FMSP Lectures

Seminar information archive ~05/28Next seminarFuture seminars 05/29~


Seminar information archive

2016/02/17

10:00-11:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Dror Varolin (Stony Brook)
L^2 Extension and its applications: A survey (2) (ENGLISH)
[ Abstract ]
We discuss certain aspects of the theory of L^2 extension, going back to the famous and fundamental work of Ohsawa and Takegoshi, and even further back to work of Donnelly and Fefferman.
The first of three lectures will recall a number of L^2 extension theorems, to some extent following an incomplete history (as I see it), and ending with a sketch of a proof of one of these theorems.
The second lecture will discuss a number of my favorite applications of L^2 extension, from Bergman kernels to deformation invariance of plurigenera.
The third lecture will discuss a new proof of the extension theorem, due to Berndtsson and Lempert. The key tool is a theorem of Berndtsson on the positivity of direct images, which we will review. Berndtsson's theorem permits the introduction of degeneration techniques, whose surprising application to L^2 extension represents one of the most beautiful and fundamental recent breakthroughs in the subject.
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Varolin.pdf

2016/02/16

10:00-11:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Dror Varolin (Stony Brook)
L^2 Extension and its applications: A survey (1) (ENGLISH)
[ Abstract ]
We discuss certain aspects of the theory of L^2 extension, going back to the famous and fundamental work of Ohsawa and Takegoshi, and even further back to work of Donnelly and Fefferman.
The first of three lectures will recall a number of L^2 extension theorems, to some extent following an incomplete history (as I see it), and ending with a sketch of a proof of one of these theorems.
The second lecture will discuss a number of my favorite applications of L^2 extension, from Bergman kernels to deformation invariance of plurigenera.
The third lecture will discuss a new proof of the extension theorem, due to Berndtsson and Lempert. The key tool is a theorem of Berndtsson on the positivity of direct images, which we will review. Berndtsson's theorem permits the introduction of degeneration techniques, whose surprising application to L^2 extension represents one of the most beautiful and fundamental recent breakthroughs in the subject.
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Varolin.pdf

2016/02/16

16:00-17:00   Room #270 (Graduate School of Math. Sci. Bldg.)
Patricia Gaitan (Aix-Marseille University)
Inverse Problem for an Hyperbolic-Parabolic System and Perspectives (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gaitan160216.pdf

2016/02/15

17:00-18:00   Room #118 (Graduate School of Math. Sci. Bldg.)
Patricia Gaitan (Aix-Marseille University)
Probing for inclusions for heat conductive bodies time independent and time dependent cases (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gaitan.pdf

2016/01/22

15:00 -16:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Aurelien Djament (Nantes/CNRS)(by video conference system) and Christine Vespa (Strasbourg) (ENGLISH)
Functor categories and stable homology of groups (8) (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

2016/01/22

16:30-17:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Aurelien Djament (Nantes/CNRS)(by video conference system) and Christine Vespa (Strasbourg)
Functor categories and stable homology of groups (9) (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

2016/01/21

15:00-16:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Aurelien Djament (Nantes/CNRS)(by video conference system) and Christine Vespa (Strasbourg)
Functor categories and stable homology of groups (6) (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

2016/01/21

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Aurelien Djament (Nantes/CNRS)(by video conference system) and Christine Vespa (Strasbourg)
Functor categories and stable homology of groups (7) (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

2016/01/20

16:00-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Aurelien Djament (Nantes/CNRS)(by video conference system) and Christine Vespa (Strasbourg)
Functor categories and stable homology of groups (5) (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

2016/01/19

13:30 -14:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Aurelien Djament (Nantes/CNRS)(by video conference system) and Christine Vespa (Strasbourg)
Functor categories and stable homology of groups (3) (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

2016/01/19

16:30 -18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Aurelien Djament (Nantes/CNRS)(by video conference system) and Christine Vespa (Strasbourg)
Functor categories and stable homology of groups (4) (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

2016/01/18

15:00-16:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Aurelien Djament (Nantes/CNRS)(by video conference system) and Christine Vespa (Strasbourg)
Functor categories and stable homology of groups (1) (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

2016/01/18

16:30-17:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Aurelien Djament (Nantes/CNRS)(by video conference system) and Christine Vespa (Strasbourg)
Functor categories and stable homology of groups (2) (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

2016/01/18

14:00-15:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Samuli Siltanen (University of Helsinki)
Blind deconvolution for human speech signals (ENGLISH)
[ Abstract ]
The structure of vowel sounds in human speech can be divided into two independent components. One of them is the “excitation signal,” which is a kind of buzzing sound created by the vocal folds flapping against each other. The other is the “filtering effect” caused by resonances in the vocal tract, or the confined space formed by the mouth and throat. The Glottal Inverse Filtering (GIF) problem is to (algorithmically) divide a microphone recording of a vowel sound into its two components. This “blind deconvolution” type task is an ill-posed inverse problem. Good-quality GIF filtering is essential for computer-generated speech needed for example by disabled people (think Stephen Hawking). Also, GIF affects the quality of synthetic speech in automatic information announcements and car navigation systems. Accurate estimation of the voice source from recorded speech is known to be difficult with current glottal inverse filtering (GIF) techniques, especially in the case of high-pitch speech of female or child subjects. In order to tackle this problem, the present study uses two different solution methods for GIF: Bayesian inversion and alternating minimization. The first method takes advantage of the Markov chain Monte Carlo (MCMC) modeling in defining the parameters of the vocal tract inverse filter. The filtering results are found to be superior to those achieved by the standard iterative adaptive inverse filtering (IAIF), but the computation is much slower than IAIF. Alternating minimization cuts down the computation time while retaining most of the quality improvement.
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Siltanen.pdf

2016/01/18

14:45-15:25   Room #126 (Graduate School of Math. Sci. Bldg.)
Tapio Helin (University of Helsinki)
Inverse scattering from random potential (ENGLISH)
[ Abstract ]
We consider an inverse scattering problem with a random potential. We assume that our far-field data at multiple angles and all frequencies are generated by a single realization of the potential. From the frequency-correlated data our aim is to demonstrate that one can recover statistical properties of the potential. More precisely, the potential is assumed to be Gaussian with a covariance operator that can be modelled by a classical pseudodifferential operator. Our main result is to show that the principal symbol of this
covariance operator can be determined uniquely. What is important, our method does not require any approximation and we can analyse also the multiple scattering. This is joint work with Matti Lassas and Pedro Caro.
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Helin.pdf

2016/01/18

15:25-16:05   Room #126 (Graduate School of Math. Sci. Bldg.)
Matti Lassas (University of Helsinki)
Geometric Whitney problem: Reconstruction of a manifold from a point cloud (ENGLISH)
[ Abstract ]
We study the geometric Whitney problem on how a Riemannian manifold $(M,g)$ can be constructed to approximate a metric space $(X,d_X)$. This problem is closely related to manifold interpolation (or manifold learning) where a smooth $n$-dimensional surface $S¥subset {¥mathbb R}^m$, $m>n$ needs to be constructed to approximate a point cloud in ${¥mathbb R}^m$. These questions are encountered in differential geometry, machine learning, and in many inverse problems encountered in applications. The determination of a Riemannian manifold includes the construction of its topology, differentiable structure, and metric.

We give constructive solutions to the above problems. Moreover, we characterize the metric spaces that can be approximated, by Riemannian manifolds with bounded geometry: We give sufficient conditions to ensure that a metric space can be approximated, in the Gromov-Hausdorff or quasi-isometric sense, by a Riemannian manifold of a fixed dimension and with bounded diameter, sectional curvature, and injectivity radius. Also, we show that similar conditions, with modified values of parameters, are necessary.

Moreover, we characterise the subsets of Euclidean spaces that can be approximated in the Hausdorff metric by submanifolds of a fixed dimension and with bounded principal curvatures and normal injectivity radius.

The above interpolation problems are also studied for unbounded metric sets and manifolds. The results for Riemannian manifolds are based on a generalisation of the Whitney embedding construction where approximative coordinate charts are embedded in ${¥mathbb R}^m$ and interpolated to a smooth surface. We also give algorithms that solve the problems for finite data.
The results are done in collaboration with C. Fefferman, S. Ivanov, Y. Kurylev, and H. Narayanan.

References:
[1] C. Fefferman, S. Ivanov, Y. Kurylev, M. Lassas, H. Narayanan: Reconstruction and interpolation of manifolds I: The geometric Whitney problem. ArXiv:1508.00674
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Lassas.pdf

2016/01/13

16:00-17:30   Room #122 (Graduate School of Math. Sci. Bldg.)
Yves Dermenjian (Aix-Marseille Universite)
A Carleman estimate for an elliptic operator in a partially anisotropic and discontinuous media (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dermenjian.pdf

2015/12/16

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Yuri Luchko (University of Applied Sciences, Berlin)
Selected topics in fractional partial differential equations (ENGLISH)
[ Abstract ]
In this talk, some remarkable mathematical and physical properties of solutions to the fractional diffusion equation, the alpha-fractional diffusion and alpha-fractional wave equations, the fractional reaction-diffusion equation, and the fractional Schrödinger equation are revisited. From the mathematical viewpoint, the maximum principle for the initial-boundary-value problems for the fractional diffusion equation, the scaling properties of the solutions to the alpha-fractional diffusion and alpha-fractional wave equations and the role of the Mellin integral transform technique for their analytical treatment, as well as the eigenvalue problem for the fractional Schrödinger equation are considered. Physical aspects include a discussion of a probabilistic interpretation of the fundamental solutions to the Cauchy problem for the alpha-fractional diffusion equation, their entropy and the entropy production rates, and some different concepts of the propagation velocities of the fractional wave processes.
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Luchko.pdf

2015/12/03

16:40-18:00   Room #123 (Graduate School of Math. Sci. Bldg.)
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 ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dalalyan.pdf

2015/12/02

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)
[ 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 ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dalalyan.pdf

2015/11/25

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)
[ 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 ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dalalyan.pdf

2015/11/18

15:00-16:00,16:30-17:00   Room #大講義室 (Graduate School of Math. Sci. Bldg.)
Yakov Eliashberg (Stanford University)
Crossroads of symplectic rigidity and flexibility (ENGLISH)
[ Abstract ]
The development of flexible and rigid sides of symplectic and contact topology towards each other shaped this subject since its inception, and continues shaping its modern development.
In the series of lectures I will discuss the history of this struggle, as well as describe recent breakthroughs on the flexible side.
[ Reference URL ]
http://faculty.ms.u-tokyo.ac.jp/Eliashberg201511.html

2015/11/18

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Alfred Ramani (Ecole Polytechnique)
Discretising systematically integrable systems (ENGLISH)
[ Abstract ]
We present various methods for discretising integrable systerms inspired by the works of Hirota and Mickens. We apply these methods to the systematical discretisation of Painlevé equations.
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ramani1118.pdf

2015/11/16

15:00-16:00,16:30-17:00   Room #大講義室 (Graduate School of Math. Sci. Bldg.)
Yakov Eliashberg (Stanford University)
Crossroads of symplectic rigidity and flexibility (ENGLISH)
[ Abstract ]
The development of flexible and rigid sides of symplectic and contact topology towards each other shaped this subject since its inception, and continues shaping its modern development.
In the series of lectures I will discuss the history of this struggle, as well as describe recent breakthroughs on the flexible side.
[ Reference URL ]
http://faculty.ms.u-tokyo.ac.jp/Eliashberg201511.html

2015/11/13

15:00-16:00,16:30-17:30   Room #大講義室 (Graduate School of Math. Sci. Bldg.)
Yakov Eliashberg (Stanford University)
Crossroads of symplectic rigidity and flexibility (ENGLISH)
[ Abstract ]
The development of flexible and rigid sides of symplectic and contact topology towards each other shaped this subject since its inception, and continues shaping its modern development.
In the series of lectures I will discuss the history of this struggle, as well as describe recent breakthroughs on the flexible side.
[ Reference URL ]
http://faculty.ms.u-tokyo.ac.jp/Eliashberg201511.html

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