Mirror Symmetry in the Midwest 2012

这项提议是关于2012年11月8日至11日在威斯康星大学举行的名为第二次中西部镜面对称的会议，这是2011年11月在堪萨斯州立大学举行的会议的延续。镜像对称是一个相对较新的课题，在过去的二十年里引起了人们的极大关注。镜像对称起源于弦理论，是对某些物体的复几何和辛几何之间的对偶的研究。多年来，研究这一主题的方法越来越多，今天，许多研究人员可以说正在研究一门受到镜面对称启发的学科。在过去的二十年里，镜像对称领域的迅速发展激发了复几何、代数几何和辛几何的大量研究。这些思想--受镜像对称启发的代数和几何理论--构成了会议的科学焦点。重要的创新包括Gromov-Witten不变量、Fukaya范畴和热带几何。此外，镜像对称性重新引起了人们对现有学科的关注，并极大地扩展了现有学科的范围--Floer理论、派生范畴和特殊的拉格朗日几何就是几个例子。对镜面对称性的解释不仅将提供复几何和辛几何之间的联系，而且还将对当前广泛的主题产生深远的影响。拟议中的会议的目标是将研究镜面对称性的广泛方面的研究人员聚集在一起。这次会议将加强中西部研究人员之间的合作，并将特别注意从中西部招募参与者以促进这一目标。这次会议的一个重要补充是引进了区域外的专家。会议将吸引具有不同背景的广泛参与者。会议的一个基本特点将是教育。讲座的一部分将构成一个面向研究生和非专家的“小型课程”，目的是介绍该领域的某些方面。迷你课程的目标有两个：一是开放和促进不同专业领域的研究人员之间的交流；二是让研究生参与、兴奋并积极参与会议的科学活动。除了上面强调的影响--增加中西部研究人员之间的合作，向研究生和年轻研究人员教授有关这一主题的知识--希望这次会议将导致建立一年一度的中西部镜像对称会议。会议的另一个目的是扩大威斯康星大学研究镜像对称相关领域的数学家小组与堪萨斯州立大学M中心(镜像对称中心)之间的地区联系。镜面对称性起源于高能物理和弦理论，而其中涉及的数学知识对这些科学产生了影响。为了利用这些联系，这次会议将有物理学家和数学家参加。更多信息请访问会议websitehttp://www.math.wisc.edu/~oh/uw-ksu-index.html

This proposal is for a conference entitled Mirror Symmetry in the Midwest II to be held at University of Wisconsin from November 8-11, 2012, which is a continuation of the one held in Kansas State University in November 2011. Mirror symmetry is a relatively new subject that has attracted a great deal of attention over the past two decades. Mirror symmetry has its roots in string theory and is the study of a duality between the complex and symplectic geometry of certain objects. The number of ways to approach the subject has grown vast over the years and today many researchers can be said to be studying a subject inspired in some way by mirror symmetry. The rapidly expanding field of mirror symmetry has inspired a great deal of the research in complex, algebraic and symplectic geometry over the past twenty years. These ideas--the algebraic and geometric theories inspired by mirror symmetry--form the scientific focus of the conference.Important innovations include Gromov-Witten invariants, Fukaya categories and tropical geometry. In addition, mirror symmetry has cast renewed attention on and greatly expanded the scope of existing disciplines--Floer theory, derived categories, and special Lagrangian geometry are a few examples. An explanation of mirror symmetry would not only provide a link between complex and symplectic geometry, but it would also have a deep impact on a wide range of current subjects.The goal of the proposed conference is to bring together researchers studying a wide range of aspects of mirror symmetry. The conference will lead to increased collaboration among researchers in the Midwest and special attention will be paid to recruiting participants from the Midwest to further this aim. An important additional point of the conference is to bring in experts from outside the region. The conference will attract a wide range of participants with a diversity of backgrounds. An essential feature of the conference will be education. A portion of the talks will constitute a ``mini-course'', aimed at graduate students and non-experts and intended to give an introduction to some aspect of the field. The goals of the mini-course are two fold: One, to open and facilitate lines of communication between researchers with different areas of expertise; and two, to get graduate students involved, excited and actively participating in the scientific activities of the conference. In addition to the impacts highlighted above--increasing collaboration among researchers in the Midwest and teaching graduate students and young researchers about the subject--it is hoped that the conference will lead to the founding of an annual Midwest mirror symmetry conference. Another intent of the the conference is to expand the regional ties between University of Wisconsin group of mathematicians working on the areas related to mirror symmetry and the M-Center (Mirror Symmetry Center) at Kansas State University. Mirror symmetry has its roots in high-energy physics and string theory and the mathematics involved has an impact on these sciences. To take advantage of these ties, the conference will feature physicists and mathematicians.More information can be found on the conference websitehttp://www.math.wisc.edu/~oh/uw-ksu-index.html