Representation Theory, Integrable Systems and Quantum Fields: Emphasis Year at Northwestern University, May 19-23, 2014

该补助金的主要目的是资助研讨会和会议，“表示论，可积系统和量子场：在西北大学的重点年”，运行5月12日至16日（研讨会）和5月19日至23日（会议）在2014年。 西北大学有着悠久的历史，成功的“重点年”以下的拟议活动的广泛模式。 今年的重点将放在连接新的物理数学。 由Nekrasov-Shatashvili，Alday-Gaiotto-Tachikawa和Kapustin-Witten开创的物理学的最新进展在地球仪上产生了数百篇论文和兴趣。 一个数学的角度已经提供了Maulik，Okounkov和有相关的工作Goncharov，凯尼恩。 这些结果不仅应该被理解为它们自身的优点，而且应该被理解为可积系统、表示论和量子场之间更广泛的新兴关系的一部分。 研讨会和会议将做到这一点。 大部分拟议的资金将直接支持研究生和博士后，通过资助他们的参与，或间接资助研究生研讨会的演讲者。 这些学生将主要是来自美国机构的美国公民，从而进一步促进了征集的目标，以支持美国专业数学家的发展。该计划的总主题是探索对称群和它们所产生的物理系统之间的相互作用。 物理现象有类似的数学描述，反之亦然：几何朗兰兹纲领通过卡普斯廷和维滕的工作，在拓扑扭曲的超对称规范理论的降维中有类似的描述。 Alday-Gaiotto-Tachikawa猜想将二维共形场论与四维超对称场论联系起来。这一猜想的数学表现是Virasoro和W-代数对由Maulik和Okounkov构造的复曲面上的丛的模空间的上同调的作用。 与奇异卡-丘三重上的弦紧化相关的可积系统在统计物理学中被描述为二聚体问题，这反过来又与簇可积系统相关（Nekrasov-Shatashvili，Kenyon-Goncharov）。 所有这些现象都将在研讨会和会议上探讨。 会议网页位于以下地址：http://www.math.northwestern.edu/emphasisyear/。

The main purpose of this grant is to fund the workshop and conference, "Representation Theory, Integrable Systems, and Quantum Fields: Emphasis Year at Northwestern University," running May 12-16 (workshop) and May 19-23 (conference) in 2014. Northwestern has a long history of successful 'emphasis years' following the broad pattern of the proposed activities. This year's emphasis will be placed on connecting new physics to mathematics. Recent advanced in physics pioneered by Nekrasov-Shatashvili, Alday-Gaiotto-Tachikawa, and Kapustin-Witten have spawned hundreds of papers and interest around the globe. A mathematical perspective has been offered by Maulik-Okounkov and there is related work of Goncharov-Kenyon. These results should be understood not only on their own merit, but also as a part of a broader emerging relationship between integrable systems, representation theory and quantum fields. The workshop and conference will do just that. The bulk of the proposed funding will support graduate students and postdocs either directly, by funding their participation, or indirectly by funding speakers at the graduate workshop. These students will largely be US nationals from US institutions, thus furthering the goal of the solicitation to support the development of professional mathematicians in the United States.The general theme of the program is to explore the interplay between symmetry groups and the physical systems in which they arise. Physical phenomena have analogous mathematical descriptions, and vice versa: the geometric Langlands program has an analogue in a dimensional reduction of a topologically twisted supersymmetric gauge theory, through the work of Kapustin and Witten. The Alday-Gaiotto-Tachikawa conjecture relates two-dimensional conformal field theory to four-dimensional supersymmetric theories. A mathematical manifestation of this conjecture is the action of Virasoro and W-algebras on the cohomology of moduli spaces of bundles on a complex surface constructed by Maulik and Okounkov. Integrable systems relating to string compactification on singular Calabi-Yau threefolds have descriptions as dimer problems in statistical physics, which in turn relate to cluster integrable systems (Nekrasov-Shatashvili, Kenyon-Goncharov). All of these phenomena will be explored in the workshop and conference. The conference webpage is located at the following address: http://www.math.northwestern.edu/emphasisyear/.