Mirror Symmetry in the Midwest 2012

本提案是关于将于2012年11月8日至11日在威斯康星州大学举行的题为“中西部镜像对称II”的会议，该会议是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性的研究。多年来，研究这个问题的方法越来越多，今天，许多研究人员可以说是在研究一个以某种方式受到镜像对称启发的主题。在过去的二十年里，镜像对称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--镜像对称所激发的代数和几何理论--形成了会议的科学焦点。重要的创新包括Gromov-Witten不变量、福谷范畴和热带几何。此外，镜像对称性重新引起了人们的注意，并极大地扩展了现有学科的范围--弗洛尔理论、派生范畴和特殊拉格朗日几何就是几个例子。镜像对称的解释不仅提供了复杂和辛几何之间的联系，但它也将有一个深刻的影响，对广泛的当前subjects.The拟议会议的目标是汇集研究人员研究镜像对称的广泛方面。这次会议将导致在中西部的研究人员之间的合作增加，并将特别注意从中西部招募参与者，以进一步实现这一目标。会议的另一个重要方面是邀请该区域以外的专家参加。会议将吸引具有不同背景的广泛参与者。会议的一个重要特点是教育。讲座的一部分将构成一个"微型课程“，针对研究生和非专家，旨在介绍该领域的某些方面。迷你课程的目标有两个方面：一是开放和促进具有不同专业领域的研究人员之间的沟通;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，并向研究生和年轻研究人员讲授这一主题--希望这次会议将导致成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州大学数学家小组在镜像对称相关领域的工作和M中心（镜像对称中心）在堪萨斯州立大学之间的区域联系。镜像对称起源于高能物理学和弦理论，而其中涉及的数学对这些科学产生了影响。为了充分利用这些联系，会议将邀请物理学家和数学家参加。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