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年在北卡罗来纳大学教堂山分校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工作和最近研究进展的主题。第一期研讨会“模数和几何不变理论的新发展”将于2015年11月20-22日举行。研讨会的网站是http://www.unc.edu/~sawon/UNCworkshop15.html.讲习班的目标是支持年轻的研究人员，为他们提供传播最新研究成果和与资深研究人员互动的机会，并加强东南部数学系之间的联系。每个研讨会将由10个讲座组成，分三天进行，以便有足够的时间进行额外的讨论。将鼓励研究生和博士后参与。预计至少有30名研究生将参加每个研讨会，在那里他们将了解该领域的最新进展。将几何对象和/或代数方程的解参数化的空间称为模空间，它是代数几何和表示理论研究的中心。通常，它们被构造为使用几何不变量理论的商空间。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，最近看到了许多变革性的新思想的涌入：Bridgeland稳定性条件和稳定复合体的理论已经发展到现在可以在层模空间的理论中找到应用的地步；模空间的双调几何现在可以利用稳定性条件的变化来研究；并且可以测量墙交叉对模空间的派生范畴的影响，就像在许多情况下可以确定更一般的双调修改对Gromov-Witten和Donaldson-Thomas不变量的影响一样。第一期研讨会将汇集这些领域的专家，重点放在年轻数学家的工作上。第二个和第三个工作坊将涵盖代数几何和表示理论的其他主题，并将集中于当前最重要的发展。

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.