MATH

Europe/Rome 2019-09-19 14:30:00 2019-09-19 15:30:00 Analysis Seminar: On the Strichartz inequalities for the Schroedinger equation Abstract: In this talk we will discuss some mixed Lp estimates obtained by Robert Strichartz in 1977 for a large class of dispersive PDEs, restricting our attention to the special case of the Schroedinger equation. Starting with simple facts about the Fourier transform, we will show how Harmonic Analysis can be applied in order to obtain a complete proof of these estimates. It is worth to mention that such estimates also have strong connections with the theory of restriction estimates for Fourier transform, and we could see the main result of this talk as the base for the companion talk of Mateus Sousa (about sharp restriction estimates for the Fourier transform). ICTP ICTP pio@ictp.it 19 Sep 2019

Europe/Rome 2019-09-19 15:30:00 2019-09-19 16:30:00 Analysis Seminar: On sharp Strichartz inequalities Abstract: In this follow-up talk we will discuss a little bit about the concept of sharp inequalities with a focus on the particular case of Strichartz inequalities. We will discuss questions related to sharp constants, existence of extremizers and characterization of extremizers. ICTP ICTP pio@ictp.it 19 Sep 2019

Europe/Rome 2019-09-16 08:00:00 2019-09-20 22:00:00 School and Workshop on Mixing and Control | (smr 3324) This activity is part of a two-week event consisting of Week 1: School and Workshop on Mixing and Control (16 - 20 September) Week 2: School and Workshop on Random Matrix Theory and Point Processes                 (23 - 27 September) To participate in both activities you need to submit two distinct applications. Week 1:  Please click on the link "Apply here" on the left hand-side column Week 2:  Please apply at: http://indico.ictp.it/event/8900/   DEADLINE for requesting participation for both weeks:  15 MAY 2019 ========================================================== Organizers: A. Agrachev, SISSA, Trieste A. Bufetov, Marseille & Steklov Institute T. Grava, SISSA & Bristol A. Guionnet, ENS Lyon S. Kuksin, Paris & Shandong University Local Organizer: S. Luzzatto, ICTP, Trieste The topics to be discussed at the activity are at the forefront of current research in Random Matrix Theory, Point Processes, Dynamical Systems and Control Theory. One of the main goals of the School and Workshop is to bring this material to both established and young mathematicians from all developing countries. Mini courses will be given as well as more advanced reserach seminars. The activity will be organized as two thematic weeks on interrelated topics. Each week will consist of one or two mini courses and some seminar speakers. Week 1: Mixing and Control Mixing and control central topic is the study, with the help of the mathematical control theory, of ergodic and mixing properties of dynamical systems stochastically perturbed by a very degenerate noise. This concerns the systems governed by nonlinear PDEs and ODEs. We also plan to discuss mathematical aspects of the non-equilibrium statistical physics and some other topics. Week 2: Random Matrix Theory and Point Processes The second week will focus on point processes arising in the study of random matrices such as determinantal point processes. These point processes satisfy the Kolmogorov 0-1 Law and the Central Limit Theorem of Soshnikov, are rigid in the sense of Ghosh and Peres and obey an analogue of the De Finetti Theorem. Palm-Khintchine theory for our point processs will be emphasized, as well as the connection with the theory of integrable systems. Numerous open problems will be discussed, in particular, those related to pfaffian point processes. Topics: Point process; Random matrices; Integrable probability; Integrable systems; Mixing; Stationary measure; Markov systems; Nonholonomic constraints; Controllability; Lecturers: A. Agrachev, SISSA, Trieste A. Bufetov, Marseille & Steklov Institute A. Guionnet, ENS Lyon S. Kuksin, Paris & Shandong University Speakers: F. Augeri, Weizmann, Israel F. Baudoin, Purdue Univ. C. Bordenave, Toulose, France U. Boscain, CNRS, Sorbonne Univ. A. Bufetov, MIT M. Cafasso, Angers, France *I. Corwin, Columbia University N. Cuneo, University Paris-Diderot A. de Bouard, Ecole Polytechnique A. Debussche, ENS Rennes A. Dymov, Steklov Insitute, Moscow J-P. Eckmann, University of Geneva *L. Erdoes, Wien, Austria N. Glatt-Holtz, Tulane University H. Guan, Tsinghua University V. Jaksitch, McGill University I. Krasovsky, Imperial College M. Krishnapur, Bangalore, India *A. Kupiainen, University of Helsinki K. Mc Laughlin, Colorado State University V. Nersesyan, University of Versailles P. Nikitin, Steklov, St. Petersburg G. Olshanski, ITP, RAS, Russia S. Peche, LPSM, Paris, France Y. Qiu, CNRS, France A. Ramirez, Pontificia Universidad Catolica de Chile R. Raquepas, University Grenoble Alpes (Institut Fourier) T. Sasamoto, Chiba, Japan M. Shcherbina, Kharkov, Ukraina A. Shirikyan, Cergy-Pontoise N. Tzvetkov, University of Cergy Pontoise A. Veselov, Loughbourogh University *H-T. Yau, Harvard * to be confirmed ICTP ICTP pio@ictp.it 16 Sep 2019 - 20 Sep 2019

Europe/Rome 2019-09-23 08:00:00 2019-09-27 22:00:00 School and Workshop on Random Matrix Theory and Point Processes | (smr 3382) This activity is part of a two-week event consisting of Week 1: School and Workshop on Mixing and Control (16 - 20 September) Week 2: School and Workshop on Random Matrix Theory and Point Processes (23 - 27 September) To participate in both activities you need to submit two distinct applications. Week 1:  Please apply at:  http://indico.ictp.it/event/8720/ Week 2:  Please click on the link "Apply here" on the left hand-side column   DEADLINE for requesting participation for both weeks:  15 MAY 2019 ======================================================= Organizers: A. Agrachev, SISSA, Trieste A. Bufetov, Marseille & Steklov Institute T. Grava, SISSA & Bristol A. Guionnet, ENS Lyon S. Kuksin, Paris & Shandong University Local Organizer: S. Luzzatto, ICTP, Trieste The topics to be discussed at the activity are at the forefront of current research in Random Matrix Theory, Point Processes, Dynamical Systems and Control Theory. One of the main goals of the School and Workshop is to bring this material to both established and young mathematicians from all developing countries. Mini courses will be given as well as more advanced reserach seminars. The activity will be organized as two thematic weeks on interrelated topics. Each week will consist of one or two mini courses and some seminar speakers. Week 1: Mixing and Control Mixing and control central topic is the study, with the help of the mathematical control theory, of ergodic and mixing properties of dynamical systems stochastically perturbed by a very degenerate noise. This concerns the systems governed by nonlinear PDEs and ODEs. We also plan to discuss mathematical aspects of the non-equilibrium statistical physics and some other topics. Week 2: Random Matrix Theory and Point Processes The second week will focus on point processes arising in the study of random matrices such as determinantal point processes. These point processes satisfy the Kolmogorov 0-1 Law and the Central Limit Theorem of Soshnikov, are rigid in the sense of Ghosh and Peres and obey an analogue of the De Finetti Theorem. Palm-Khintchine theory for our point processs will be emphasized, as well as the connection with the theory of integrable systems. Numerous open problems will be discussed, in particular, those related to pfaffian point processes. Topics: Point process; Random matrices; Integrable probability; Integrable systems; Mixing; Stationary measure; Markov systems; Nonholonomic constraints; Controllability. Lecturers: A. Agrachev, SISSA, Trieste A. Bufetov, Marseille & Steklov Institute A. Guionnet, ENS Lyon S. Kuksin, Paris & Shandong University Speakers: F. Augeri, Weizmann, Israel F. Baudoin, Purdue Univ. C. Bordenave, Toulose, France U. Boscain, CNRS, Sorbonne Univ. A. Bufetov, MIT M. Cafasso, Angers, France *I. Corwin, Columbia University N. Cuneo, University Paris-Diderot A. de Bouard, Ecole Polytechnique A. Debussche, ENS Rennes A. Dymov, Steklov Insitute, Moscow J-P. Eckmann, University of Geneva *L. Erdoes, Wien, Austria N. Glatt-Holtz, Tulane University H. Guan, Tsinghua University V. Jaksitch, McGill University I. Krasovsky, Imperial College M. Krishnapur, Bangalore, India *A. Kupiainen, University of Helsinki K. Mc Laughlin, Colorado State University V. Nersesyan, University of Versailles P. Nikitin, Steklov, St. Petersburg G. Olshanski, ITP, RAS, Russia S. Peche, LPSM, Paris, France Y. Qiu, CNRS, France A. Ramirez, Pontificia Universidad Catolica de Chile R. Raquepas, University Grenoble Alpes (Institut Fourier) T. Sasamoto, Chiba, Japan M. Shcherbina, Kharkov, Ukraine A. Shirikyan, Tzvetkov, University of Cergy Pontoise A. Veselov, Loughbourogh University *H-T. Yau, Harvard * to be confirmed PLEASE NOTE:  Additional funds are available for participants based in the US through the National Science Foundation. Please complete and submit the application at the following link in ADDITION to the regular online request for participation to the activity.  https://www.dropbox.com/s/m0ra2m0j2oomz2s/NSF_application.docx?dl=0 ICTP ICTP pio@ictp.it 23 Sep 2019 - 27 Sep 2019

Europe/Rome 2019-09-23 08:00:00 2019-10-04 22:00:00 School on Smooth and Homogeneous Dynamics | (smr 3271) Ergodic theory has its origins in the the work of L. Boltzmann on the kinetic theory of gases. The closely related field of dynamical systems has a much older origin, going back at least to Newtonian mechanics. Both subjects have since flourished into extremely active subjects with connections to many parts of mathematics and the physical sciences. Progress has been especially rapid in the last few years in differentiable dynamics and homogeneous dynamics. Differentiable dynamics studies flows on smooth manifolds and has links with geometry while homogeneous dynamics is the study of subgroup actions on homogeneous spaces of Lie groups and has connections to number theory. It is the aim of this two week workshop to ga ther top experts in these two subjects to deliver expositions on the state of the art in these subjects. The first week will be devoted to differentiable dynamics and the second week to homogeneous dynamics. Special Lectures: Infosys-ICTS Ramanujan lectures - by Elon Lindenstrauss ICTS Distinguished lecture -  by Marcelo Viana. List of invited Speakers Speakers week 1: Alex Blumenthal, Maryland, USA Sylvain Crovisier, Paris Sud Carlangelo Liverani, Rome, Italy Federico Rodriguez-Hertz, Penn State, USA Jana Rodriguez-Hertz, Shenzen, China  Marcelo Viana, IMPA Khadim War, IMPA, Brazil Zhiyuan Zhang, Princeton                                               Speakers week 2: Victor Beresnevich, University of York S. G. Dani, University of Mumbai Manfred Einsiedler, ETH Zurich Alexander Gorodnik, University of Zurich Seonhee Lim, Seoul National University Elon Lindenstrauss, Hebrew University of Jerusalem Jens Marklof, University of Bristol Shahar Mozes, Hebrew University of Jerusalem Amos Nevo, Technion, Haifa Sanju Velani, University of York Barak Weiss, Tel Aviv University Minicourse Lecturers Sylvain Crovisier, Paris Sud, France Stefano Luzzatto, ICTP Both weeks will feature research talks by leading mathematicians as well as mini courses. A number of slots will be available in the program for younger participants to present their research and a poster session will also be organized. A number of slots will be available in the programme for younger participants to present their research and a poster session will also be organized. The program is jointly organised and supported by ICTS and IMPA. Program link: https://www.icts.res.in/program/etds2019 General Information: https://www.icts.res.in/program/Information-for-Participants Bangalore - India ICTP pio@ictp.it 23 Sep 2019 - 4 Oct 2019

Europe/Rome 2019-09-30 08:00:00 2019-10-11 22:00:00 School and Workshop on Gauge Theories and Differential Invariants | (smr 3326) The main focus is on recent developments in gauge theories, both in theoretical physics and in mathematics. This area is very fruitful for active interplays between Mathematics and Physics. In theoretical physics  exact results in supersymmetric quantum field theories and superstrings on curved backgrounds prompted the interest in explicit calculations of (equivariant) Donaldson invariants also in higher rank and the possible definition of new invariants for four manifolds using non-Lagrangian theories. On the mathematical side, new results have been obtained for higher rank Donaldson invariants and Vafa-Witten invariants.  A key role is played by the interplay of with representation theory and quantum integrable systems. These developments are also expected to have impact on enumerative geometry, knot theory and representation theory of infinite dimensional algebras. A key technical tool in these developments is equivariant localization which allows the extraction of exact results. Topics : higher rank Donaldson invariants Vafa-Witten invariants Donaldson-Thomas invariants study of the BPS spectra of (non Lagrangean) N=2 Gauge Theories and new four-dimensional invariants relation to matrix models and topological strings quantum Hitchin systems  and character varieties gauge theories on complex toric surfaces and their instanton moduli spaces surface operators in gauge theory and moduli spaces of principal bundles with parabolic structure quantum cohomology of the instanton moduli space K-theory of quiver varietes quantum integrability, quantum Yang-Baxter equations relations to knot theory and Khovanov Homology higher dimensional supersymmetric gauge theories and M-theory Lecturers: L. GÖTTSCHE, ICTP G. MOORE, Rudgers (tbc) H. NAKAJIMA, Kavli IPMU N. NEKRASOV, Simons Center (tbc) P. PUTROV, ICTP Speakers include: A. DAEMI, Simons Center A. GOLAMPOUR, University of Maryland S. GUKOV, Caltech S. JEONG, Stony Brook A. KLEMM, Universität Bonn M. KOOL, Utrecht University J. MANSCHOT, Trinity College Dublin A. MELLIT, Universität Wien D. OPREA, University of California, San Diego D. PEI, Caltech Z. RUIDONG, Tokyo University A. SHESHMANI, Harvard University Y. TANAKA, Oxford University K. YOSHIOKA, Kobe Unversity ICTP ICTP pio@ictp.it 30 Sep 2019 - 11 Oct 2019