This award supports the participation of junior US researchers in the international conference 'Symmetries in Mathematics and Physics II,' held at the Instituto Nacional de Matematica Pura e Aplicada (IMPA) in Rio de Janeiro, Brazil during June 24-28, 2013. The conference features approximately twenty plenary speakers who are world-class researchers, including three Fields medal recipients. This is the second installment of an international conference on the role played by symmetry in mathematics and theoretical physics. The first such conference was held in Cortona, Italy in 2008. The talks involve many aspects of representation theory and especially the geometric approaches and connections to physics. In particular, the following subjects will be discussed: quantum groups, Lie superalgebras, W-algebras, chiral algebras, invariant theory, Jordan algebras, toroidal algebras, Poisson algebras, integrable systems, geometric Langlands program, Gromov-Witten invariants, Donaldson-Thomas invariants, Springer resolutions, Koszul duality, motivic integration, conformal nets, quantum field theory, string theory, and more. The conference web page with the latest updated information is located at www.impa.br/opencms/pt/eventos/store/evento_1301
The notion of symmetry has long played a fundamental role in both mathematics and physics. For example, the solvability of an algebraic equation in terms of radicals depends on the symmetries of the set of roots. The existence of symmetry in a physical system implies the conservation of energy, momentum or other quantities. In modern mathematics, symmetries are investigated in the branch of Algebra called Representation Theory. It is a thriving area with many applications and connections to other parts of mathematics and theoretical physics. This conference will gather leading mathematicians and physicists working in the field.
" was held at the Instituto Nacional de Matemática Pura e Aplicada (IMPA) in Rio de Janeiro, Brazil during June 24-28, 2013. The five-day event featured 17 plenary speakers who are world-class researchers in mathematics and theoretical physics, including two Fields medal recipients. There were also 22 posters presented by junior researchers. More information is available at conference web page www.impa.br/opencms/pt/eventos/store/evento_1301. Intellectual Merit The aim of the conference was to present some of the most important and current developments in mathematics and theoretical physics through the concept of "symmetry", which encompasses the major algebraic ideas involved in the description of physical phenomena. In the last five years since the first such conference, important developments in the area have been made, including great advances in the Langlands program. The 2013 conference covered an even broader range of topics than the 2008 one. The talks touched upon many aspects of representation theory, and especially the geometric approaches and connections to physics. In particular, the following subjects were discussed: quantum groups, Lie superalgebras, W-algebras, chiral algebras, invariant theory, Jordan algebras, toroidal algebras, Poisson algebras, integrable systems, geometric Langlands program, Gromov-Witten invariants, Donaldson-Thomas invariants, Springer resolutions, Koszul duality, motivic integration, conformal nets, quantum field theory, string theory, and other. There were 151 mathematicians and theoretical physicists participating in the event. The concentration of so many leading researchers gave rise to a fertile exchange of ideas and fostered new collaborations. Broader Impacts The NSF grant supported the travel expenses of a total of 14 U.S. participants, which included 3 speakers, 1 organizer, 2 postdoctoral researchers, and 8 graduate students. The senior participants received only partial support, while the graduate students and postdocs had full travel support. Four of the supported participants are female, and one is Hispanic. The conference gathered leading researchers from all over the world working in many diverse areas of mathematics and theoretical physics. It was beneficial for the research of all participants, by exposing them to the latest advances and by fostering the exchange of ideas among different areas of mathematics and physics. For the junior researchers, it brought unprecedented opportunities to gain insights and to meet senior experts. The participation of U.S. graduate students also helped them to gain international working experience, and to get exposure to other cultures and to Latin-American culture in particular. Holding the conference in Rio de Janeiro had a direct impact in the local community by bringing to Latin-America mathematicians and physicists of the highest quality. All talks were videotaped (with the permission of the speakers) and are freely available online.
