International Conference Symmetries in Mathematics and Physics II

该奖项支持美国青年研究人员参加2013年6月24日至28日在巴西巴西首都里约热内卢举行的“数学与物理对称性II”国际会议。会议邀请了大约20位世界一流的研究人员，其中包括三位菲尔兹奖获得者。这是关于对称性在数学和理论物理中所扮演角色的国际会议的第二部分。第一次这样的会议于2008年在意大利科尔托纳举行。讲座涉及表征理论的许多方面，特别是几何方法及其与物理学的联系。特别地，以下主题将被讨论：量子群，李超代数，w -代数，手性代数，不变量理论，Jordan代数，环面代数，泊松代数，可积系统，几何Langlands程序，Gromov-Witten不变量，Donaldson-Thomas不变量，施普林格解决方案，Koszul对偶，动力积分，共形网，量子场论，弦理论，等等。会议最新信息的网页位于http://www.impa.br/opencms/pt/eventos/store/evento_1301The，对称的概念长期以来在数学和物理学中都扮演着重要的角色。例如，一个用根表示的代数方程的可解性取决于根集合的对称性。物理系统中对称性的存在意味着能量、动量或其他量的守恒。在现代数学中，对称是在代数的一个分支——表示论中研究的。这是一个蓬勃发展的领域，与数学和理论物理的其他部分有许多应用和联系。这次会议将聚集在该领域工作的顶尖数学家和物理学家。

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 http://www.impa.br/opencms/pt/eventos/store/evento_1301The 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.