MATH

Europe/Rome 2021-08-12 08:00:00 2021-08-20 22:00:00 EAUMP-ICTP School: Topics in Concrete Mathematics | (smr 3604) This is an EMA (Ecole Mathematique Africaine) School of CIMPA. This hybrid School is nominally based at the ICTP-East African Institute for Fundamental Research [EAIFR] in Kigali, Rwanda; it will offer students concrete and effective mathematical tools from algebra, group theory and geometry that can be applied to any scientific field. Consisting of 8 working days 12-15 August and 17-20 August, with one rest day the  2+2 courses shall be running concurrently. Lectures will be given remotely by video link. Description of Courses: WEEK 1 [12-15 August] R. K. Ramakrishna: Class numbers of number rings A. Taribi: Group representation theory and combinatorics WEEK 2 [17-20 August]: C. Kurujyibwami / B. Szendroi: Lie algebras K. Wendland: Modular forms Online - ICTP pio@ictp.it 12 Aug 2021 - 20 Aug 2021

Europe/Rome 2021-08-16 08:00:00 2021-08-20 22:00:00 AGRA IV (Arithmetic, Groups and Analysis) - Part I (smr 3617) An IMPA - ICTP Online School -  held in Spanish and Portuguese The AGRA series of summer schools (Santiago de Chile, 2012; Cusco, 2015; Córdoba, 2018) has as its goal to foster the development of number theory in Latin America: it provides a formative experience for young researchers, and it also brings together senior and mid-career mathematicians working in the field. The primary languages for this event are going to be Spanish and Portugese. Description: The target audience of AGRA includes undergraduate students, graduate students and young researchers with a serious interest in number theory and neighboring fields. The AGRA IV has been divided into two parts: part 1 is this online school in August 2021, while part 2 is preliminarily scheduled to take place in the first semester of 2022 in Cabo Frio, Brazil. The adjoined list of topics is representative of the two parts. The AGRA series has traditionally been held in Spanish but, this time, Spanish and Portuguese will share a role as primary languages of the school. Part 1 will consist of 4 minicourses delivered by a pool of distinguished mathematicians, followed by tutorials and problem sessions.   Topics: • Arithmetic geometry • Group approximations • Arithmetic combinatorics • Mahler measure • Model theory • Square-tiled surfaces • Analytic methods in number theory Programme: Minicourse 1: Introducción al análisis de Fourier de orden superior (Introduction to higher order Fourier analysis) • Julia Wolf (Cambridge, UK) • Pablo Candela (UAM / ICMAT, Spain) Syllabus   Minicourse 2: Aritmética de variedades de alta dimensión (Arithmetic of high dimensional varieties) * • Tony Varilly-Alvarado (Rice, USA) • Damiano Testa (Warwick, UK) Minicourse 3: Combinatória de superfícies quadriculadas e geometria de espaços de módulos (Combinatorics of lattice surfaces and geometry of moduli spaces) • Carlos Matheus (École Polytechnique / CNRS, France) • Vincent Delecroix (Bordeaux / CNRS, France) Syllabus Minicourse 4: Ecuaciones diofantinas con pocas soluciones (Diophantine equations with few solutions) • Hector Pasten (PUC, Chile) *preliminary title. Registration:  There is no registration fee   Online - ICTP pio@ictp.it 16 Aug 2021 - 20 Aug 2021

Europe/Rome 2021-11-15 07:00:00 2021-12-10 21:00:00 Markov Partitions and Young Towers in Dynamics | (smr 3642) In the 1970s, Sinai, Ruelle, and Bowen, developed groundbreaking new ideas and techniques which made it possible to apply the powerful results of Ergodic Theory to concrete, and sometimes quite explicit, differentiable dynamical systems. In particular they showed that smooth Uniformly Hyperbolic systems admit Markov Partitions, from which one can obtain a Symbolic Coding with a finite number of symbols. This Symbolic Coding makes it possible to apply methods from statistical mechanics to describe the statistical properties of the system through the construction of a particular class of invariant measures which are now called Sinai-Ruelle-Bowen (SRB) measures. Over the last 20 years there has been a huge progress in extending the results of Sinai, Ruelle, and Bowen, to the much larger class of more general (Nonuniformly) Hyperbolic systems, including systems with discontinuities/singularities. The geometry of these systems is much more complicated and one cannot expect to be able to code them with a symbolic dynamics with a finite number of symbols, making them much more challenging to study. Two inter-related but distinct approaches have emerged. At the end of the 1990s, Lai-Sang Young introduced a construction which is now generally refereed to as a Young Tower, based on constructing an induced uniformly hyperbolic system within the given system. More recently, around 2013, Sarig generalised the original Sinai-Ruelle-Bowen approach to construct infinite Markov Partitions. Both approaches have proved quite powerful and have been used to construct SRB measures and to study their statistical properties in a number of classes of dynamical systems of great interest. On the other hand, both approaches are also technically non-trivial and as a consequence, notwithstanding the applications of both to similar systems and their inevitable underlying connections, most researchers have developed an expertise in either one or the other. The main purpose of this event is to bring together experts in both areas in order to create opportunities to understand better the similarities and differences between them, and the advantages and disadvantages of the two approaches. The entire event will be held online with 2 mini courses by José Ferreira Alves on Young Towers and Yuri Lima on Markov Partitions. These mini-courses will be introductory and require only some familiarity with Uniformly Hyperbolic Dynamics and will be spread out over a period of 2 to 3 weeks, and be accompanied by some additional tutorial sessions, in order to give participants time to actually study the material and consolidate their knowledge. The mini courses will then be followed by a week of research level seminars describing recent results on these topics. Mini-Course Lecturers: José Ferreira Alves, U. of Porto, Portugal Yuri Lima, UFC, Brazil Speakers: Jerome Buzzi (Paris) Sylvain Crovisier (Paris) Peyman Eslami (Rome) Carlos Matheus (Paris) Ian Melbourne (Warwick) Snir Ben Ovadia (Weizmann) Yakov Pesin (Penn State) Omri Sarig (Weizmann) Agnieska Zelerowicz (F, Maryland) Hong-Kun Zhang (F, Amherst) Online - ICTP pio@ictp.it 15 Nov 2021 - 10 Dec 2021

Europe/Rome 2021-12-09 07:00:00 2021-12-18 21:00:00 Geometric, Algebraic and Topological Methods in Quantum Field Theory | (smr 3618) Villa de Leyva - Colombia ICTP pio@ictp.it 9 Dec 2021 - 18 Dec 2021