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Seminar information archive
Seminar information archive ～04/18｜Today's seminar 04/19 | Future seminars 04/20～
Number Theory Seminar
18:00-19:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Ted Chinburg (University of Pennsylvania & IHES)
Chern classes in Iwasawa theory (English)
Ted Chinburg (University of Pennsylvania & IHES)
Chern classes in Iwasawa theory (English)
[ Abstract ]
Many of the main conjectures in Iwasawa theory can be phrased as saying that the first Chern class of an Iwasawa module is generated by a p-adic L-series. In this talk I will describe how higher Chern classes pertain to the higher codimension behavior of Iwasawa modules. I'll then describe a template for conjectures which would link such higher Chern classes to elements in the K-theory of Iwasawa algebras which are constructed from tuples of Katz p-adic L-series. I will finally describe an instance in which a result of this kind, for the second Chern class of an unramified Iwasawa module, can be proved over an imaginary quadratic field. This is joint work with F. Bleher, R. Greenberg, M. Kakde, G. Pappas, R. Sharifi and M. J. Taylor.
Many of the main conjectures in Iwasawa theory can be phrased as saying that the first Chern class of an Iwasawa module is generated by a p-adic L-series. In this talk I will describe how higher Chern classes pertain to the higher codimension behavior of Iwasawa modules. I'll then describe a template for conjectures which would link such higher Chern classes to elements in the K-theory of Iwasawa algebras which are constructed from tuples of Katz p-adic L-series. I will finally describe an instance in which a result of this kind, for the second Chern class of an unramified Iwasawa module, can be proved over an imaginary quadratic field. This is joint work with F. Bleher, R. Greenberg, M. Kakde, G. Pappas, R. Sharifi and M. J. Taylor.
2015/12/08
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Yuichi Yamada (The Univ. of Electro-Comm.)
Lens space surgery and Kirby calculus of 4-manifolds (JAPANESE)
Yuichi Yamada (The Univ. of Electro-Comm.)
Lens space surgery and Kirby calculus of 4-manifolds (JAPANESE)
[ Abstract ]
The problem asking "Which knot yields a lens space by Dehn surgery" is
called "lens space surgery". Berge's list ('90) is believed to be the
complete list, but it is still unproved, even after some progress by
Heegaard Floer Homology.
This problem seems to enter a new aspect: study using 4-manifolds, lens
space surgery from lens spaces, checking hyperbolicity by computer.
In the talk, we review the structure of Berge's list and talk on our
study on pairs of distinct knots but yield same lens spaces, and
4-maniolds constructed from such pairs. This is joint work with Motoo
Tange (Tsukuba University).
The problem asking "Which knot yields a lens space by Dehn surgery" is
called "lens space surgery". Berge's list ('90) is believed to be the
complete list, but it is still unproved, even after some progress by
Heegaard Floer Homology.
This problem seems to enter a new aspect: study using 4-manifolds, lens
space surgery from lens spaces, checking hyperbolicity by computer.
In the talk, we review the structure of Berge's list and talk on our
study on pairs of distinct knots but yield same lens spaces, and
4-maniolds constructed from such pairs. This is joint work with Motoo
Tange (Tsukuba University).
2015/12/07
Tokyo Probability Seminar
16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)
Jean-Dominique Deuschel (TU Berlin)
Quenched invariance principle for random walks in time-dependent balanced random environment
Jean-Dominique Deuschel (TU Berlin)
Quenched invariance principle for random walks in time-dependent balanced random environment
[ Abstract ]
We prove an almost sure functional limit theorem for a random walk in an space-time ergodic balanced environment under certain moment conditions. The proof is based on the maximal principle for parabolic difference operators. We also deal with the non-elliptic case, where the corresponding limiting diffusion matrix can be random in higher dimensions. This is a joint work with N. Berger, X. Guo and A. Ramirez.
We prove an almost sure functional limit theorem for a random walk in an space-time ergodic balanced environment under certain moment conditions. The proof is based on the maximal principle for parabolic difference operators. We also deal with the non-elliptic case, where the corresponding limiting diffusion matrix can be random in higher dimensions. This is a joint work with N. Berger, X. Guo and A. Ramirez.
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Tatsuki Hayama (Senshu Univ.)
Cycle connectivity and pseudoconcavity of flag domains (Japanese)
Tatsuki Hayama (Senshu Univ.)
Cycle connectivity and pseudoconcavity of flag domains (Japanese)
[ Abstract ]
We consider an open real group orbit in a complex flag variety which has no non-constant function. We introduce Huckleberry's results on cycle connectivity and show that it is pseudoconcave if it satisfies a certain condition on the root system of the Lie algebra. In Hodge theory, we are mainly interested in the case where it is a Mumford-Tate domain. We also discuss Hodge theoretical meanings of this work.
We consider an open real group orbit in a complex flag variety which has no non-constant function. We introduce Huckleberry's results on cycle connectivity and show that it is pseudoconcave if it satisfies a certain condition on the root system of the Lie algebra. In Hodge theory, we are mainly interested in the case where it is a Mumford-Tate domain. We also discuss Hodge theoretical meanings of this work.
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Alexey Bondal (IPMU)
Flops and spherical functors (English)
Alexey Bondal (IPMU)
Flops and spherical functors (English)
[ Abstract ]
I will describe various functors on derived categories of coherent sheaves
related to flops and relations between these functors. A categorical
version of deformation theory of systems of objects in abelian categories
will be outlined and its relation to flop spherical functors will be
presented.
I will describe various functors on derived categories of coherent sheaves
related to flops and relations between these functors. A categorical
version of deformation theory of systems of objects in abelian categories
will be outlined and its relation to flop spherical functors will be
presented.
2015/12/04
Colloquium
16:50-17:50 Room #123 (Graduate School of Math. Sci. Bldg.)
Makiko Sasada (Graduate School of Mathematical Sciences, University of Tokyo)
Exact forms and closed forms on some infinite product spaces appearing in the study of probability theory
(JAPANESE)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/teacher/sasada.html
Makiko Sasada (Graduate School of Mathematical Sciences, University of Tokyo)
Exact forms and closed forms on some infinite product spaces appearing in the study of probability theory
(JAPANESE)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/teacher/sasada.html
Geometry Colloquium
10:00-11:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Yoshihiro Takeyama (Graduate School of Pure and Applied Sciences, University of Tsukuba)
The q-Boson system and a deformation of the affine Hecke algebra (Japanese)
Yoshihiro Takeyama (Graduate School of Pure and Applied Sciences, University of Tsukuba)
The q-Boson system and a deformation of the affine Hecke algebra (Japanese)
[ Abstract ]
The q-Boson system due to Sasamoto and Wadati is a one-dimensional "integrable" stochastic particle model. Its Q-matrix is constructed in the framework of the quantum inverse scattering method and we obtain the eigenvectors by means of the algebraic Bethe ansatz method. Recently it is found that the q-Boson model can be derived also from a representation of a deformation of the affine Hecke algebra and its representation. In this formulation we get the eigenvectors of the transpose of the Q-matrix which were constructed by the technique called the coordinate Bethe ansatz. In this talk I review the above results and discuss the relationship between the two methods.
The q-Boson system due to Sasamoto and Wadati is a one-dimensional "integrable" stochastic particle model. Its Q-matrix is constructed in the framework of the quantum inverse scattering method and we obtain the eigenvectors by means of the algebraic Bethe ansatz method. Recently it is found that the q-Boson model can be derived also from a representation of a deformation of the affine Hecke algebra and its representation. In this formulation we get the eigenvectors of the transpose of the Q-matrix which were constructed by the technique called the coordinate Bethe ansatz. In this talk I review the above results and discuss the relationship between the two methods.
2015/12/03
Seminar on Probability and Statistics
16:40-18:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Arnak Dalalyan (ENSAE ParisTech)
Learning theory and sparsity ～ Sparsity and low rank matrix learning ～
Arnak Dalalyan (ENSAE ParisTech)
Learning theory and sparsity ～ Sparsity and low rank matrix learning ～
[ Abstract ]
In this third lecture, we will present extensions of the previously introduced sparse recovery techniques to the problems of machine learning and statistics in which a large matrix should be learned from data. The analogue of the sparsity, in this context, is the low-rankness of the matrix. We will show that such matrices can be effectively learned by minimizing the empirical risk penalized by the nuclear norm. The resulting problem is a problem of semi-definite programming and can be solved efficiently even when the dimension is large. Theoretical guarantees for this method will be established in the case of matrix completion with known sampling distribution.
In this third lecture, we will present extensions of the previously introduced sparse recovery techniques to the problems of machine learning and statistics in which a large matrix should be learned from data. The analogue of the sparsity, in this context, is the low-rankness of the matrix. We will show that such matrices can be effectively learned by minimizing the empirical risk penalized by the nuclear norm. The resulting problem is a problem of semi-definite programming and can be solved efficiently even when the dimension is large. Theoretical guarantees for this method will be established in the case of matrix completion with known sampling distribution.
FMSP Lectures
16:40-18:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Arnak Dalalyan (ENSAE ParisTech)
(3)Sparsity and low rank matrix learning. (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dalalyan.pdf
Arnak Dalalyan (ENSAE ParisTech)
(3)Sparsity and low rank matrix learning. (ENGLISH)
[ Abstract ]
In this third lecture, we will present extensions of the previously introduced sparse recovery techniques to the problems of machine learning and statistics in which a large matrix should be learned from data. The analogue of the sparsity, in this context, is the low-rankness of the matrix. We will show that such matrices can be effectively learned by minimizing the empirical risk penalized by the nuclear norm. The resulting problem is a problem of semi-definite programming and can be solved efficiently even when the dimension is large. Theoretical guarantees for this method will be established in the case of matrix completion with known sampling distribution.
[ Reference URL ]In this third lecture, we will present extensions of the previously introduced sparse recovery techniques to the problems of machine learning and statistics in which a large matrix should be learned from data. The analogue of the sparsity, in this context, is the low-rankness of the matrix. We will show that such matrices can be effectively learned by minimizing the empirical risk penalized by the nuclear norm. The resulting problem is a problem of semi-definite programming and can be solved efficiently even when the dimension is large. Theoretical guarantees for this method will be established in the case of matrix completion with known sampling distribution.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dalalyan.pdf
2015/12/02
Operator Algebra Seminars
16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)
Makoto Yamashita (Ochanomizu Univ.)
Drinfeld center and representation theory for monoidal categories
Makoto Yamashita (Ochanomizu Univ.)
Drinfeld center and representation theory for monoidal categories
Seminar on Probability and Statistics
14:55-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Arnak Dalalyan (ENSAE ParisTech)
Learning theory and sparsity ～ Lasso, Dantzig selector and their statistical properties ～
Arnak Dalalyan (ENSAE ParisTech)
Learning theory and sparsity ～ Lasso, Dantzig selector and their statistical properties ～
[ Abstract ]
In this second lecture, we will focus on the problem of high dimensional linear regression under the sparsity assumption and discuss the three main statistical problems: denoising, prediction and model selection. We will prove that convex programming based predictors such as the lasso and the Dantzig selector are provably consistent as soon as the dictionary elements are normalized and an appropriate upper bound on the noise-level is available. We will also show that under additional assumptions on the dictionary elements, the aforementioned methods are rate-optimal and model-selection consistent.
In this second lecture, we will focus on the problem of high dimensional linear regression under the sparsity assumption and discuss the three main statistical problems: denoising, prediction and model selection. We will prove that convex programming based predictors such as the lasso and the Dantzig selector are provably consistent as soon as the dictionary elements are normalized and an appropriate upper bound on the noise-level is available. We will also show that under additional assumptions on the dictionary elements, the aforementioned methods are rate-optimal and model-selection consistent.
FMSP Lectures
14:55-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Arnak Dalalyan (ENSAE ParisTech)
(2)Lasso, Dantzig selector and their statistical properties. (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dalalyan.pdf
Arnak Dalalyan (ENSAE ParisTech)
(2)Lasso, Dantzig selector and their statistical properties. (ENGLISH)
[ Abstract ]
In this second lecture, we will focus on the problem of high dimensional linear regression under the sparsity assumption and discuss the three main statistical problems: denoising, prediction and model selection. We will prove that convex programming based predictors such as the lasso and the Dantzig selector are provably consistent as soon as the dictionary elements are normalized and an appropriate upper bound on the noise-level is available. We will also show that under additional assumptions on the dictionary elements, the aforementioned methods are rate-optimal and model-selection consistent.
[ Reference URL ]In this second lecture, we will focus on the problem of high dimensional linear regression under the sparsity assumption and discuss the three main statistical problems: denoising, prediction and model selection. We will prove that convex programming based predictors such as the lasso and the Dantzig selector are provably consistent as soon as the dictionary elements are normalized and an appropriate upper bound on the noise-level is available. We will also show that under additional assumptions on the dictionary elements, the aforementioned methods are rate-optimal and model-selection consistent.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dalalyan.pdf
Mathematical Biology Seminar
14:55-16:40 Room #128 (Graduate School of Math. Sci. Bldg.)
Kenta Yajima ( The Graduate University for Advanced Studies (Sokendai), School of Advanced Sciences)
Network centrality measure based on sensitivity analysis of the basic reproductive ratio
[ Reference URL ]
http://www.soken.ac.jp/
Kenta Yajima ( The Graduate University for Advanced Studies (Sokendai), School of Advanced Sciences)
Network centrality measure based on sensitivity analysis of the basic reproductive ratio
[ Reference URL ]
http://www.soken.ac.jp/
2015/12/01
Tuesday Seminar of Analysis
16:50-18:20 Room #126 (Graduate School of Math. Sci. Bldg.)
Stéphane Malek (Université de Lille, France)
On complex singularity analysis for some linear partial differential equations
Stéphane Malek (Université de Lille, France)
On complex singularity analysis for some linear partial differential equations
[ Abstract ]
We investigate the existence of local holomorphic solutions Y of linear partial differential equations in three complex variables whose coefficients are holomorphic on some polydisc outside some singular set S. The coefficients are written as linear combinations of powers of a solution X of some first order nonlinear partial differential equation following an idea :we have initiated in a previous joint work with C. Stenger. The solutions Y are shown to develop singularities along the singular set S with estimates of exponential type depending on the growth's rate of X near the singular set. We construct these solutions with the help of series of functions with infinitely many variables which involve derivatives of all orders of X in one variable. Convergence and bounds estimates of these series are studied using a majorant series method which leads to an auxiliary functional equation that contains differential operators in infinitely many variables. Using a fixed point argument, we show that these functional equations actually have solutions in some Banach spaces of formal power series. (Joint work with A. Lastra and C. Stenger).
We investigate the existence of local holomorphic solutions Y of linear partial differential equations in three complex variables whose coefficients are holomorphic on some polydisc outside some singular set S. The coefficients are written as linear combinations of powers of a solution X of some first order nonlinear partial differential equation following an idea :we have initiated in a previous joint work with C. Stenger. The solutions Y are shown to develop singularities along the singular set S with estimates of exponential type depending on the growth's rate of X near the singular set. We construct these solutions with the help of series of functions with infinitely many variables which involve derivatives of all orders of X in one variable. Convergence and bounds estimates of these series are studied using a majorant series method which leads to an auxiliary functional equation that contains differential operators in infinitely many variables. Using a fixed point argument, we show that these functional equations actually have solutions in some Banach spaces of formal power series. (Joint work with A. Lastra and C. Stenger).
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Takayuki Okuda (The University of Tokyo)
Monodromies of splitting families for singular fibers (JAPANESE)
Takayuki Okuda (The University of Tokyo)
Monodromies of splitting families for singular fibers (JAPANESE)
[ Abstract ]
A degeneration of Riemann surfaces is a family of complex curves
over a disk allowed to have a singular fiber.
A singular fiber may split into several simpler singular fibers
under a deformation family of such families,
which is called a splitting family for the singular fiber.
We are interested in the topology of splitting families.
For the topological types of degenerations of Riemann surfaces,
it is known that there is a good relationship with
the surface mapping classes, via topological monodromy.
In this talk,
we introduce the "topological monodromies of splitting families",
and give a description of those of certain splitting families.
A degeneration of Riemann surfaces is a family of complex curves
over a disk allowed to have a singular fiber.
A singular fiber may split into several simpler singular fibers
under a deformation family of such families,
which is called a splitting family for the singular fiber.
We are interested in the topology of splitting families.
For the topological types of degenerations of Riemann surfaces,
it is known that there is a good relationship with
the surface mapping classes, via topological monodromy.
In this talk,
we introduce the "topological monodromies of splitting families",
and give a description of those of certain splitting families.
2015/11/30
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Jean-Pierre Demailly (Univ. de Grenoble I)
Extension of holomorphic functions defined on non reduced analytic subvarieties (English)
Jean-Pierre Demailly (Univ. de Grenoble I)
Extension of holomorphic functions defined on non reduced analytic subvarieties (English)
[ Abstract ]
The goal of this talk will be to discuss $L^2$ extension properties of holomorphic sections of vector bundles satisfying weak semi-positivity properties. Using techniques borrowed from recent proofs of the Ohsawa-Takegoshi extension theorem, we obtain several new surjectivity results for the restriction morphism to a non necessarily reduced subvariety, provided the latter is defined as the zero variety of a multiplier ideal sheaf. These extension results are derived from $L^2$ approximation techniques, and they hold under (probably) optimal curvature conditions.
The goal of this talk will be to discuss $L^2$ extension properties of holomorphic sections of vector bundles satisfying weak semi-positivity properties. Using techniques borrowed from recent proofs of the Ohsawa-Takegoshi extension theorem, we obtain several new surjectivity results for the restriction morphism to a non necessarily reduced subvariety, provided the latter is defined as the zero variety of a multiplier ideal sheaf. These extension results are derived from $L^2$ approximation techniques, and they hold under (probably) optimal curvature conditions.
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Fabrizio Catanese (Universität Bayreuth)
Interesting surfaces which are coverings of a rational surface branched over few lines (English)
Fabrizio Catanese (Universität Bayreuth)
Interesting surfaces which are coverings of a rational surface branched over few lines (English)
[ Abstract ]
Surfaces which are covers of the plane branched over 5 or 6 lines have provided answers to long standing questions, for instance the BCD surfaces for Fujita's question on semiampleness of VHS (Dettweiler-Cat); and examples of ball quotients (Hirzebruch), automorphisms acting trivially on integral cohomology (Cat-Gromadtzki), canonical maps with high degree or image-degree (Pardini, Bauer-Cat). I shall speak especially about the above Abelian coverings of the plane, the geometry of the del Pezzo surface of degree 5, the rigidity of BCD surfaces, and a criterion for a fibred surface to be a projective classifying space.
Surfaces which are covers of the plane branched over 5 or 6 lines have provided answers to long standing questions, for instance the BCD surfaces for Fujita's question on semiampleness of VHS (Dettweiler-Cat); and examples of ball quotients (Hirzebruch), automorphisms acting trivially on integral cohomology (Cat-Gromadtzki), canonical maps with high degree or image-degree (Pardini, Bauer-Cat). I shall speak especially about the above Abelian coverings of the plane, the geometry of the del Pezzo surface of degree 5, the rigidity of BCD surfaces, and a criterion for a fibred surface to be a projective classifying space.
Tokyo Probability Seminar
16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)
Raoul Normand (Institute of Mathematics, Academia Sinica)
Self-organized criticality in a discrete model of limited aggregation
Raoul Normand (Institute of Mathematics, Academia Sinica)
Self-organized criticality in a discrete model of limited aggregation
[ Abstract ]
We consider a discrete model of coagulation, where a large number of particles are initially given a prescribed number of arms. We successively choose arms uniformly at random and bind them two by two, unless they belong to "large" clusters. In that sense, the large clusters are frozen and become inactive. We study the graph structure obtained, and describe what a typical cluster looks like. We show that there is a fixed time T such that, before time T, a typical cluster is a subcritical Galton-Watson tree, whereas after time T, a typical cluster is a critical Galton-Watson tree. In that sense, we observe a phenomenon called self-organized criticality.
We consider a discrete model of coagulation, where a large number of particles are initially given a prescribed number of arms. We successively choose arms uniformly at random and bind them two by two, unless they belong to "large" clusters. In that sense, the large clusters are frozen and become inactive. We study the graph structure obtained, and describe what a typical cluster looks like. We show that there is a fixed time T such that, before time T, a typical cluster is a subcritical Galton-Watson tree, whereas after time T, a typical cluster is a critical Galton-Watson tree. In that sense, we observe a phenomenon called self-organized criticality.
2015/11/27
Colloquium
16:50-17:50 Room #056 (Graduate School of Math. Sci. Bldg.)
Yoshikata Kida (Graduate School of Mathematical Sciences, University of Tokyo)
Recent development in amenable groups (JAPANESE)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kida/
Yoshikata Kida (Graduate School of Mathematical Sciences, University of Tokyo)
Recent development in amenable groups (JAPANESE)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kida/
Geometry Colloquium
10:00-11:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Hisamoto Tomoyuki (Nagoya University)
The strong version of K-stability derived from the coercivity property of the K-energy (Japanese)
Hisamoto Tomoyuki (Nagoya University)
The strong version of K-stability derived from the coercivity property of the K-energy (Japanese)
[ Abstract ]
This is a joint work with S. Boucksom and M. Jonsson. We introduced the notion of J-uniform K-stability in relation to the coercivity property of the K-energy. As a result, one can see that any Kähler-Einstein
manifolds with no non-zero holomorphic vector field is J-uniformly K-stable.
This is a joint work with S. Boucksom and M. Jonsson. We introduced the notion of J-uniform K-stability in relation to the coercivity property of the K-energy. As a result, one can see that any Kähler-Einstein
manifolds with no non-zero holomorphic vector field is J-uniformly K-stable.
2015/11/26
Lie Groups and Representation Theory
17:00-18:45 Room # (Graduate School of Math. Sci. Bldg.)
Birgit Speh (Cornell University)
Introduction to the cohomology of discrete groups and modular symbols 2 (English)
Birgit Speh (Cornell University)
Introduction to the cohomology of discrete groups and modular symbols 2 (English)
[ Abstract ]
The course is an introduction to the cohomology of torsion free discrete subgroups $\Gamma \subset G $ of a semi simple group $G$. The discrete group $\Gamma$ acts freely on the symmetric space $X= G/K$ and we will always assume that $\Gamma \backslash G/K$ is compact or has finite volume. An example is a torsion free subgroup $\Gamma_n $ of finite index n in Sl(2,Z) acting on $Sl(2.R)/SO(2) \simeq {\mathcal H}=\{z=x+iy \in C| y >0 \}$ by fractional linear transformations. $\Gamma_n \backslash {\mathcal H}$ can be determined explicitly and it can be visualized as an area in the upper half plane glued at the boundary. It is easy to see that it has some nice compactifications.
The cohomology $H^*(\Gamma, C)$ of the group $\Gamma$ is equal to the deRham cohomology $H^*_{deRham}(\Gamma \backslash X, C)$ of the manifold $\Gamma\backslash X$. This cohomology is studied by proving that it is isomorphic to the $H^*(g,K,{\mathcal A}(\Gamma \backslash G))$. Here ${\mathcal A}(\Gamma \backslash G)$ of automorphic functions on $\Gamma \backslash G$. In the case $\Gamma_n \subset Sl(2,Z)$ the space ${\mathcal A}(\Gamma \backslash G)$ is the space of classical automorphic functions on the upper half plane containing holomorphic cusp form, Eisenstein series, Maass forms and it is often introduced in an introductory course in analytic number theory.
On the geometric side we will construct some of the cycles (modular symbols) in the homology $H_*(\Gamma\backslash X)$ which are dual to the cohomology classes we constructed. In our example $\Gamma_n\backslash Sl(2,R)/SO(2)$ these cycles correspond to geodesics and can easily be visualized.
In this course I will explain these results and show how to use them to prove vanishing and non vanishing theorem for $H^*_{deRham}(\Gamma \backslash X)$. I will state the results in full generality, but I will prove them only in the classical case: G=SL$(2,R)$ and the subgroup $\Gamma= \Gamma_n$ a congruence subgroup. Some familiarity with Lie groups and Lie algebras is only prerequisite for the course.
The course is an introduction to the cohomology of torsion free discrete subgroups $\Gamma \subset G $ of a semi simple group $G$. The discrete group $\Gamma$ acts freely on the symmetric space $X= G/K$ and we will always assume that $\Gamma \backslash G/K$ is compact or has finite volume. An example is a torsion free subgroup $\Gamma_n $ of finite index n in Sl(2,Z) acting on $Sl(2.R)/SO(2) \simeq {\mathcal H}=\{z=x+iy \in C| y >0 \}$ by fractional linear transformations. $\Gamma_n \backslash {\mathcal H}$ can be determined explicitly and it can be visualized as an area in the upper half plane glued at the boundary. It is easy to see that it has some nice compactifications.
The cohomology $H^*(\Gamma, C)$ of the group $\Gamma$ is equal to the deRham cohomology $H^*_{deRham}(\Gamma \backslash X, C)$ of the manifold $\Gamma\backslash X$. This cohomology is studied by proving that it is isomorphic to the $H^*(g,K,{\mathcal A}(\Gamma \backslash G))$. Here ${\mathcal A}(\Gamma \backslash G)$ of automorphic functions on $\Gamma \backslash G$. In the case $\Gamma_n \subset Sl(2,Z)$ the space ${\mathcal A}(\Gamma \backslash G)$ is the space of classical automorphic functions on the upper half plane containing holomorphic cusp form, Eisenstein series, Maass forms and it is often introduced in an introductory course in analytic number theory.
On the geometric side we will construct some of the cycles (modular symbols) in the homology $H_*(\Gamma\backslash X)$ which are dual to the cohomology classes we constructed. In our example $\Gamma_n\backslash Sl(2,R)/SO(2)$ these cycles correspond to geodesics and can easily be visualized.
In this course I will explain these results and show how to use them to prove vanishing and non vanishing theorem for $H^*_{deRham}(\Gamma \backslash X)$. I will state the results in full generality, but I will prove them only in the classical case: G=SL$(2,R)$ and the subgroup $\Gamma= \Gamma_n$ a congruence subgroup. Some familiarity with Lie groups and Lie algebras is only prerequisite for the course.
2015/11/25
Operator Algebra Seminars
16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)
Max Lein (AIMR, Tohoku Univ.)
Combining Pseudodifferential and Vector Bundle Techniques, and Their Applications to Topological Insulators
Max Lein (AIMR, Tohoku Univ.)
Combining Pseudodifferential and Vector Bundle Techniques, and Their Applications to Topological Insulators
Seminar on Probability and Statistics
14:55-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Arnak Dalalyan (ENSAE ParisTech)
Learning theory and sparsity ～ Introduction into sparse recovery and compressed sensing ～
Arnak Dalalyan (ENSAE ParisTech)
Learning theory and sparsity ～ Introduction into sparse recovery and compressed sensing ～
[ Abstract ]
In this introductory lecture, we will present the general framework of high-dimensional statistical modeling and its applications in machine learning and signal processing. Basic methods of sparse recovery, such as the hard and the soft thresholding, will be introduced in the context of orthonormal dictionaries and their statistical accuracy will be discussed in detail. We will also show the relation of these methods with compressed sensing and convex programming based procedures.
In this introductory lecture, we will present the general framework of high-dimensional statistical modeling and its applications in machine learning and signal processing. Basic methods of sparse recovery, such as the hard and the soft thresholding, will be introduced in the context of orthonormal dictionaries and their statistical accuracy will be discussed in detail. We will also show the relation of these methods with compressed sensing and convex programming based procedures.
FMSP Lectures
14:55-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Arnak Dalalyan (ENSAE ParisTech)
(1)Introduction into sparse recovery and compressed sensing. (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dalalyan.pdf
Arnak Dalalyan (ENSAE ParisTech)
(1)Introduction into sparse recovery and compressed sensing. (ENGLISH)
[ Abstract ]
In this introductory lecture, we will present the general framework of high-dimensional statistical modeling and its applications in machine learning and signal processing. Basic methods of sparse recovery, such as the hard and the soft thresholding, will be introduced in the context of orthonormal dictionaries and their statistical accuracy will be discussed in detail. We will also show the relation of these methods with compressed sensing and convex programming based procedures.
[ Reference URL ]In this introductory lecture, we will present the general framework of high-dimensional statistical modeling and its applications in machine learning and signal processing. Basic methods of sparse recovery, such as the hard and the soft thresholding, will be introduced in the context of orthonormal dictionaries and their statistical accuracy will be discussed in detail. We will also show the relation of these methods with compressed sensing and convex programming based procedures.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dalalyan.pdf
2015/11/24
Tuesday Seminar of Analysis
16:50-18:20 Room #126 (Graduate School of Math. Sci. Bldg.)
Pen-Yuan Hsu (Graduate School of Mathematical Sciences, the University of Tokyo)
A local analysis of the swirling flow to the axi-symmetric Navier-Stokes equations near a saddle point and no-slip flat boundary (English)
Pen-Yuan Hsu (Graduate School of Mathematical Sciences, the University of Tokyo)
A local analysis of the swirling flow to the axi-symmetric Navier-Stokes equations near a saddle point and no-slip flat boundary (English)
[ Abstract ]
As one of the violent flow, tornadoes occur in many place of the world. In order to reduce human losses and material damage caused by tornadoes, there are many research methods. One of the effective methods is numerical simulations. The swirling structure is significant both in mathematical analysis and the numerical simulations of tornado. In this joint work with H. Notsu and T. Yoneda we try to clarify the swirling structure. More precisely, we do numerical computations on axi-symmetric Navier-Stokes flows with no-slip flat boundary. We compare a hyperbolic flow with swirl and one without swirl and observe that the following phenomenons occur only in the swirl case: The distance between the point providing the maximum velocity magnitude $|v|$ and the $z$-axis is drastically changing around some time (which we call it turning point). An ``increasing velocity phenomenon'' occurs near the boundary and the maximum value of $|v|$ is obtained near the axis of symmetry and the boundary when time is close to the turning point.
As one of the violent flow, tornadoes occur in many place of the world. In order to reduce human losses and material damage caused by tornadoes, there are many research methods. One of the effective methods is numerical simulations. The swirling structure is significant both in mathematical analysis and the numerical simulations of tornado. In this joint work with H. Notsu and T. Yoneda we try to clarify the swirling structure. More precisely, we do numerical computations on axi-symmetric Navier-Stokes flows with no-slip flat boundary. We compare a hyperbolic flow with swirl and one without swirl and observe that the following phenomenons occur only in the swirl case: The distance between the point providing the maximum velocity magnitude $|v|$ and the $z$-axis is drastically changing around some time (which we call it turning point). An ``increasing velocity phenomenon'' occurs near the boundary and the maximum value of $|v|$ is obtained near the axis of symmetry and the boundary when time is close to the turning point.
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