MATH

Europe/Rome 2022-05-16 14:00:00 2022-07-25 22:00:00 Graduate Course on Tight Closure of Ideals and its Applications | (smr 3707) An ICTP Virtual Meeting The aim of the course is to provide training in the foundations of commutative algebra and algebraic geometry in prime characteristic and to present some of the exciting recent developments. The local theory of prime characteristic singularities is a beautiful and historically important subject. Singularities which are defined in terms of the behaviour of the Frobenius endomorphism have been labeled “F-singularities”. The course gives an introduction on the most prominent F-singularity classes that emerged from Hochster–Huneke’s tight closure theory. Since its introduction in the late 1980s, it has had a dramatic effect on the field of commutative algebra. Tight closure gives unified proofs and strong generalisations of many major theorems in commutative algebra, as well stimulated recent proofs of longstanding conjectures. Topics: An overview of tight closure of ideals Test ideals Direct summands F-rational rings and rational singularities Hilbert-Kunz multiplicities Briançon-Skoda Theorems Big Cohen-Macaulay algebras The absolute integral closure Symbolic powers of ideals The localisation problem Uniform Artin-Rees results  Speakers: I. ABERBACH, University of Missouri, USA F. ENESCU, Georgia State University, USA N. EPSTEIN, George Mason University, USA E. GRIFO, University of Nebraska, USA G. LYUBEZNIK, University of Minnesota, USA L. MA, Purdue University, USA T. POLSTRA, University of Virginia, USA I. SWANSON, Purdue University, USA V. TRIVEDI, Tata Institute of Fundamental Research, India K. TUCKER, University of Illinois, USA W. ZHANG, University of Illinois, USA Schedule: Mondays and Wednesdays 1.00-3.00 pm GMT (link)   Lectures. There will be 3  lectures  and  a  tutorial  on each topic  each week.  The speakers will provide detailed   typed notes of their lectures on the day  they finish their lectures. These notes will contain exercises  which the participants should try to solve  and submit to the tutorial instructor before 12 pm GMT on Fridays.   Tutorials. The tutorial on each topic will be held a week after the lectures are delivered. The tutorial instructor will present solutions to problems assigned by the Lecturer that are received from the participants and discuss some  material covered during the lectures. Grades will be assigned to the solutions. Registration: There is no registration fee. Online - ICTP pio@ictp.it 16 May 2022 - 25 Jul 2022

Europe/Rome 2022-06-20 08:00:00 2022-06-25 22:00:00 AGRA IV (Arithmetic, Groups and Analysis) - Part 2 | (smr 3695) The AGRA series of summer schools (Santiago de Chile, 2012; Cusco, 2015; Córdoba, 2018; Online, 2021) 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 helps bring together more senior or mid-career mathematicians working in the field. It has been our tradition to have all courses and associated discussions in Spanish or Portuguese, in part so as to make all activities accessible to all students in Latin America, regardless of their English proficiency. The target audience of AGRA includes undergraduate students, graduate students and young researchers with a serious interest in number theory and neighboring fields. Due to the pandemic situation, AGRA IV was divided in two instalments. The first one was an ICTP – IMPA Online School that took place on August 16 – 20, 2021, with four minicourses covering topics in arithmetic combinatorics, arithmetic geometry, square-tiled surfaces and algebraic number theory (see http://indico.ictp.it/event/9617/). The plan for this second instalment, which shall happen in hybrid mode in the state of Rio de Janeiro – Brazil, is to have another group of minicourses, followed by tutorials and problem sessions. Minicourses will be as follows: Minicourse 1: Interactions between ergodic theory and number theory • Joel Moreira (Warwick, UK) • Sebastián Donoso (Univ. de Chile)   Minicourse 2: Applications of homology and cohomology in group theory • Lev Glebsky (Universidad Autonoma de San Luis Potosi, Mexico) • Dessislava Kochloukova (Unicamp, Brazil)   Minicourse 3: Expansion, divisibility and parity: a walk on numbers and graphs • Harald Helfgott (Univ. Göttingen, Germany/ CNRS, France) • Adrián Ubis (UAM, Spain)   Minicourse 4: Arithmetic groups and homogenous dynamics • Sebastian Hurtado-Salazar (Univ. Chicago, USA) • Plinio Pino (UFF, Brazil) Minicourse 5: Mori dream surfaces • Michela Artebani (Univ. de Concepción, Chile) • Antonio Laface (Univ. de Concepción, Chile) Cabo Frio (Rio de Janeiro) - Brazil ICTP pio@ictp.it 20 Jun 2022 - 25 Jun 2022

Europe/Rome 2022-07-11 08:00:00 2022-07-29 22:00:00 ICTP-EAUMP School on Mathematical Programming and Algorithms - an African Mathematical School | (smr 3725) An ICTP-EAUMP Hybrid Meeting. You can submit your application for participation in presence or online. This African Mathematical School is also an activity of AMU, supported by CIMPA Organised by the University of Nairobi, to be held at Kenya School of Government, Nairobi, Kenya The school will include: An intensive course in Programming in Python, coordinated by Jean-Baptiste Yunès (Institut de Recherche en Informatique Fondamentale, Université Paris Cité) where the participants will learn to write correct programs. An intensive course in Algorithms, coordinated by Roberto Mantaci (Institut de Recherche en Informatique Fondamentale, Université Paris Cité) where the participants will learn to write efficient programs. An intensive course on SageMath, a free, open-source, Python-based mathematics software system, coordinated by Anna Vanden Wyngaerd (Institut de Recherche en Informatique Fondamentale, Paris and Université libre de Bruxelles) where the participants will learn to apply to Mathematical Research the efficient programming techniques learnt in the two other courses. All courses will be composed of main lectures and applications in the form of exercise sessions or work sessions on machines. 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.   Nairobi - Kenya ICTP pio@ictp.it 11 Jul 2022 - 29 Jul 2022

Europe/Rome 2022-08-01 08:00:00 2022-08-05 22:00:00 Frontiers in Geometry and Topology Summer School | (smr 3648) An ICTP Hybrid Meeting. You can submit your application for participation in presence or online. Organised in partnership with the Clay Mathematics Institute The conference is intended as an appreciation of the contributions of Tomasz Mrowka Geometry and Topology have seen spectacular recent developments, including the solution of classical problems. As a consequence, the established picture of how various parts of these areas fit together is evolving rapidly. On the topological side, among the topics that have progressed are: four-manifolds obtained as knot traces; knot concordance and homology cobordism, Stein fillings. On the Floer homology side, we have powerful new computational methods and new invariants of embedded graphs and webs. On the more analytic side, we have new compactness results and potential new invariants. Topics: Interplay of 3-dimensional and 4-dimensional Topology Floer homology theories and associated invariants Khovanov homology Geometric and analytic aspects of gauge theoretic equations Speakers: J. GREENE, Boston College, USA J. HOM, Georgia Tech, USA F. LIN, Columbia University, USA J. PARDON, Princeton University, USA T. WALPUSKI, HU Berlin, Germany Here is the link to the Frontiers in Geometry and Topology Research Conference Registration: 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. In person participation: As regards the COVID-19 policy, we advise to follow the updated rules available on the ICTP page Access Guidelines for Visitors.     ICTP ICTP pio@ictp.it 1 Aug 2022 - 5 Aug 2022