MATH

Europe/Rome 2018-12-12 11:00:00 2018-12-12 12:00:00 Mock modular forms II The theory of mock modular forms is fairly new, having been initiated formally only in 2002, but is motivated by the 17 ”mock theta functions” that Ramanujan described in a letter to Hardy much earlier, in 1920. Since 2002 these objects have occurred in many places in both mathematics and mathematical physics, notably in the string theory of black holes and in the so-called ”Mathieu” and ”umbral” moonshine, and they also occur in connection with quantum invariants of knots and 3-dimensional manifolds. These talks, which assume no prerequisites, will give an introduction to the subject and some of the applications. ICTP ICTP pio@ictp.it 12 Dec 2018

Europe/Rome 2018-12-14 14:30:00 2018-12-14 15:30:00 Tropical and log geometric techniques for open invariants in mirror symmetry Abstract: We will discuss an algebro-geometric approach to the symplectic cohomology ring, in terms of tropical geometry and punctured log Gromov-Witten theory of Abramovich-Chen-Gross-Siebert. During this talk, we will restrict ourselves to the Tate curve, the total space of a degeneration of elliptic curves to a nodal elliptic curve. To understand the symplectic cohomology of the Tate curve (minus its central fiber), we will go through the Fukaya category of the elliptic curve and describe this category using tropical Morse trees introduced by Abouzaid-Gross-Siebert. ICTP ICTP pio@ictp.it 14 Dec 2018

Europe/Rome 2018-12-17 11:00:00 2018-12-17 12:00:00 Maximal and Variational Fourier Restriction Theory Müller, Ricci, and Wright recently established the first "maximal restriction theorem" for the Fourier transform. As a direct consequence, they clarified certain subtle measure theoretic aspects underlying Fourier restriction theory. In the first part of this talk, we will give a brief introduction to the restriction problem, and illustrate its importance in modern analysis. We will then focus on the endpoint Tomas-Stein inequality in 3-dimensional Euclidean space, together with its maximal and variational variants, for which especially simple proofs are available. Finally, we will describe a recent generalisation, and present some open problems. This is partly based on joint work with Vjekoslav Kovac. ICTP ICTP pio@ictp.it 17 Dec 2018

Europe/Rome 2019-01-17 14:30:00 2019-01-17 15:30:00 On some generalizations of the category of Soergel bimodules Abstract: The category of Soergel bimodules plays an essential role in (higher) representation theory and for the construction of homological invariants in knot theory. The aim of this talk is to present a generalization of Soergel category attached to a Coxeter group of type A_2. While Soergel category counts a generating bimodule per simple reflection, this generalization is obtained by taking one generator per reflection. I will give a complete description of this category through a classification of its indecomposable objects and study its split Grothendieck ring. This gives rise to an algebra which is a quotient of the corresponding affine Hecke algebra of type A_2, that can be presented by generators and relations. This is joint work with Thomas Gobet. ICTP ICTP pio@ictp.it 17 Jan 2019

Europe/Rome 2019-06-17 08:00:00 2019-06-28 22:00:00 1st Latin American School in Applied Mathematics | (smr 3301) Quito - Ecuador ICTP pio@ictp.it 17 Jun 2019 - 28 Jun 2019

Europe/Rome 2019-07-01 08:00:00 2019-07-05 22:00:00 Trieste Algebraic Geometry Summer School (TAGSS) 2019 - Algebraic Geometry towards Applications | (smr 3306) A growing number of researchers use algebraic geometry in industrial and applied mathematics: applications include biology, coding theory, cryptography, combustion, computational geometry, computer graphics, quantum computing, control theory, geometric design, complexity theory, machine learning, nonlinear PDE, optimization, and robotics. Algebraic Geometry of data clouds - density of cloud data - reach of a manifold and topological data analysis - classical theory of polar classes of a variety - the nearest points to a variety - the EDD degree of a manifold and its properties - the Bottleneck degree of varieties   Biochemical reaction networks modeled by mass-action kinetics - basics on reaction networks with mass-action kinetics: biochemical notions, algebraic notions, dynamical notions 
 - steady state invariants and computational algebraic geometry 
 - networks with toric steady states 
 - counting the number of positive steady states and real solutions to  polynomial 
systems 
 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. Women are particularly encouraged to apply. ICTP ICTP pio@ictp.it 1 Jul 2019 - 5 Jul 2019

Europe/Rome 2019-07-15 08:00:00 2019-07-26 22:00:00 ICTP School on Geometry and Gravity | (smr 3311) ICTP ICTP pio@ictp.it 15 Jul 2019 - 26 Jul 2019

Europe/Rome 2019-07-15 08:00:00 2019-08-02 22:00:00 2019 EAUMP School on Algebraic Topology and its Applications | (smr 3310) Kampala - Uganda ICTP pio@ictp.it 15 Jul 2019 - 2 Aug 2019