MATH

Europe/Rome 2018-08-02 14:30:00 2018-08-02 15:30:00 Smooth invariant manifolds of renormalization Abstract: Topological classes are often invariant manifolds of renormalization. Unfortunately, renormalization is not a differentiable dynamical system. The stable manifold theorem for hyperbolic dynamics can not be applied. The talk will discuss a technique to construct smooth invariant manifolds in such a non-differentiable context. ICTP ICTP pio@ictp.it 2 Aug 2018

Europe/Rome 2018-08-02 16:00:00 2018-08-02 17:00:00 The rigidity conjecture Abstract: A central question in dynamics is whether the topology of a system determines its geometry, whether the system is rigid. Under mild topological conditions rigidity holds in many classical cases, including: Kleinian groups, circle diffeomorphisms, unimodal interval maps, critical circle maps, and circle maps with a break point. More recent developments show that under similar topological conditions, rigidity does not hold for slightly more general systems. We will discuss the case of circle maps with a flat interval. The class of maps with Fibonacci rotation numbers is a C1 manifold which is foliated with co dimension three rigidity classes. Finally, we summarize the known non-rigidity phenomena in a conjecture which describes how topological classes are organized into rigidity classes. ICTP ICTP pio@ictp.it 2 Aug 2018

Europe/Rome 2018-07-09 08:00:00 2018-07-20 22:00:00 ICTP-CIMPA School: AGRA III (Aritmética, Grupos y Analisis III) | (smr 3222) ICTP-CIMPA School: AGRA III (Aritmetica, Grupos y Analisis III) from the 9 - 20 July 2018 in Cordoba, Argentina to held at the Academia Nacional de Ciencias and at FaMAF Please note:   Arrival date should be 8 July 2018 and                        Departure date should be 21 July 2018 For Schedule and further information please refer to following link:  http://www.famaf.unc.edu.ar/agra3/ http://www.anc-argentina.org.ar/web/actividades/bienvenida   Deadline for requesting participation: 4 MARCH 2018 The area of the School is number theory, broadly understood - analytic, algebraic, combinatiorial, with links to groups and geometry. All of the course topics lie at thematic intersections. The course on Galois representations will focuse on their connections with modular forms and elliptic curves. The course on arithmetic groups will involve familiarizing students with topics in group theory and modular forms. Equidistribution in a diophantine context will be the main subject of a course. Another lecture series will focus on analysis, combinatorics and discrete geometry. The study of curves over finite fields, and the resulting codes, will allow for an accessible introduction to deep issues in algebraic geometry, with immediate applications. Finally, the course on primes, parity and analysis will combine classical tools and the use of entropy and independence. The plan is, then, to introduce advanced students to a variety of fields and tools and to notable recent developments. Scienfific Committee: Michael Harris Harald Helfgott Roberto Miatello Nuria Vila Oliva Fernando Rodriguez Villegas Local Committee: Maria Chara Emilio Lauret Ariel Pacetti Ricardo Podesta Diego Sulca Invited Speakers: Miram Abdon, Universidade Federal Fluminense, Brazil Mikhail Belolipetsky, IMPA - Instit.  Nac. de Matematica Pura e Aplicada, Brazil José Burgos Gil, ICMAT, Spain Luis Dieulefait, Universitat de Barcelona, Spain Cicero Fernandes De Carvalho, Universidade Federal de Uberlandia, Brazil Michael Harris, Université Paris VII, France & Columbia University, U.S.A. Harald Helfgott, Georg-August Universität Göttingen & CNRS - Centre National  de la Recherche Scientifique & Université Paris VI/VII, France Marc Hindry, Univesité Paris VII, France Benjamin Linowitz, Oberlin College,  Ohio, U.S.A. Ricardo Menares, PUCV - Pontificia Universidad Católica de Valparaíso, Chile Roberto Miatello, Universidad Nacional de Córdoba, Argentina Ariel Pacetti, Universidad Nacional de Córdoba, Argentina Daniel Panario, Carleton University, Canada Marusia Rebolledo, Université Blaise Pascal Clermont-Ferrand 2, France David Roberts, University of Minnesota, Morris, U.S.A. Fernando Rodriguez Villegas, ICTP - the Abdus Salam International Centre for Theoretical Physics, Italy Adrián Ubis Martínez, Universidad Autonoma de Madrid, Spain Co-sponsors: Academia Nacional de Ciencias Alexander von Humboldt Centre International de Mathematiques Pures et Appliques (CIMPA) Facultad de Matematica, Astronomia, Fisica y Computacion (FAMAF) Foundation Compositio Mathematica Universidad Nacional de Cordoba (UNC) Cordoba - Argentina ICTP pio@ictp.it 9 Jul 2018 - 20 Jul 2018

Europe/Rome 2018-07-09 08:00:00 2018-07-28 22:00:00 EAUMP-ICTP School and Workshop on Homological Methods in Algebra and Geometry II | (smr 3219) This is a three-week school and workshop on homological methods in algebra and geometry. The first two weeks will be a school for students from East Africa and beyond. International and African researchers will join for a workshop in the third week. The school begins with two introductory courses on some basic techniques that are widely used in the area. These are then built upon in the second week with slightly more advanced topics. The goal here is to give the participants a glimpse into some ideas used in algebraic geometry and homological algebra with the hope of inspiring them to pursue further research in a related topic. The school is intended for advanced graduate students (M.Sc. and Ph.D.) and young academic staff members from East Africa and beyond. Senior academic members are also welcome to participate. In the last week, the activity turns into a research focus-session involving international and African experts. The focus-session will study tensor categories and how they arise naturally in algebraic geometry with the aim of exploiting them using homological algebra. School Website: eaumpictp2018.weebly.com School Topics: Advanced linear algebra Galois theory Elementary algebraic geometry Introduction to homological algebra Workshop topic: Tensor categories of coherent sheaves Organizers: Tarig Abdelgadir (UNSW Sydney) Ulrich Krähmer (TU Dresden) Sylvester Rugeihyamu (Dar Es Salaam) David Ssevviiri (Makerere) Balázs Szendrői (Oxford) Fernando Rodriguez Villegas (ICTP) School speakers: Ravi Ramakrishna (Cornell) David Ssevviiri (Makerere) Chelsea Walton (Temple) Paul Wedrich (ANU Canberra) Michael Wemyss (Glasgow) Workshop speakers: Raf Bocklandt (Amsterdam) John Boiquaye (Accra) Andre Saint-Eudes Mialebama Bouesso (AIMS-South Africa) Alexandru Chirvasitu (Boulder) Joshua Greene (Boston College) Pinhas Grossman (UNSW Sydney) Yujiro Kawamata (Tokyo) Shinnosuke Okawa (Osaka) Sue Sierra (Edinburgh) Hermann Sore (Burkina Faso) Angela Tabiri (Glasgow) Ralph Twum (Accra) ICTP Scientific Contact: L. GOETTSCHE (ICTP) Application is open to all mathematicians and graduate students from developing countries. Applicants from EAUMP member states will be given priority. We encourage participants to secure their own funding for travel and subsistence from their home institution. Limited funds are available for participants from Sub- Saharan African Countries. There is no registration fee. Deadline: 1st of April 2018 Activity e-mail: smr3219@ictp.it Dar-es-Salaam - United Republic of Tanzania ICTP pio@ictp.it 9 Jul 2018 - 28 Jul 2018

Europe/Rome 2018-07-16 08:00:00 2018-07-27 22:00:00 Summer School in Dynamics (Introductory and Advanced) | (smr 3226) Week 1 A circle of concepts and methods in dynamics.   Basic concepts in dynamics will be introduced, with many examples, especially in the setting of circle maps. Topics include rotations of the circle, doubling map, Gauss map and continued fractions and an introduction to the basic ideas of symbolic codings and invariant measures. At the end of the week we will discuss some simple examples of structural stability and renormalization.     Week 2   Ergodicity in smooth dynamics (10h, Jana Rodriguez-Hertz and Amie Wilkinson)   The concept of ergodicity is a central hypothesis in statistical mechanics, one whose origins can be traced to Boltzmann's study of ideal gases in the 19th century.  Loosely speaking, a dynamical system is ergodic if it does not contain any proper subsystem, where the notion of "proper" is defined using measures.  A powerful theorem of Birkhoff from the 1930's states that ergodicity is equivalent to the property that "time averages = space averages:" that is, the average value of a function taken along an orbit is the same as the average value over the entire space. The property of ergodicity is the first stepping stone in a path through the study of statistical properties of dynamical systems, a field known as Ergodic Theory.   We will develop the ergodic theory of smooth dynamical systems, starting with the fundamental, linear examples of rotations and doubling maps on the circle introduced in Week 1.  We will develop some tools necessary to establish ergodicity of nonlinear smooth systems, such as those investigated by Boltzmann and Poincaré in the dawn of the subject of Dynamical Systems.  Among these tools are distortion estimates, density points, invariant foliations and absolute continuity.   Closer to the end of the course, we will focus on the ergodic theory of Anosov diffeomorphisms, an important family of "toy models" of chaotic dynamical systems.     Renormalization in entropy zero systems (5h, Corinna Ulcigrai)   Rotations of the circle are perhaps the most basic examples of low complexity (or "entropy zero") dynamical systems. A key idea to study systems with low complexity is renormalization. The Gauss map and continued fractions can be seen as a tool to renormalize rotations, i.e.study the behaviour of a rotation on finer and finer scales.  We will see two more examples of renormalization in action.    The first is the characterization of Sturmian sequences, which arise as symbolic coding of trajectories of rotations (and hint at more recent developments, such as the characterization of cutting sequences for billiards in the regular octagon). The second concerns interval exchange maps (IETs), which are generalizations of rotations. We will introduce the Rauzy-Veech algorithm as a tool to renormalize IETs. As applications, we will give some ideas of how it can be used (in some simplified settings) to study invariant measures and (unique) ergodicity and deviations of ergodic averages for IETs.   -----------------------------------------------------------------------------------------   Tutorial and exercise sessions will be held regularly and constitute an essential part of the school. Tutors: Oliver BUTTERLEY (ICTP), Irene PASQUINELLI (Durham University, UK), Davide RAVOTTI, (University of Bristol, UK), Lucia SIMONELLI (ICTP), Kadim WAR (Ruhr-Universität, Bochum, Germany).   Women in Mathematics: Activities directed to encourage and support women in mathematics, such as panel discussions and small groups mentoring and networking, will be organized during the event. ICTP ICTP pio@ictp.it 16 Jul 2018 - 27 Jul 2018

Europe/Rome 2018-07-18 08:00:00 2018-07-21 22:00:00 Mediterranean Youth Mathematical Championship 2018 | (smr 3254) MYMC 2018 web page: http://www.mymc.it/2018/ REGULATIONS: http://www.mymc.it/2018/doc/MYMC2018REGULATIONS.pdf PARTICIPATING COUNTRIES: Albania, Algeria, Bosnia and Herzegovina, Croatia, Cyprus, Egypt, France, Greece, Italy, Lebanon, Montenegro, Morocco, Palestine, Slovenia, Spain, Tunisia, Turkey TRAINING EXERCISES: http://www.mymc.it/2018/doc/training_exercises.pdf Roma - Italy ICTP pio@ictp.it 18 Jul 2018 - 21 Jul 2018