Workshops on Algebraic Geometry and Representation Theory; Fall, 2015, 2016, and 2017; Chapel Hill, NC

该奖项支持参加将于2015年秋季，2016年和2017年在北卡罗来纳州，查佩尔山大学举行的代数几何和表示理论研讨会。 这些数学主题是当前紧张的工作和最近的研究进展的主题。 第一次研讨会，“在模量和几何不变理论的新发展，”将于2015年11月20日至22日举行。研讨会的网址是http://www.unc.edu/~sawon/UNCworkshop15.html。讲习班的目标是支持年轻的研究人员，为他们提供机会，传播他们的最新研究成果，并与高级研究人员互动，并加强东南部数学系之间的联系。每个研讨会将包括10个演讲，分布在三天内，允许有足够的时间进行额外的讨论。研究生和博士后的参与将受到鼓励。每个研讨会预计至少有30名研究生参加，在那里他们将了解该领域的最新进展。参数化几何对象和/或代数方程的解的空间被称为模空间，并且是代数几何和表示论研究的核心。通常，它们被构造为商空间使用几何不变理论。这些模空间的结构，以及它们如何依赖于商结构，是一个重要的研究领域，最近出现了大量变革性的新思想：Bridgeland稳定性条件和稳定复形理论已经发展到现在在层的模空间理论中找到应用的地步;模空间的双有理几何现在可以用稳定性条件的变化来研究;并且可以测量跨壁对模空间的导出范畴的影响，正如更一般的双有理修改对Gromov-Witten和Donaldson-Thomas不变量的影响在许多情况下可以确定一样。第一个讲习班将汇集这些领域的专家，重点是年轻数学家的工作。第二次和第三次讲习班将涵盖代数几何和表示论的其他主题，并将侧重于最重要的当前发展。

This award supports participation in workshops on algebraic geometry and representation theory to be held in Fall 2015, 2016, and 2017 at the University of North Carolina, Chapel Hill. These mathematical topics are subjects of intense current work and much recent research progress. The first workshop, "New Developments in Moduli and Geometric Invariant Theory," will be held November 20-22, 2015. The workshop website is http://www.unc.edu/~sawon/UNCworkshop15.html. The goals of the workshops are to support younger researchers, by providing them with opportunities to disseminate their latest research results and interact with senior researchers, and to strengthen ties between mathematics departments in the Southeast. Each workshop will consist of ten talks spread over three days, allowing plenty of time for additional discussions. Participation of graduate students and postdocs will be encouraged. At least thirty graduate students are expected to attend each workshop, where they will learn about the latest progress in the field. Spaces that parameterize geometric objects and/or solutions to algebraic equations are known as moduli spaces, and are central to the study of algebraic geometry and representation theory. Typically they are constructed as quotient spaces using geometric invariant theory. The structure of these moduli spaces, and how they depend on the quotient construction, is an important area of investigation that has recently seen the influx of transformative new ideas: The theory of Bridgeland stability conditions and stable complexes has advanced to the point where it is now finding applications in the theory of moduli spaces of sheaves; the birational geometry of moduli spaces can now be studied using variation of stability conditions; and the effect of a wall-crossing on the derived category of a moduli space can be measured, just as the effect of more general birational modifications on Gromov-Witten and Donaldson-Thomas invariants can be determined in many cases. The first workshop will bring together experts in these areas, with an emphasis on the work of younger mathematicians. The second and third workshops will cover other topics in algebraic geometry and representation theory, and will focus on the most significant current developments.