Workshop on Moduli Spaces, Derived Geometry, and Representation Theory

该奖项支持2014年10月31日至11月2日在查佩尔山的北卡罗来纳州大学举办的研讨会。会谈涵盖了一系列的主题跨越代数，组合，几何和拓扑。讲习班的目标是为即将到来的初级研究人员提供一个机会，介绍他们的工作，并与更高级的研究人员互动，从而鼓励新的研究合作。该补助金还支持研究生和博士后研究人员参加研讨会，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。鼓励附近大学的学生参与，以加强与区域同行机构的联系，并优先考虑演讲者和参与者的多样性。研讨会的一般主题是模空间，导出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简化为线性代数中的简单问题的有力方法。同样，推导几何是将几何问题简化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，还发现了这些不同领域之间的新联系。导出范畴和跨壁公式揭示了研究模空间几何的新方法。来自派生几何和几何表示理论的方法和思想也开始趋同。研讨会汇集了研究这些专题的专家，将有助于促进互动和促进新的合作。更多细节可以在会议网站http://www.unc.edu/~sawon/UNCworkshop14.html上找到。

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.