MATH

Europe/Rome 2019-08-22 14:30:00 2019-08-22 15:30:00 Two-fold covering, ergodicity of higher dimensional actions Please see attached abstract ICTP ICTP pio@ictp.it 22 Aug 2019

Europe/Rome 2019-08-27 14:30:00 2019-08-27 15:30:00 B-branes and Anomalous Gauged Linear Sigma Models Abstract: B-branes on Calabi-Yau (CY) X manifolds are in 1-1 correspondence with objects in the derived category of coherent sheaves. B-branes on Gauged Linear Sigma Models (GLSM) can be roughly interpreted as objects of the derived category of a CY stack. This interpretation can be used to generate equivalences between various categories associated to geometric and nongeometric phases of a CY. I will introduce these concepts and present some results for the case when the stack is not CY (physically, this means the GLSM is anomalous), that can be derived from physics. In particular I will explain how the equivalences between categories associated to phases are modified and comment on some consequence on K-theory using as a guide the example of Hirzebruch-Jung resolutions of cyclic surface singularities. IGAP ICTP pio@ictp.it 27 Aug 2019

Europe/Rome 2019-08-30 14:30:00 2019-08-30 17:00:00 Mathematics Seminars 14:30 - 15:30  José Ramón Madrid Padilla (UCLA) Title: Directional maximal function along the primes abstract: In this talk we will discuss the l2-boundedness of the directional maximal operators along primes. Through Fourier Analysis we will make a reduction to study two different situations, in one of them we will appeal to the Bourgain best constant argument and in the other we will use a nice incidence result established recently 15:30 - 16:00 break 16:00 - 17:00 Mariana Smit Vega Garcia (Western Washington University) Title: Free boundary problems Abstract: The study of one of the most renowned examples of free boundary problems, the classical obstacle problem, began in the 60’s with the pioneering works of G. Stampacchia, H. Lewy and J. L. Lions. During the past five decades, it has led to beautiful and deep developments in the calculus of variations and geometric partial differential equations. One of its crowning achievements has been the development, due to L. Caffarelli, of the theory of free boundaries. Nowadays the obstacle problem continues to offer many challenges and its study is as active as ever.  In this talk, I will overview the obstacle problem and describe a few methods used to tackle two fundamental questions: what is the optimal regularity of the solution, and what can be said about the free boundary. This is based on joint works with Mark Allen, Nicola Garofalo & Arshak Petrosyan.   ICTP ICTP pio@ictp.it 30 Aug 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 2019-10-04 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 Aaron Brown, Chicago, USA Sylvain Crovisier, Paris Sud Carlangelo Liverani, Rome, Italy Federico Rodriguez-Hertz, Penn State, USA Jana Rodriguez-Hertz, Shenzen, China Sebastian van Strien, Imperial College, UK        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 2019-09-23 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 2019-09-30 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