MATH

Europe/Rome 2022-12-05 14:00:00 2022-12-08 16:00:00 CIMPA/ICTP Course on "Introduction to Optimization and Operator Theory" This is a recurring meeting, therefore please register just once for all 4 sessions: https://zoom.us/meeting/register/tJUodOihqDMvE9fOe6s-MziaNCKeZeoaVSDt Venue (for in-person attendees): Luigi Stasi Seminar Room Timetable: Monday 5 December:   14:00 - 16:00 Tuesday 6 December:  14:00 - 16:00 Wednesday 7 December: 14:00 - 16:00 Thursday 8 December: 14:00 - 16:00 Abstract: An introductory lecture on operator and optimization theory will be given. To be specific, various notions of derivatives for mappings between Normed spaces will be discussed, with a special emphasis on mappings taking values in <span lang="EN-GB" style="font-size:12.0pt;font-family:Times;mso-fareast-font-family: Times;mso-bidi-font-family:Times;mso-ansi-language:EN-GB;mso-fareast-language: IT;mso-bidi-language:AR-SA">R connecting derivatives with optimization problems. We discuss the continuity, lower semicontinuity, differentiability, and, most importantly, optimization properties of convex functions in normed spaces. We will also go over the Fenchel conjugate and biconjugate for convex functions, as well as their properties. With these tools at our disposal, we move on to the duality methods in optimization, which allows us to solve unconstrained and constrained minimization problems (called the primal) by relating them to their dual problems obtained via the Fenchel conjugate. Finally, after discussing the Moreau proximity operator in Hilbert spaces, we will look at a popular class of optimization algorithms.   References: [1] Kravvaritis, D. C., & Yannacopoulos, A. N. (2020). Variational methods in nonlinear analysis: with applications in optimization and partial differential equations. Walter De Gruyter Gmbh & Co Kg. [2] Bauschke, H. H., & Combettes, P. L. (2011). Convex analysis and monotone operator theory in Hilbert spaces (Vol. 408). New York: Springer. Hybrid ICTP pio@ictp.it 5 Dec 2022 - 8 Dec 2022

Europe/Rome 2022-12-09 16:00:00 2022-12-09 17:30:00 Basic Notions Seminar - What is a moduli space? Venue: for in-person attendees (Leonardo da Vinci, Luigi Stasi Seminar Room).   For virtual attendees: https://zoom.us/meeting/register/tJ0od-ihrTIjH9F3K0rVN45vAwYwC2diqLtL After registering, you will receive a confirmation email containing information about joining the meeting. Abstract: There is a beautiful connection between the prime numbers and the zeros of Riemann zeta-function in the complex plane, and understanding the distribution of these zeros can lead to remarkable consequences in our understanding of the primes. A famous open problem, known as the Riemann Hypothesis, states that the non-real zeros of the Riemann zeta-function lie on a vertical line. I will motivate this conjecture, describe some evidence for it, and describe some of the consequences it would lead to in our understanding of the primes. In particular, I will describe how to bound on the maximum gap between prime numbers assuming the Riemann Hypothesis (which is based on joint work with Carneiro and Soundararajan). hybrid ICTP pio@ictp.it 9 Dec 2022

Europe/Rome 2022-12-09 16:00:00 2022-12-09 17:00:00 BASIC NOTIONS SEMINAR: What is a moduli space? Register in advance for this meeting: https://zoom.us/meeting/register/tJ0od-ihrTIjH9F3K0rVN45vAwYwC2diqLtL After registering, you will receive a confirmation email containing information about joining the meeting. Abstract: Given a certain set of mathematical objects, a guiding question is often the classification problem. In algebraic geometry, the objects that you would like to classify have usually some geometry interests, like for instance manifolds, vector bundles, algebraic curves. The attempt to reach a meaningful classification often leads to the construction of a moduli space: a parameter space whose points correspond to all the objects you would like to study. In the talk, I will give a very gentle introduction to the notion of parameter space focusing on elementary examples. If time permits, at the end I will give some hints towards more complicated but also more interesting examples. hybrid seminar ICTP pio@ictp.it 9 Dec 2022

Europe/Rome 2023-02-27 07:00:00 2023-03-03 21:00:00 Learning Workshop on BPS States and 3-Manifolds | (smr 3818) The main scientific theme of the workshop is counting BPS states in physical systems associated to 3-manifolds or links, and interpretation of these counts as old or new topological invariants.   Although the ideas behind such relations appeared already in the late 90s, the recent years have seen some dramatic new developments. The goal of this learning workshop is to bring together physicists and mathematicians who are experts in the subject and also those who would like to enter the field. In particular, the talks will be given both by senior scientists and junior ones, including PhD students who only recently began working on the subject. The talks will be supplemented by dedicated discussion sessions where experts can answer questions that will be submitted by participants to the moderator in advance, or asked directly during the session.    Topics: "Z-hat" and F_K invariants counting BPS states in 6d superconformal field theory compactified on 3- manifolds, and their relation to known invariants of 3-manifolds and links Knots-quivers correspondence and its generalization to knot complements  Properties of generating functions counting BPS states, including: modularity, relation to characters of (logarithmic) Vertex Operator Algebras, GW/DT invariants Speakers: R. AKHMECHET, Columbia University *M. CHENG, University of Amsterdam  H-J. CHUNG, Jeju National University F. COSTANTINO, Toulouse University T. EKHOLM, Uppsala University B. HAGHIGHAT, Tsinghua University S. HARICHURN, Bonn University J. JANKOWSKI, Wrocław University P. JOHNSON, Michigan State University S. KRUSHKAL, University of Virginia H. LARRAGUIVEL, Jagiellonian University P. LONGHI, Uppsala University D. NOSHCHENKO, University of Amsterdam S. PARK, University of Texas at Austin D. PASSARO, University of Amsterdam *D. PEI, University of Southern Denmark P. RAMADEVI, Indian Institute of Technology, Mumbai S.J. RI, ICTP M. STOSIC, Instituto Superior Técnico P. SULKOWSKI, Warsaw University J. SVOBODA, University of Miami *C. VAFA, Harvard University *  to be confirmed   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 27 Feb 2023 - 3 Mar 2023