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Seminar information archive
Seminar information archive ～07/26｜Today's seminar 07/27 | Future seminars 07/28～
2014/06/03
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Tatsuru Takakura (Chuo University)
Vector partition functions and the topology of multiple weight varieties
(JAPANESE)
Tatsuru Takakura (Chuo University)
Vector partition functions and the topology of multiple weight varieties
(JAPANESE)
[ Abstract ]
A multiple weight variety is a symplectic quotient of a direct product
of several coadjoint orbits of a compact Lie group $G$, with respect to
the diagonal action of the maximal torus. Its geometry and topology are
closely related to the combinatorics concerned with the weight space
decomposition of a tensor product of irreducible representations of $G$.
For example, when considering the Riemann-Roch index, we are naturally
lead to the study of vector partition functions with multiplicities.
In this talk, we discuss some formulas for vector partition functions,
especially a generalization of the formula of Brion-Vergne. Then, by
using
them, we investigate the structure of the cohomology of certain multiple
weight varieties of type $A$ in detail.
A multiple weight variety is a symplectic quotient of a direct product
of several coadjoint orbits of a compact Lie group $G$, with respect to
the diagonal action of the maximal torus. Its geometry and topology are
closely related to the combinatorics concerned with the weight space
decomposition of a tensor product of irreducible representations of $G$.
For example, when considering the Riemann-Roch index, we are naturally
lead to the study of vector partition functions with multiplicities.
In this talk, we discuss some formulas for vector partition functions,
especially a generalization of the formula of Brion-Vergne. Then, by
using
them, we investigate the structure of the cohomology of certain multiple
weight varieties of type $A$ in detail.
2014/06/02
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Atsushi Hayashimoto (Nagano National College of Technology)
Generalized pseudoellipsoids and proper holomorphic mappings between them (JAPANESE)
Atsushi Hayashimoto (Nagano National College of Technology)
Generalized pseudoellipsoids and proper holomorphic mappings between them (JAPANESE)
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Yusuke Nakamura (University of Tokyo)
On base point free theorem for log canonical three folds over the algebraic closure of a finite field (JAPANESE)
Yusuke Nakamura (University of Tokyo)
On base point free theorem for log canonical three folds over the algebraic closure of a finite field (JAPANESE)
[ Abstract ]
We will discuss about the base point free theorem on three-dimensional
pairs defined over the algebraic closure of a finite field.
We know the base point free theorem on arbitrary-dimensional Kawamata
log terminal pairs in characteristic zero. By Birkar and Xu, the base
point free theorem in positive characteristic is known for big line
bundles on three-dimensional Kawamata log terminal pairs defined over
an algebraically closed field of characteristic larger than 5. Over the
algebraic closure of a finite field, a stronger result was proved by Keel.
The purpose of this talk is to generalize the Keel's result. We will
prove the base point free theorem for big line bundles on
three-dimensional log canonical pairs defined over the algebraic closure
of a finite field. This theorem is not valid for another field.
This is joint work with Diletta Martinelli and Jakub Witaszek.
We will discuss about the base point free theorem on three-dimensional
pairs defined over the algebraic closure of a finite field.
We know the base point free theorem on arbitrary-dimensional Kawamata
log terminal pairs in characteristic zero. By Birkar and Xu, the base
point free theorem in positive characteristic is known for big line
bundles on three-dimensional Kawamata log terminal pairs defined over
an algebraically closed field of characteristic larger than 5. Over the
algebraic closure of a finite field, a stronger result was proved by Keel.
The purpose of this talk is to generalize the Keel's result. We will
prove the base point free theorem for big line bundles on
three-dimensional log canonical pairs defined over the algebraic closure
of a finite field. This theorem is not valid for another field.
This is joint work with Diletta Martinelli and Jakub Witaszek.
2014/05/28
Number Theory Seminar
16:40-17:40 Room #056 (Graduate School of Math. Sci. Bldg.)
Gantsooj Batzaya (University of Tokyo)
On simultaneous approximation to powers of a real number by rational numbers (ENGLISH)
Gantsooj Batzaya (University of Tokyo)
On simultaneous approximation to powers of a real number by rational numbers (ENGLISH)
Operator Algebra Seminars
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Makoto Yamashita (Ochanomizu University)
Poisson boundary of monoidal categories (ENGLISH)
Makoto Yamashita (Ochanomizu University)
Poisson boundary of monoidal categories (ENGLISH)
Mathematical Biology Seminar
14:50-16:20 Room #128 (Graduate School of Math. Sci. Bldg.)
Keisuke Ejima (Department of Global Health Policy, Graduate School of Medicine, The University of Tokyo
)
Modeling the social contagion: The obesity epidemic and its control (JAPANESE)
Keisuke Ejima (Department of Global Health Policy, Graduate School of Medicine, The University of Tokyo
)
Modeling the social contagion: The obesity epidemic and its control (JAPANESE)
[ Abstract ]
:As an obesity epidemic has grown worldwide, a variety of
intervention programs have been considered, but a scientific approach
to comparatively assessing the control programs has still to be
considered. The present study aims to describe an obesity epidemic by
employing a simple mathematical model that accounts for both social
contagion and non-contagious hazards of obesity, thereby comparing the
effectiveness of different types of interventions.
An epidemiological model is devised to describe the time- and
age-dependent risk of obesity, the hazard of which is dealt with as
both dependent on and independent of obesity prevalence, and
parameterizing the model using empirically observed data. The
equilibrium prevalence is investigated as our epidemiological outcome,
assessing its sensitivity to different parameters that regulate the
impact of intervention programs and qualitatively comparing the
effectiveness. We compare the effectiveness of different types of
interventions, including those directed to never-obese individuals
(i.e. primary prevention) and toward obese and ex-obese individuals
(i.e. secondary prevention).
The optimal choice of intervention programs considerably varies with
the transmission coefficient of obesity, and a limited
transmissibility led us to favour preventing weight gain among
never-obese individuals. An abrupt decline in the prevalence is
expected when the hazards of obesity through contagious and
non-contagious routes fall into a particular parameter space, with a
high sensitivity to the transmission potential of obesity from person
to person. When a combination of two control strategies can be
selected, primary and secondary preventions yielded similar population
impacts and the superiority of the effectiveness depends on the
strength of the interventions at an individual level.
The optimality of intervention programs depends on the contagiousness
of obesity. Filling associated data gaps of obesity transmission would
help systematically understand the epidemiological dynamics and
consider required control programs.
:As an obesity epidemic has grown worldwide, a variety of
intervention programs have been considered, but a scientific approach
to comparatively assessing the control programs has still to be
considered. The present study aims to describe an obesity epidemic by
employing a simple mathematical model that accounts for both social
contagion and non-contagious hazards of obesity, thereby comparing the
effectiveness of different types of interventions.
An epidemiological model is devised to describe the time- and
age-dependent risk of obesity, the hazard of which is dealt with as
both dependent on and independent of obesity prevalence, and
parameterizing the model using empirically observed data. The
equilibrium prevalence is investigated as our epidemiological outcome,
assessing its sensitivity to different parameters that regulate the
impact of intervention programs and qualitatively comparing the
effectiveness. We compare the effectiveness of different types of
interventions, including those directed to never-obese individuals
(i.e. primary prevention) and toward obese and ex-obese individuals
(i.e. secondary prevention).
The optimal choice of intervention programs considerably varies with
the transmission coefficient of obesity, and a limited
transmissibility led us to favour preventing weight gain among
never-obese individuals. An abrupt decline in the prevalence is
expected when the hazards of obesity through contagious and
non-contagious routes fall into a particular parameter space, with a
high sensitivity to the transmission potential of obesity from person
to person. When a combination of two control strategies can be
selected, primary and secondary preventions yielded similar population
impacts and the superiority of the effectiveness depends on the
strength of the interventions at an individual level.
The optimality of intervention programs depends on the contagiousness
of obesity. Filling associated data gaps of obesity transmission would
help systematically understand the epidemiological dynamics and
consider required control programs.
2014/05/27
Tuesday Seminar of Analysis
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yoichi Miyazaki (NIHON UNIVERSITY, SCHOOL OF DENTISTRY)
The regularity theorem for elliptic equations and the smoothness of domains (JAPANESE)
Yoichi Miyazaki (NIHON UNIVERSITY, SCHOOL OF DENTISTRY)
The regularity theorem for elliptic equations and the smoothness of domains (JAPANESE)
[ Abstract ]
We consider the Dirichlet boundary problem for a strongly elliptic operator of order $2m$ with non-smooth coefficients, and prove the regularity theorem for $L_p$-based Sobolev spaces when the domain has a boundary of limited smoothness. Compared to the known results, we can weaken the smoothness assumption on the boundary by $m-1$.
We consider the Dirichlet boundary problem for a strongly elliptic operator of order $2m$ with non-smooth coefficients, and prove the regularity theorem for $L_p$-based Sobolev spaces when the domain has a boundary of limited smoothness. Compared to the known results, we can weaken the smoothness assumption on the boundary by $m-1$.
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Ege Fujikawa (Chiba University)
The Teichmuller space and the stable quasiconformal mapping class group for a Riemann surface of infinite type (JAPANESE)
Ege Fujikawa (Chiba University)
The Teichmuller space and the stable quasiconformal mapping class group for a Riemann surface of infinite type (JAPANESE)
[ Abstract ]
We explain recent developments of the theory of infinite dimensional Teichmuller space. In particular, we observe the dynamics of the orbits by the action of the stable quasiconformal mapping class group on the Teichmuller space and consider the relationship with the asymptotic Teichmuller space. We also introduce the generalized fixed point theorem and the Nielsen realization theorem. Furthermore, we investigate the moduli space of Riemann surface of infinite type.
We explain recent developments of the theory of infinite dimensional Teichmuller space. In particular, we observe the dynamics of the orbits by the action of the stable quasiconformal mapping class group on the Teichmuller space and consider the relationship with the asymptotic Teichmuller space. We also introduce the generalized fixed point theorem and the Nielsen realization theorem. Furthermore, we investigate the moduli space of Riemann surface of infinite type.
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Masaki Watanabe (the University of Tokyo, Graduate School of Mathematical Sciences)
On the structure of Schubert modules and filtration by Schubert modules
(JAPANESE)
Masaki Watanabe (the University of Tokyo, Graduate School of Mathematical Sciences)
On the structure of Schubert modules and filtration by Schubert modules
(JAPANESE)
[ Abstract ]
One of the methods for studying Schubert polynomials is using
Schubert modules introduced by Kraskiewicz and Pragacz.
In this seminar I will talk about a new result on the structure of
Schubert modules, and give a criterion for a module to have a filtration by Schubert modules.
I will also talk about a problem concerning Schubert polynomials
which motivated this research.
One of the methods for studying Schubert polynomials is using
Schubert modules introduced by Kraskiewicz and Pragacz.
In this seminar I will talk about a new result on the structure of
Schubert modules, and give a criterion for a module to have a filtration by Schubert modules.
I will also talk about a problem concerning Schubert polynomials
which motivated this research.
2014/05/22
Geometry Colloquium
10:00-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Boris Hasselblatt (Tufts Univ)
Godbillon-Vey invariants for maximal isotropic foliations (ENGLISH)
Boris Hasselblatt (Tufts Univ)
Godbillon-Vey invariants for maximal isotropic foliations (ENGLISH)
[ Abstract ]
The combination of a contact structure and an orientable maximal isotropic foliation gives rise to m+1 Godbillon-Vey invariants for an m+1-dimensional maximal isotropic foliation that are of interest with respect to geometric rigidity: by studying these jointly, we give new proofs of famous "rigidity'' results from the 1980s that require only a very few simple lines of reasoning rather than the elaborate original proofs.
The combination of a contact structure and an orientable maximal isotropic foliation gives rise to m+1 Godbillon-Vey invariants for an m+1-dimensional maximal isotropic foliation that are of interest with respect to geometric rigidity: by studying these jointly, we give new proofs of famous "rigidity'' results from the 1980s that require only a very few simple lines of reasoning rather than the elaborate original proofs.
2014/05/21
Number Theory Seminar
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Shenghao Sun (Mathematical Sciences Center of Tsinghua University)
Parity of Betti numbers in étale cohomology (ENGLISH)
Shenghao Sun (Mathematical Sciences Center of Tsinghua University)
Parity of Betti numbers in étale cohomology (ENGLISH)
[ Abstract ]
By Hodge symmetry, the Betti numbers of a complex projective smooth variety in odd degrees are even. When the base field has characteristic p, Deligne proved the hard Lefschetz theorem in etale cohomology, and the parity result follows from this. Suh has generalized this to proper smooth varieties in characteristic p, using crystalline cohomology.
The purity of intersection cohomology group of proper varieties suggests that the same parity property should hold for these groups in characteristic p. We proved this by investigating the symmetry in the categorical level.
In particular, we reproved Suh's result, using merely etale cohomology. Some related results will be discussed. This is joint work with Weizhe Zheng.
By Hodge symmetry, the Betti numbers of a complex projective smooth variety in odd degrees are even. When the base field has characteristic p, Deligne proved the hard Lefschetz theorem in etale cohomology, and the parity result follows from this. Suh has generalized this to proper smooth varieties in characteristic p, using crystalline cohomology.
The purity of intersection cohomology group of proper varieties suggests that the same parity property should hold for these groups in characteristic p. We proved this by investigating the symmetry in the categorical level.
In particular, we reproved Suh's result, using merely etale cohomology. Some related results will be discussed. This is joint work with Weizhe Zheng.
Operator Algebra Seminars
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Masato Mimura (Tohoku Univ.)
Group approximation in Cayley topology and coarse geometry
part I: coarse embeddings of amenable groups (ENGLISH)
Masato Mimura (Tohoku Univ.)
Group approximation in Cayley topology and coarse geometry
part I: coarse embeddings of amenable groups (ENGLISH)
2014/05/20
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Shintaro Kuroki (The Univeristy of Tokyo)
An application of torus graphs to characterize torus manifolds
with extended actions (JAPANESE)
Shintaro Kuroki (The Univeristy of Tokyo)
An application of torus graphs to characterize torus manifolds
with extended actions (JAPANESE)
[ Abstract ]
A torus manifold is a compact, oriented 2n-dimensional T^n-
manifolds with fixed points. This notion is introduced by Hattori and
Masuda as a topological generalization of toric manifolds. For a given
torus manifold, we can define a labelled graph called a torus graph (
this may be regarded as a generalization of some class of GKM graphs).
It is known that the equivariant cohomology ring of some nice class of
torus manifolds can be computed by using a combinatorial data of torus
graphs. In this talk, we study which torus action of torus manifolds can
be extended to a non-abelian compact connected Lie group. To do this, we
introduce root systems of (abstract) torus graphs and characterize
extended actions of torus manifolds. This is a joint work with Mikiya
Masuda.
A torus manifold is a compact, oriented 2n-dimensional T^n-
manifolds with fixed points. This notion is introduced by Hattori and
Masuda as a topological generalization of toric manifolds. For a given
torus manifold, we can define a labelled graph called a torus graph (
this may be regarded as a generalization of some class of GKM graphs).
It is known that the equivariant cohomology ring of some nice class of
torus manifolds can be computed by using a combinatorial data of torus
graphs. In this talk, we study which torus action of torus manifolds can
be extended to a non-abelian compact connected Lie group. To do this, we
introduce root systems of (abstract) torus graphs and characterize
extended actions of torus manifolds. This is a joint work with Mikiya
Masuda.
Seminar on Probability and Statistics
13:00-14:10 Room #052 (Graduate School of Math. Sci. Bldg.)
OGIHARA, Teppei (Center for the Study of Finance and Insurance, Osaka University)
Maximum likelihood type estimation of diffusion processes with non synchronous observations contaminated by market microstructure noise (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2014/02.html
OGIHARA, Teppei (Center for the Study of Finance and Insurance, Osaka University)
Maximum likelihood type estimation of diffusion processes with non synchronous observations contaminated by market microstructure noise (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2014/02.html
2014/05/19
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Shigeharu Takayama (University of Tokyo)
On degenerations of Ricci-flat Kähler manifolds (JAPANESE)
Shigeharu Takayama (University of Tokyo)
On degenerations of Ricci-flat Kähler manifolds (JAPANESE)
2014/05/17
Harmonic Analysis Komaba Seminar
13:30-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yohei Tsutsui (The University of Tokyo) 13:30-15:00
Bounded small solutions to a chemotaxis system with non-diffusive chemical (JAPANESE)
Heat kernel and Schroedinger kernel on the Heisenberg group (JAPANESE)
Yohei Tsutsui (The University of Tokyo) 13:30-15:00
Bounded small solutions to a chemotaxis system with non-diffusive chemical (JAPANESE)
[ Abstract ]
We consider a chemotaxis system with a logarithmic sensitivity and a non-diffusive chemical substance. For some chemotactic sensitivity constants, Ahn and Kang proved the existence of bounded global solutions to the system. An entropy functional was used in their argument to control the cell density by the density of the chemical substance. Our purpose is to show the existence of bounded global solutions for all the chemotactic sensitivity constants. Assuming the smallness on the initial data in some sense, we can get uniform estimates for time. These estimates are used to extend local solutions.
This talk is partially based on joint work with Yoshie Sugiyama (Kyusyu Univ.) and Juan J.L. Vel\\'azquez (Univ. of Bonn).
Toshinao Kagawa (Tokyo City University) 15:30-17:00We consider a chemotaxis system with a logarithmic sensitivity and a non-diffusive chemical substance. For some chemotactic sensitivity constants, Ahn and Kang proved the existence of bounded global solutions to the system. An entropy functional was used in their argument to control the cell density by the density of the chemical substance. Our purpose is to show the existence of bounded global solutions for all the chemotactic sensitivity constants. Assuming the smallness on the initial data in some sense, we can get uniform estimates for time. These estimates are used to extend local solutions.
This talk is partially based on joint work with Yoshie Sugiyama (Kyusyu Univ.) and Juan J.L. Vel\\'azquez (Univ. of Bonn).
Heat kernel and Schroedinger kernel on the Heisenberg group (JAPANESE)
2014/05/15
Geometry Colloquium
10:00-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Homare TADANO (Osaka University)
Gap theorems for compact gradient Sasaki Ricci solitons (JAPANESE)
Homare TADANO (Osaka University)
Gap theorems for compact gradient Sasaki Ricci solitons (JAPANESE)
[ Abstract ]
In this talk we give some necessary and sufficient conditions for compact gradient Sasaki-Ricci solitons to be Sasaki-Einstein. Our result may be considered as a Sasaki geometry version of recent works by H. Li, and M. Fern¥'andez-L¥'opez-E. Garc¥'ia-Rio.
In this talk we give some necessary and sufficient conditions for compact gradient Sasaki-Ricci solitons to be Sasaki-Einstein. Our result may be considered as a Sasaki geometry version of recent works by H. Li, and M. Fern¥'andez-L¥'opez-E. Garc¥'ia-Rio.
Lectures
16:30-17:30 Room #050 (Graduate School of Math. Sci. Bldg.)
Cédric Villani (Université de Lyon, Institut Henri Poincaré)
Synthetic theory of Ricci curvature
― When Monge, Riemann and Boltzmann meet ― (ENGLISH)
http://faculty.ms.u-tokyo.ac.jp/Villani.html
Cédric Villani (Université de Lyon, Institut Henri Poincaré)
Synthetic theory of Ricci curvature
― When Monge, Riemann and Boltzmann meet ― (ENGLISH)
[ Abstract ]
Optimal transport theory, non-Euclidean geometry and statistical physics met fifteen years ago with the discovery that Ricci curvature can be studied quantitatively thanks to entropy and
Monge-Kantorovich transport.
This unexpected encounter was very fruitful, leading to progress in each of these fields.
[ Reference URL ]Optimal transport theory, non-Euclidean geometry and statistical physics met fifteen years ago with the discovery that Ricci curvature can be studied quantitatively thanks to entropy and
Monge-Kantorovich transport.
This unexpected encounter was very fruitful, leading to progress in each of these fields.
http://faculty.ms.u-tokyo.ac.jp/Villani.html
FMSP Lectures
16:30-17:30 Room #050 (Graduate School of Math. Sci. Bldg.)
Cédric Villani (Université de Lyon, Institut Henri Poincaré)
Synthetic theory of Ricci curvature ― When Monge, Riemann and Boltzmann meet ― (ENGLISH)
[ Reference URL ]
http://faculty.ms.u-tokyo.ac.jp/Villani.html
Cédric Villani (Université de Lyon, Institut Henri Poincaré)
Synthetic theory of Ricci curvature ― When Monge, Riemann and Boltzmann meet ― (ENGLISH)
[ Reference URL ]
http://faculty.ms.u-tokyo.ac.jp/Villani.html
2014/05/14
Operator Algebra Seminars
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Yul Otani (Univ. Tokyo)
A Supersymmetric model in AQFT (after Buchholz and Grundling) (ENGLISH)
Yul Otani (Univ. Tokyo)
A Supersymmetric model in AQFT (after Buchholz and Grundling) (ENGLISH)
2014/05/13
Tuesday Seminar of Analysis
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yasunori Okada (Graduate School of Science and Technology, Chiba University)
Ultra-differentiable classes and intersection theorems (JAPANESE)
Yasunori Okada (Graduate School of Science and Technology, Chiba University)
Ultra-differentiable classes and intersection theorems (JAPANESE)
[ Abstract ]
There are two ways to define notions of
ultra-differentiability: one in terms of estimates on derivatives, and
the other in terms of growth properties of Fourier transforms of
suitably localized functions.
In this talk, we study the relation between BMT-classes and
inhomogeneous Gevrey classes, which are examples of such two kinds of
notions of ultra-differentiability.
We also mention intersection theorems on these classes.
This talk is based on a joint work with Otto Liess (Bologna University).
There are two ways to define notions of
ultra-differentiability: one in terms of estimates on derivatives, and
the other in terms of growth properties of Fourier transforms of
suitably localized functions.
In this talk, we study the relation between BMT-classes and
inhomogeneous Gevrey classes, which are examples of such two kinds of
notions of ultra-differentiability.
We also mention intersection theorems on these classes.
This talk is based on a joint work with Otto Liess (Bologna University).
Seminar on Probability and Statistics
13:00-14:10 Room #052 (Graduate School of Math. Sci. Bldg.)
Selma Chaker (Bank of Canada)
On High Frequency Estimation of the Frictionless Price: The Use of Observed Liquidity Variables (ENGLISH)
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2014/01.html
Selma Chaker (Bank of Canada)
On High Frequency Estimation of the Frictionless Price: The Use of Observed Liquidity Variables (ENGLISH)
[ Abstract ]
Observed high-frequency prices are always contaminated with liquidity costs or market microstructure noise. Inspired by the market microstructure literature, I explicitly model this noise and remove it from observed prices to obtain an estimate of the frictionless price. I then formally test whether the prices adjusted for the estimated liquidity costs are either totally or partially free from noise. If the liquidity costs are only partially removed, the residual noise is smaller and closer to an exogenous white noise than the original noise is. To illustrate my approach, I use the adjusted prices to improve volatility estimation in the presence of noise. If the noise is totally absorbed, I show that the sum of squared returns - which would be inconsistent for return variance when based on observed returns - becomes consistent when based on adjusted returns.
[ Reference URL ]Observed high-frequency prices are always contaminated with liquidity costs or market microstructure noise. Inspired by the market microstructure literature, I explicitly model this noise and remove it from observed prices to obtain an estimate of the frictionless price. I then formally test whether the prices adjusted for the estimated liquidity costs are either totally or partially free from noise. If the liquidity costs are only partially removed, the residual noise is smaller and closer to an exogenous white noise than the original noise is. To illustrate my approach, I use the adjusted prices to improve volatility estimation in the presence of noise. If the noise is totally absorbed, I show that the sum of squared returns - which would be inconsistent for return variance when based on observed returns - becomes consistent when based on adjusted returns.
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2014/01.html
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Taro Asuke (The University of Tokyo)
Transverse projective structures of foliations and deformations of the Godbillon-Vey class (JAPANESE)
Taro Asuke (The University of Tokyo)
Transverse projective structures of foliations and deformations of the Godbillon-Vey class (JAPANESE)
[ Abstract ]
Given a smooth family of foliations, we can define the derivative of the Godbillon-Vey class
with respect to the family. The derivative is known to be represented in terms of the projective
Schwarzians of holonomy maps. In this talk, we will study transverse projective structures
and connections, and show that the derivative is in fact determined by the projective structure
and the family.
Given a smooth family of foliations, we can define the derivative of the Godbillon-Vey class
with respect to the family. The derivative is known to be represented in terms of the projective
Schwarzians of holonomy maps. In this talk, we will study transverse projective structures
and connections, and show that the derivative is in fact determined by the projective structure
and the family.
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Ivan Cherednik (The University of North Carolina at Chapel Hill, RIMS
)
Global q,t-hypergeometric and q-Whittaker functions (ENGLISH)
Ivan Cherednik (The University of North Carolina at Chapel Hill, RIMS
)
Global q,t-hypergeometric and q-Whittaker functions (ENGLISH)
[ Abstract ]
The lectures will be devoted to the new theory of global
difference hypergeometric and Whittaker functions, one of
the major applications of the double affine Hecke algebras
and a breakthrough in the classical harmonic analysis. They
integrate the Ruijsenaars-Macdonald difference QMBP and
"Q-Toda" (any root systems), and are analytic everywhere
("global") with superb asymptotic behavior.
The definition of the global functions was suggested about
14 years ago; it is conceptually different from the definition
Heine gave in 1846, which remained unchanged and unchallenged
since then. Algebraically, the new functions are closer to
Bessel functions than to the classical hypergeometric and
Whittaker functions. The analytic theory of these functions was
completed only recently (the speaker and Jasper Stokman).
The construction is based on DAHA. The global functions are defined
as reproducing kernels of Fourier-DAHA transforms. Their
specializations are Macdonald polynomials, which is a powerful
generalization of the Shintani and Casselman-Shalika p-adic formulas.
If time permits, the connection of the Harish-Chandra theory of global
q-Whittaker functions will be discussed with the Givental-Lee formula
(Gromov-Witten invariants of flag varieties) and its generalizations due
to Braverman and Finkelberg (algebraic theory of affine flag varieties).
The lectures will be devoted to the new theory of global
difference hypergeometric and Whittaker functions, one of
the major applications of the double affine Hecke algebras
and a breakthrough in the classical harmonic analysis. They
integrate the Ruijsenaars-Macdonald difference QMBP and
"Q-Toda" (any root systems), and are analytic everywhere
("global") with superb asymptotic behavior.
The definition of the global functions was suggested about
14 years ago; it is conceptually different from the definition
Heine gave in 1846, which remained unchanged and unchallenged
since then. Algebraically, the new functions are closer to
Bessel functions than to the classical hypergeometric and
Whittaker functions. The analytic theory of these functions was
completed only recently (the speaker and Jasper Stokman).
The construction is based on DAHA. The global functions are defined
as reproducing kernels of Fourier-DAHA transforms. Their
specializations are Macdonald polynomials, which is a powerful
generalization of the Shintani and Casselman-Shalika p-adic formulas.
If time permits, the connection of the Harish-Chandra theory of global
q-Whittaker functions will be discussed with the Givental-Lee formula
(Gromov-Witten invariants of flag varieties) and its generalizations due
to Braverman and Finkelberg (algebraic theory of affine flag varieties).
2014/05/12
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Joe Kamimoto (Kyushu university)
Resolution of singularities via Newton polyhedra and its application to analysis (JAPANESE)
Joe Kamimoto (Kyushu university)
Resolution of singularities via Newton polyhedra and its application to analysis (JAPANESE)
[ Abstract ]
In the 1970s, A. N. Varchenko precisely investigated the leading term of the asymptotic expansion of an oscillatory integral with real analytic phase by using the geometry of the Newton polyhedron of the phase. Since his study, the importance of the resolution of singularities by means of Newton polyhedra has been strongly recognized. The purpose of this talk is to consider studies around this theme and to explain their relationship with some problems in several complex variables.
In the 1970s, A. N. Varchenko precisely investigated the leading term of the asymptotic expansion of an oscillatory integral with real analytic phase by using the geometry of the Newton polyhedron of the phase. Since his study, the importance of the resolution of singularities by means of Newton polyhedra has been strongly recognized. The purpose of this talk is to consider studies around this theme and to explain their relationship with some problems in several complex variables.
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