MATH

Europe/Rome 2018-11-19 16:00:00 2018-11-19 17:00:00 D-brane masses and the motivic Hodge conjecture Abstract: We consider one complex structure parameter mirror families W of Calabi-Yau 3-folds with Picard-Fuchs equations of hypergeometric type. By mirror symmetry the even D-brane masses of the orginal Calabi-Yau M can be identified with four periods w.r.t. to an inte- gral symplectic basis of H3(W, Z) at the point of maximal unipotent monodromy. It was discovered by Chad Schoen in 1986 that the sin- gular fibre of the quintic at the conifold point gives rise to a Hecke eigen form of weight four f4 on Γ0(25) whose Fourier coefficients ap are determined by counting solutions in that fibre over the finite field Fpk . The D-brane masses at the conifold are given by the transition matrix Tmc between the integral symplectic basis and a Frobenius basis at the conifold. We predict and verify to very high precision that the entries of Tmc relevant for the D2 and D4 brane masses are given by the two periods (or L-values) of f4. These values also deter- mine the behaviour of the Weil-Petersson metric and its curvature at the conifold. Moreover we describe a notion of quasi periods and find that the two quasi period of f4 appear in Tmc. We extend the analy- sis to the other hypergeometric one parameter 3-folds and comment on simpler applications to local Calabi-Yau 3-folds. ICTP pio@ictp.it 19 Nov 2018

Europe/Rome 2018-11-21 14:30:00 2018-11-21 15:30:00 On noncommutative cubic surfaces and their moduli Abstract: This is based on joint work with Shinnosuke Okawa and Kazushi Ueda. The zero loci of a cubic equations in three dimensional projective space are pretty cool! As varieties, they may be deformed in four directions. However, they may also be deformed as "noncommutative" spaces in an extra four dimensions. Here we realise these noncommutative deformations as certain quiver algebras. We then go on to study their moduli and compare them to existing theories of noncommutative cubic surfaces. Time permitting we will discuss generalisations of these ideas to other del Pezzo surfaces. ICTP ICTP pio@ictp.it 21 Nov 2018

Europe/Rome 2018-11-22 14:30:00 2018-11-22 15:30:00 New complex analytic methods in the theory of minimal surfaces Abstract: In this talk, I will present some recent developments in the theory of minimal surfaces in Euclidean spaces which have been obtained as applications of both classical and modern complex analytic methods. The emphasis will be on results pertaining to the global theory of minimal surfaces, including the Calabi-Yau problem, constructions of properly immersed and embedded minimal surfaces in R^n and in minimally convex domains of R^n, results on the complex Gauss map, and isotopies of conformal minimal immersions. ICTP ICTP pio@ictp.it 22 Nov 2018

Europe/Rome 2018-11-26 11:00:00 2018-11-26 12:00:00 Endomorphism rings of Jacobians Abstract: Over the last two centuries mathematicians have developed a very rich theory of abelian varieties; however, certain kinds of explicit calculations have remained out of reach of our computational power until quite recently, when theoretical and technological advances have led to a renewed interest in the computational side of the theory. In this talk I will discuss one of the fundamental algorithmic problems one would like to solve, namely that of determining the endomorphism ring of the Jacobian of an explicitly given curve over a number field. I will describe a method to compute the endomorphism ring of such a Jacobian, starting with the case of genus-2 curves, and show the connection between this problem and a certain local-global principle for the center of the endomorphism algebra. If time permits, I will also outline how to prove the necessary local-global principle for abelian surfaces and, under the assumption of the Mumford-Tate conjecture, for all abelian varieties. ICTP ICTP pio@ictp.it 26 Nov 2018

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) ICTP ICTP pio@ictp.it 1 Jul 2019 - 5 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

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