MATH

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 generalized 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 2018-06-01 14:30:00 2018-06-01 15:30:00 BASIC NOTIONS SEMINAR: The Geometry of Tensors Abstract: Tensors are fundamental objects in multilinear algebra, with important applications to the complexity of matrix multiplication, signal processing, phylogenetics and algebraic statistics. In applications, one generally looks for minimal decomposition of tensors as linear combinations of undecomposable tensors. The smallest integer r needed to write a tensor T as a linear combination of r undecomposable tensors is called the rank of T. Determining the rank of a tensor is a problem that has received much attention in recent years, and has a nice geometric interpretation. In this talk I will explain some applications of tensors decomposition and interpret the problem from the point of view of algebraic geometry. In particular, I will present new results about ranks of tensors, in collaboration with Alex Massarenti and Rick Rischter. ICTP ICTP pio@ictp.it 1 Jun 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. Summer School on Global Differential Geometry (14-18 May) web page: http://home.mathematik.uni-freiburg.de/mathphys/konf/diffgeo-summerschool/index.html   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 Kindly note 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

Europe/Rome 2018-07-09 08:00:00 2018-07-28 22:00:00 EAUMP-ICTP School and Workshop on Homological Methods in Algebra and Geometry II | (smr 3219) This is a three-week school and workshop on homological methods in algebra and geometry. The first two weeks will be a school for students from East Africa and beyond. International and African researchers will join for a workshop in the third week. The school begins with two introductory courses on some basic techniques that are widely used in the area. These are then built upon in the second week with slightly more advanced topics. The goal here is to give the participants a glimpse into some ideas used in algebraic geometry and homological algebra with the hope of inspiring them to pursue further research in a related topic. The school is intended for advanced graduate students (M.Sc. and Ph.D.) and young academic staff members from East Africa and beyond. Senior academic members are also welcome to participate. In the last week, the activity turns into a research focus-session involving international and African experts. The focus-session will study tensor categories and how they arise naturally in algebraic geometry with the aim of exploiting them using homological algebra. School Website: eaumpictp2018.weebly.com School Topics: Advanced linear algebra Galois theory Elementary algebraic geometry Introduction to homological algebra Workshop topic: Tensor categories of coherent sheaves Organizers: Tarig Abdelgadir (UNSW Sydney) Ulrich Krähmer (TU Dresden) Sylvester Rugeihyamu (Dar Es Salaam) David Ssevviiri (Makerere) Balázs Szendrői (Oxford) Fernando Rodriguez Villegas (ICTP) School speakers: Ravi Ramakrishna (Cornell) David Ssevviiri (Makerere) Chelsea Walton (Temple) Paul Wedrich (ANU Canberra) Michael Wemyss (Glasgow) Workshop speakers: Raf Bocklandt (Amsterdam) John Boiquaye (Accra) Andre Saint-Eudes Mialebama Bouesso (AIMS-South Africa) Alexandru Chirvasitu (Boulder) Joshua Greene (Boston College) Pinhas Grossman (UNSW Sydney) Yujiro Kawamata (Tokyo) Shinnosuke Okawa (Osaka) Sue Sierra (Edinburgh) Hermann Sore (Burkina Faso) Angela Tabiri (Glasgow) Ralph Twum (Accra) ICTP Scientific Contact: L. GOETTSCHE (ICTP) Application is open to all mathematicians and graduate students from developing countries. Applicants from EAUMP member states will be given priority. We encourage participants to secure their own funding for travel and subsistence from their home institution. Limited funds are available for participants from Sub- Saharan African Countries. There is no registration fee. Deadline: 1st of April 2018 Activity e-mail: smr3219@ictp.it Dar-es-Salaam - United Republic of Tanzania ICTP pio@ictp.it 9 Jul 2018 - 28 Jul 2018