International Conference Symmetries in Mathematics and Physics II

该奖项支持美国初级研究人员参加2013年6月24日至28日在巴西里约热内卢国家纯粹数学和应用数学研究所（IMPA）举行的国际会议“数学和物理对称性II”。会议有大约20位世界级的研究人员，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起作用的国际会议的第二部分。 第一次此类会议于2008年在意大利科尔托纳举行。 会谈涉及许多方面的代表性理论，特别是几何方法和连接到物理学。 特别是，以下主题将被讨论：量子群，李超代数，W-代数，手征代数，不变理论，约旦代数，环面代数，泊松代数，可积系统，几何朗兰兹计划，格罗莫夫-威滕不变量，唐纳森-托马斯不变量，施普林格决议，Koszul对偶，motivic积分，共形网，量子场论，弦理论，等等。 具有最新更新信息的会议网页位于http://www.impa.br/opencms/pt/eventos/store/evento_1301The对称性的概念长期以来在数学和物理学中发挥着重要作用。 例如，一个代数方程的根的可解性取决于根的对称性。 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，对称性在代数的分支中被称为表示论。 这是一个蓬勃发展的领域，有许多应用程序和连接到数学和理论物理的其他部分。 这次会议将聚集在该领域工作的领先的数学家和物理学家。

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.