves of Illusie, Milne, Kato, et al. of a smooth variety in characteristic p provide a concrete realisation of its p-adic motivic cohomology, thanks to results of Geisser-Levine and Bloch-Kato-Gabber which link them to algebraic K-theory. I will explain an analogous theory for formal schemes, as well as applications to algebraic cycles, such as a weak Lefschetz theorem for formal Chow groups.

The logarithmic Hodge-Witt sheaves of Illusie, Milne, Kato, et al. of a smooth variety in characteristic p provide a concrete realisation of its p-adic motivic cohomology, thanks to results of Geisser-Levine and Bloch-Kato-Gabber which link them to algebraic K-theory. I will explain an analogous theory for formal schemes, as well as applications to algebraic cycles, such as a weak Lefschetz theorem for formal Chow groups.

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