Program on Motivic Invariants and Singularities

该提案是为了支持圣母大学数学中心的动机不变量和奇点计划，该计划包括一个本科生暑期学校。（2013年5月21日至25日），研究生和博士后暑期学校（2013年5月27日至31日），会议（2013年6月3日至7日），以及整个程序的杰出讲座系列。本科生暑期学校将包括三个迷你课程的p-adic数和p-adic集成，热带几何，统计学习理论和奇点。高级暑期学校将包括五个小型课程，包括D-模和消失循环，Donaldson-Thomas不变量和motivic Milnor纤维，Monodromy猜想，motivic整合和Nash猜想。会议将汇集与动机整合和奇点理论相关领域的顶级研究人员。 此外，杰出讲座系列，将由扬Denef交付，将传播给广大观众一个令人兴奋的主题有关的程序。会议的网站是：http://nd.edu/~cmnd/programs/mis2013/Since，由M. Kontsevich在1995年，动机整合已经成为一个快速发展的学科，连接到代数几何，奇点理论，数论和模型理论。该理论发现了大量的应用程序，以一套不同的主题，如麦凯对应，奇点的最小模型计划，并研究轨道积分出现在朗兰兹计划。虽然在这方面已经做了大量工作并取得了显著进展，但一些根本问题仍然悬而未决。这样一个问题是单值猜想，它预言了p-adic和motivic积分与更经典的奇点不变量之间的联系。最近对这个话题的兴趣来自于与唐纳森-托马斯理论的联系。鉴于最近的多项发展，这是一个很好的时间有一个程序之间的联系动机整合和奇点理论。虽然动机整合已经达到了一定的成熟度，一些新的有趣的研究方向正在被发现。通过汇集来自不同但相关领域的专家，该计划可以实现富有成效的思想交流，从而在重要问题（如单值猜想）和制定新问题方面取得进展。

This proposal is for support of the Program on Motivic Invariants and Singularities at the Center for Mathematics at the University of Notre Dame, which consists of an Undergraduate Summer School (May 21-25, 2013), a Graduate and Post-doc Summer School (May 27-31, 2013), a conference (June 3 -7, 2013), as well as a Distinguished Lecture Series throughout the program. The Undergraduate Summer School will consist of three mini course on p-adic numbers and p-adic integration, tropical geometry, and statistical learning theory and singularities. The advanced Summer School will consist of five mini-courses on D-modules and vanishing cycles, Donaldson-Thomas invariants and the motivic Milnor fiber, the Monodromy Conjecture, motivic integration, and the Nash Conjecture. The conference will bring together top researchers in areas related to motivic integration and singularity theory. In addition, the Distinguished Lecture Series, to be delivered by Jan Denef, will disseminate to a wide audience an exciting topic related to the program. The website of the conference is: http://nd.edu/~cmnd/programs/mis2013/Since its creation by M. Kontsevich in 1995, motivic integration has been a rapidly developing subject connected to Algebraic Geometry, Singularity Theory, Number Theory, and Model Theory. The theory found a lot of applications to a diverse set of topics such as the McKay correspondence, singularities in the Minimal Model Program, and the study of orbital integrals that appear in the Langlands program. While there has been a lot of work and notable progress in this direction, some fundamental problems are still open. Such a problem is the Monodromy Conjecture, which predicts a connection between p-adic and motivic integrals and more classical invariants of singularities. Further recent interest in the topic comes from connections with Donaldson-Thomas theory. In light of recent multiple developments, this is a good time to have a program on connections between motivic integration and singularity theory. While motivic integration has achieved a certain maturity, several new interesting research directions are being uncovered. By bringing together experts from different but related fields, the program can achieve a fruitful exchange of ideas that will result in progress on important problems (such as the Monodromy Conjecture) and in formulating new questions.