MATH

Europe/Rome 2020-02-20 16:30:00 2020-02-20 17:30:00 Introduction to stacks Abstract: The goal of this talk is to construct the quotient stack by a smooth group scheme and to see that it is an Artin stack. The talk will be divided into four parts. First, we define the algebraic space over a fixed scheme S. Algebraic spaces are sheaves on the big étale site Sch/S with the representable diagonal morphism and an étale covering. Then, we give the original definition of the stack. Stacks are categories fibered in groupoid over a site for which every covering is of effective descent. We also provide a necessary and sufficient condition for a category fibered in groupoid to be a stack. Third, we define the Artin stack. Artin stacks are stacks over the big étale site Sch/S with the representable diagonal morphism and an smooth covering. Here, algebraic spaces play a role to describe property of morphisms of stacks. Finally, given a smooth group scheme G acting on a scheme X over S, we construct the quotient [X/G] and check that [X/G] satisfies the all conditions to be a stack, moreover an Artin stack. If time allows, we will provide some examples of quotient stacks. SISSA ICTP pio@ictp.it 20 Feb 2020

Europe/Rome 2020-02-26 14:00:00 2020-02-26 15:00:00 Semi-stable laws for wobbly intermittent maps Abstract: A classical problem in probability theory is to understand the behaviour of centred and scaled sums of independent identically distributed (iid) random variables. A well known result in this area is the central limit theorem which loosely states that if X_1, X_2, ... is an iid sequence of mean 0 random variables of finite variance then (1/\sqrt{n}) \sum_{j=1}^{n} X_j will converge in distribution to a Gaussian random variable. Generalisations of the central limit theorem exists for the case that the variance of the X_i is no longer finite, in this case the scaling 1/\sqrt{n} is altered and the limiting distribution may no longer be Gaussian. One may generalise even further and consider all weak limit points of the sequence (1/A_n)(\sum_{j=1}^n X_j). It turns out that under some very mild restrictions all the limit points of this sequence have distribution belonging to the same class - namely they are semi-stable. In this talk we will be interested in what happens when the iid sequence X_1, X_2, ... is replaced by a deterministic one. We will take a particular map T:[0,1] \to [0,1] (a so called wobbly intermittent map) and a function u:[0,1] \to R and replace the sequence X_1, X_2, ... with the sequence u, u \circ T, u \circ T^2, .... I will present recent work joint with M. Holland and D. Terhesiu in which we show that for all functions u belonging to wide class the sequence u, u \circ T, u \circ T^2, ... will satisfy semi-stable limit theorems. ICTP ICTP pio@ictp.it 26 Feb 2020

Europe/Rome 2020-03-09 07:00:00 2020-03-13 21:00:00 Workshop on Differential Geometry Week 1 | (smr 3431) Conference venue is Hotel Ponta Verde in Praia do Francês.  Please, find detailed information on the local website.  https://geometry-maceio.sciencesconf.org The "Workshop on Differential Geometry” has become a traditional event that takes place every year in the state of Alagoas, Brazil, during the Brazilian summer, congregating renowned international experts and members of the Brazilian geometry community. The 2020 edition will celebrate the 10th anniversary of the event, which has been organized since 2011 by the Institute of Mathematics of the Federal University of Alagoas (UFAL). There will be a balance of topics that are active in Brazil and research directions that need to be stimulated and further developed. In the  first week 5 advanced mini courses will be given by international experts while the second week will be devoted to research seminars. Applicants should specify if they want to take part to only one of the two weeks of the Workshop. Topics: • Minimal surfaces, constant mean curvature surfaces • Kahler geometry, extremal metrics • Mathematical relativity, stability/rigidity phenomena • Mean curvature  ow • Gluing and desingularization techniques, phase transition PDEs Minicourses: Lucas Ambrozio, University of Warwick   Joel Fine, Université Libre de Bruxelles    Laurent Hauswirth, Université de Marne-la-Vallée    Celso Viana, University of California - Irvine   Lu Wang, University of Wisconsin-Madison Invited Speakers: Sérgio Almaraz, Universidade Federal Fluminense Claudio Arezzo, International Centre for Theoretical Physics Gérard Besson, Institut Fourier - Université de Grenoble José María Espinar, Universidad de Cadiz Abigail Folha, Universidade Federal Fluminense Ailana Fraser, University of British Columbia Gregory Galloway, University of Miami Casey Kelleher, Princeton University* Levi Lima, Universidade Federal do Ceará Vanderson Lima, Universidade Federal do Rio Grande do Sul Jorge Lira, Universidade Federal do Ceará Andrea Loi, Università di Cagliari Andrea Malchiodi, Scuola Normale Superiore Ana Menezes, Princeton University Frank Pacard, École Polytechnique Paolo Piccione, Universidade de São Paulo Álvaro Ramos, Universidade Federal do Rio Grande do Sul Tristan Rivière, ETH Zürich Richard Schoen, University of California - Irvine Gang Tian, Beijing University Feliciano Vitorio, Universidade Federal de Alagoas Jun-cheng Wei, University of British Columbia Xi-Ping Zhu, Sun Yat-sen University *To be confirmed Attention for application to the 2nd week of the "Workshop on Differential Geometry - Week 2", 16 - 20 March 2020 go to link: http://indico.ictp.it/event/9228/ Maceio - Brazil ICTP pio@ictp.it 9 Mar 2020 - 13 Mar 2020

Europe/Rome 2020-03-16 07:00:00 2020-03-20 21:00:00 Workshop on Differential Geometry Week 2 | (smr 3503) Conference venue is Hotel Ponta Verde in Praia do Francês.  Please, find detailed information on the local website.  https://geometry-maceio.sciencesconf.org The "Workshop on Differential Geometry” has become a traditional event that takes place every year in the state of Alagoas, Brazil, during the Brazilian summer, congregating renowned international experts and members of the Brazilian geometry community. The 2020 edition will celebrate the 10th anniversary of the event, which has been organized since 2011 by the Institute of Mathematics of the Federal University of Alagoas (UFAL). There will be a balance of topics that are active in Brazil and research directions that need to be stimulated and further developed. In the  first week 5 advanced mini courses will be given by international experts while the second week will be devoted to research seminars. Applicants should specify if they want to take part to only one of the two weeks of the Workshop. Topics: • Minimal surfaces, constant mean curvature surfaces • Kahler geometry, extremal metrics • Mathematical relativity, stability/rigidity phenomena • Mean curvature  ow • Gluing and desingularization techniques, phase transition PDEs Minicourses: Lucas Ambrozio, University of Warwick   Joel Fine, Université Libre de Bruxelles    Laurent Hauswirth, Université de Marne-la-Vallée    Celso Viana, University of California - Irvine   Lu Wang, University of Wisconsin-Madison Invited Speakers: Sérgio Almaraz, Universidade Federal Fluminense Claudio Arezzo, International Centre for Theoretical Physics Gérard Besson, Institut Fourier - Université de Grenoble José María Espinar, Universidad de Cadiz Abigail Folha, Universidade Federal Fluminense Ailana Fraser, University of British Columbia Gregory Galloway, University of Miami Casey Kelleher, Princeton University* Levi Lima, Universidade Federal do Ceará Vanderson Lima, Universidade Federal do Rio Grande do Sul Jorge Lira, Universidade Federal do Ceará Andrea Loi, Università di Cagliari Andrea Malchiodi, Scuola Normale Superiore Ana Menezes, Princeton University Frank Pacard, École Polytechnique Paolo Piccione, Universidade de São Paulo Álvaro Ramos, Universidade Federal do Rio Grande do Sul Tristan Rivière, ETH Zürich Richard Schoen, University of California - Irvine Gang Tian, Beijing University Feliciano Vitorio, Universidade Federal de Alagoas Jun-cheng Wei, University of British Columbia Xi-Ping Zhu, Sun Yat-sen University *To be confirmed Attention for application to the 1st week of the "Workshop on Differential Geometry - Week 1", 9 - 13 March 2020 go to link: http://indico.ictp.it/event/9028/ Maceio - Brazil ICTP pio@ictp.it 16 Mar 2020 - 20 Mar 2020

Europe/Rome 2020-06-29 08:00:00 2020-07-03 22:00:00 Complex Analysis, Geometry and Dynamics ECM-ICTP 2020 | (smr 3457) The goal is to bring together leading researchers worldwide in complex analysis, geometry, and dynamics, with the aim of enhanced future collaboration. These fields are strongly interrelated, and in order to be able to solve deep challenging problems it is becoming necessary to pursue synergies among them to a bigger degree than in the past. Topics: Holomorphic approximation theory L2 techniques, plurisubharmonic functions, complex pluripotential theory Complex dynamics in higher dimensions Holomorphic directed systems, contact systems Applications of complex analysis to minimal surfaces Flexibility versus rigidity in complex geometry Cauchy-Riemann geometry Monge-Ampėre equations and Kähler manifolds There have been major recent advances in all these topics which the speakers will report on. It is becoming increasingly evident that a deeper level of cooperation will be needed for further progress. Speakers: A. ALARCÓN, University of Granada, Spain D. ANGELLA, University of Firenze, Italy F. BRACCI, University of Rome II-Tor Vergata, Italy F. DENG, University of Chinese Academy of Sciences, China B. DRINOVEC DRNOVŠEK, University of Ljubljana, Slovenia P. EBENFELT, University of California-San Diego, USA V. GUEDJ, University of Toulouse, France                       J.-M. HWANG, Korea Institute for Advanced Study, Korea S. KOLODZIEJ, University of Cracow, Poland       F. KUTZSCHEBAUCH, University of Berne, Switzerland B. LAMEL, University of Vienna, Austria F. LÁRUSSON, University of Adelaide, Australia S. NEMIROVSKI, Steklov Mathematical Institute, Russia     H. PETERS, University of Amsterdam, The Netherlands D. PHONG, Columbia University, USA T. OHSAWA, Nagoya University, Japan N. SHCHERBINA, University of Wuppertal, Germany B. STENSØNES, NTNU, Norway L. STUDER, Universidad Complutense de Madrid, Spain J. WINKELMANN, Bochum University, Germany E. F. WOLD, University of Oslo, Norway E. WULCAN, University of Gothenburg, Sweden M. XIAO, University of California-San Diego, USA A. ZIMMER, Louisiana State University, USA Grants: A limited number of grants are available to support the attendance of selected participants, with priority given to participants from developing countries. There is no registration fee. ICTP ICTP pio@ictp.it 29 Jun 2020 - 3 Jul 2020

Europe/Rome 2020-07-21 08:00:00 2020-07-31 22:00:00 International Conference on Representations of Algebras, ICRA 2020 Workshop and Conference | (smr 3463) ICRA is  a biannual international conference series started in 1974. It brings together well-established experts and young researchers in representation theory and in allied fields where representation theory is applied. The first week will consist of a workshop with six lecture series, including introductory talks and on topics of particular current interest, such  as recent links to both topological data analysis and to mathematical physics. One of the lecture series will be devoted to the mathematical heritage of Ragnar Buchweitz. The second week will be a conference with invited speakers in addition to contributed talks, both in plenary and in parallel sessions. Topics: Representation theory of algebras and its applications, including: -Topological Data Analysis -Cluster algebras -Non-commutative algebraic geometry -Modular representation theory. Workshop Speakers : M. BOTNAN, Amsterdam P. ETINGOF, MIT S. FOMIN, Michigan S. IYENGAR, Utah B. KELLER, Paris 7 S. SCHROLL, Leicester Conference Speakers: P. BALMER, UCLA A. BARBIERI, Sheffield M. CAORSI, former SISSA T. HAUSEL, IST Austria L. WILLIAMS, Harvard S. WITHERSPOON, Texas Scientific Committee: J. ASADOLLAHI, Isfahan C. GEISS, Mexico City O. IYAMA, Nagoya B. KELLER, Paris S. OPPERMANN, NTNU J. PEVTSOVA, Washington R. SCHIFFLER, Connecticut S. SCHROLL, Leicester J. TRLIFAJ, Prague M. VAN DEN BERGH, Hasselt Grants: A limited number of grants are available to support the attendance of selected participants, with priority given to participants from developing countries. There is a registration fee, but this is waived for supported participants from developing countries. For further information regarding the International Conference on Representations of Algebras, ICRA 2020 Workshop and Conference please visit the following link: https://wiki.math.ntnu.no/icra2020/start Applications for both the Workshop and the Conference can be submitted here Applications for the Conference ONLY can be submitted here   ICTP ICTP pio@ictp.it 21 Jul 2020 - 31 Jul 2020