MATH

Europe/Rome 2018-04-26 14:30:00 2018-04-26 15:30:00 Studying geometry with arithmetic techniques Abstract: See file below ICTP ICTP pio@ictp.it 26 Apr 2018

Europe/Rome 2018-05-03 14:30:00 2018-05-03 15:30:00 Global Existence of Solutions to Scalar Equations on Spatially Flat Universe as a Background with Non-minimal Coupling Abstract: We prove the wellposedness of scalar wave equations on spatially at universe as a background with nonminimal coupling with the scalar potential turned on by introducing the k-order linear energy and the corresponding energy norm. In the local case, we show that both the k-order linear energy and the energy norm are bounded for finite time with initial data in Hk+1 × Hk. Whereas in the global case, we have to add three assumptions related to the nonminimal coupling constant, the scale factor of spacetimes, and the form of the scalar that has to be a polynomial with a small positive parameter. Then, we show that the solution does globally exist with a particular decay estimate that depends on the scale factor of the spacetimes. Finally, we provide some physical models that support our general setup. ICTP ICTP pio@ictp.it 3 May 2018

Europe/Rome 2018-05-23 14:30:00 2018-05-23 15:30:00 BASIC NOTIONS SEMINAR: Introduction to Quantum Computation Abstract: I will give a very brief introduction to the concept of computation on a computer, and in particular on a quantum computer. I will try to describe for which kind of problems we could expect a speed-up due to quantum mechanics and discuss the status of the technology in this direction. ICTP ICTP pio@ictp.it 23 May 2018

Europe/Rome 2018-05-24 14:30:00 2018-05-24 15:30:00 A Geometric View on Tsen's Theorem Abstract: In 1936 Tsen proved that a 1-dimensional family of hypersurfaces of degree d in projective n-space always admits a section provided that d is less than or equal to n. This simple statement has been gen- eralized in many ways, and still inspires developments in algebraic geometry. In this talk I will survey the history of Tsen’s Theorem, mostly from the geometric point of view, and describe current re- search toward new interpretations and generalizations. ICTP ICTP pio@ictp.it 24 May 2018

Europe/Rome 2018-05-05 08:00:00 2018-05-10 22:00:00 TMU-ICTP School and Conference on Dynamical Systems and Ergodic Theory | (smr 3200) Dynamical Systems and Ergodic Theory constitute a vibrant and exciting eld of current research in pure mathematics, with lots of connections to other areas such as probability theory, differential geometry, ODEs, and potential applications to such diverse areas as natural and biological sciences, economics, engineering, climate and disease modeling and many others. It can be thought of as a modern development of classical theories of Differential Equations and the fundamental concepts and guiding ideas go back more than a century to pioneering thinkers such as Poincaré, Birkhoff and Kolmogorov. Its interest and importance has only grown in time and several Fields Medals have been awarded in the area. The ICTP-TMU School on Dynamical Systems and Ergodic Theory will consist of introductory mini-courses aimed specifically at masters and beginning PhD students who are expected to have an excellent general mathematics background but not necessarily any previous experience of the particular topics covered in the courses. The mini-courses will be complemented by a series of research-level seminars, given by internationally renowned scholars in the eld, and aimed at more advanced PhD students and local faculty and researchers. All students and researchers are welcome to all the lectures. Scientific Committee S. LUZZATTO, ICTP, Italy M. NASSIRI, IPM, Iran A. TAHZIBI, ICMC, Brazil   Lecturers C. BONATTI, Dijon, France P. ESLAMI, Warwick, UK C. LIVERANI, Rome, Italy   Speakers J.F. ALVES, Porto, Portugal P. BERGER, Paris, France O. BUTTERLEY, ICTP, Italy S. LUZZATTO, ICTP, Italy M. POLLICOTT, Warwick, UK M. TSUJII, Kyushu, Japan Tutor L.D. SIMONELLI, ICTP, Italy   Tehran - Islamic Republic of Iran ICTP pio@ictp.it 5 May 2018 - 10 May 2018

Europe/Rome 2018-05-21 08:00:00 2018-05-25 22:00:00 Workshop on Global Differential Geometry | (smr 3205) The German Research Foundation (DFG) and the International Center for Theoretical Physics (ICTP) are organizing a Workshop on Global Differential Geometry, to be held at the African Institute of Mathematical Sciences (AIMS) in Mbour, Sénégal, May 21 - 25, 2018. The workshop will focus on recent developments in Global Differential Geometry, in particular on symplectic and Poisson geometry, including foliations and Lie theory, as well as classical differential geometry with its connections to differential topology and global analysis. There are close relations to the index theory of elliptic operators, generalized complex geometry and geometric flows, all of which open the door to applications in mathematical physics.   Organizing Committee: Hamidou Dathe (Dakar) Bernhard Hanke (Augsburg) Aissa Wade (Penn State and AIMS Mbour) Katrin Wendland (Freiburg) DFG Coordinators: Carsten Balleier Alida Höbener Beate Wilhelm The list of speakers includes: Claudio Arezzo (ICTP) Augustin Banyaga (Penn State) Augustin Tshidibi Batubenge (South Africa) Kai Cieliebak (Augsburg) A. Degeratu (Stuttgart) Hassimou Diallo (Cote d’Ivoire) Abdoul Salam Diallo (Senegal) Cheikh Mbacke Diop* (Senegal) Jonathan Mboyo Esole* (Northeastern) Urs Frauenfelder (Augsburg) Sebastian Goette (Freiburg) Djideme Franck Houenou (Benin) El-Kaioum Mohamed Moutuou* (USF Florida) Karl-Hermann Neeb (Erlangen) Sylvie Paycha (Postdam) Philippe Rukimbira (FIU Florida) Thomas Schick (Göttingen) Léonard Todjihoundé (Benin) Joel Tossa (Benin) Burkhard Wilking (Münster) *to be confirmed Mbour - Senegal ICTP pio@ictp.it 21 May 2018 - 25 May 2018

Europe/Rome 2018-06-04 08:00:00 2018-06-15 22:00:00 International School on Extrinsic Curvature Flows | (smr 3209) NOTICE TO PARTICIPANTS While a detaliled programme of the School will be posted at a later stage, please be informed that foreseen daily schedule is Monday to Friday,  9 a.m. to 5 p.m. It is recommended that participants invited through selection process plan their trip so to arrive in Trieste the day before the School starts, and stay until the day after it ends,  to secure continous attendance. * * *   The School aims at introducing students both to the basic ideas  and to the most recent breakthroughs in the field of extrinsic curvature flows, a fundamental research direction at the intersection of Analysis and Geometry, with deep connections to the theories of minimal surfaces and of diffusive partial differential equations. Extrinsic flows have important applications to the geometry of submanifolds, as their study provides an effective strategy for obtaining topological classification results and for proving sharp geometric inequalities. In a broader context, extrinsic flows arise in describing the dynamics of interfaces in physical and biological sciences, a fact that provides a strong scientific motivation for their mathematical inquiry. Virtually all the different approaches to mean curvature flows will be accounted for, with particular emphasis on the fundamental problem of singularities formation. A major goal of the School will indeed be putting the best students in the position of understanding the many open problems in the field. PRELIMINARY LIST OF LECTURERS S. Angenent, University of Wisconsin-Madison P. Daskalopoulos, Columbia University G. Huisken, Universität Tübingen C. Mantegazza, Università di Napoli Federico II F. Otto, MPI for Mathematics in the Sciences C. Sinestrari, Università di Roma Tor Vergata T. Souganidis, University of Chicago Y. Tonegawa, Tokyo Institute of Technology Interested candidates should apply online (see link "Apply here" on the left-hand menu).     *   DEADLINE FOR APPLICATION: EXPIRED  * -------------------------------------------------------------- Organised in partnership with the Clay Mathematics Institute -------------------------------------------------------------- ICTP Secretariat contact:  smr3209@ictp.it   ICTP ICTP pio@ictp.it 4 Jun 2018 - 15 Jun 2018

Europe/Rome 2018-06-18 08:00:00 2018-06-22 22:00:00 Summer School on Geometry of Moduli Spaces of Curves | (smr 3215) Moduli spaces of stable pointed curves play an important role in algebraic geometry. This School will have one course on vector bundles of coinvariants and on conformal blocks and another one on their cohomology classes in relation with those of moduli of abelian varieties. The cohomology of moduli spaces of curves and abelian varieties carries several natural classes. We focus on the tautological classes and the cohomology classes related to spaces of modular forms. The problem of determining relationships between the tautological classes turns out to be particularly interesting. Moduli spaces of curves carry vector bundles of coinvariants and conformal blocks; they are invariants of a curve C attached to a Lie group G that are canonically isomorphic to global sections of an ample line bundle on the moduli stack of certain G-bundles on C. These are generalized theta functions in case C is smooth. In case g=0, the bundles of co-invariants are globally generated, and their first Chern classes are semi-ample line bundles on the moduli of curves, and shed light on its birational geometry. We can also use the moduli space of curves to learn about generalized theta functions. TOPICS: Cohomology classes on moduli of curves and abelian varieties moduli spaces of curves and abelian varieties properties of the moduli spaces and their compactifications natural cohomology classes and their relations tautological classes and cohomology classes related to spaces of modular forms   Vector bundles of coinvariants and conformal blocks introduction to moduli spaces of curves open problems and F-conjecture vector bundles of coinvariants and conformal blocks case g=0: global generation and semi-ample divisors any genus: nef divisors Chern classes of bundles of coinvariants Global sections of ample line bundles on Bun_G(C): smooth and nodal case   PARTICIPATION: Women are particularly encouraged to apply. Should you come to Trieste with your child(ren), please send an e-mail to smr3215@ictp.it to describe your family needs and we will do our best to meet them. 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. To apply, please use the link on the left side of this web page. The deadline for submitting applications expired on 15 March 2018. ICTP ICTP pio@ictp.it 18 Jun 2018 - 22 Jun 2018