Workshop on Moduli Spaces, Derived Geometry, and Representation Theory

该奖项支持2014年10月31日至11月2日在北卡罗来纳大学教堂山分校举办的研讨会。讲座涵盖了代数、组合学、几何学和拓扑学等一系列主题。讲习班的目标是让主要是即将到来的初级研究人员有机会介绍他们的工作，并与更资深的研究人员互动，从而鼓励新的研究合作。这笔赠款还支持研究生和博士后研究人员参加讲习班，因此将有助于在一些最活跃的数学研究领域培训年轻的数学家。鼓励来自附近大学的学生参与，以加强与地区同行机构的联系，讲者和参与者之间的多样性是优先考虑的。研讨会的总主题是模空间、衍生几何和几何表示理论。模空间是将某种几何对象参数化的空间，在代数几何中无处不在。表示论是将抽象代数中的问题归结为线性代数中更简单问题的有力方法。类似地，派生几何是将几何问题归结为同调代数问题的一种方法。最近在这些领域取得了重大进展。此外，还发现了这些不同地区之间的新联系。派生范畴和穿墙公式揭示了研究模空间几何的新方法。衍生几何和几何表示理论的方法和思想也开始趋同。研讨会汇集了从事这些主题的专家，并将有助于促进互动和促进新的合作。欲了解更多详情，请访问会议网站http://www.unc.edu/~sawon/UNCworkshop14.html.

This award supports a workshop at the University of North Carolina at Chapel Hill, held from October 31st to November 2nd, 2014. The talks cover a range of topics spanning algebra, combinatorics, geometry, and topology. The goal of the workshop is to give predominantly upcoming junior researchers an opportunity to present their work and to interact with more senior researchers, thereby encouraging new research collaborations. The grant also supports the attendance of graduate students and postdoctoral researchers at the workshop, and hence will contribute to the the training of younger mathematicians in some of the most active areas of mathematical research. Participation of students from nearby universities is encouraged, to strengthen ties with regional peer institutions, and diversity among the speakers and the participants is a priority.The general themes of the workshop are moduli spaces, derived geometry, and geometric representation theory. Moduli spaces are spaces that parametrize geometric objects of some kind, and are ubiquitous in algebraic geometry. Representation theory is a powerful method of reducing problems in abstract algebra to simpler problems in linear algebra. Similarly, derived geometry is a way of reducing geometric problems to problems in homological algebra. There have been significant recent advances in these areas. Moreover, new connections between these different areas have been discovered. Derived categories and wall-crossing formulas have revealed new ways of studying the geometry of moduli spaces. Methods and ideas from derived geometry and geometric representation theory are also starting to converge. The workshop brings together experts working on these topics, and will serve to promote interaction and foster new collaborations. More details can be found at the conference website http://www.unc.edu/~sawon/UNCworkshop14.html.