Graduate Summer School on the Mathematics and Physics of Hitchin Systems

暑期学校“希钦系统数学和物理研究生暑期学校”将于2019年5月27日至31日在西蒙斯几何和物理中心举行。暑期学校的目标是促进和促进数学和物理学这一快速发展领域的跨学科研究。该活动将汇集来自不同机构和背景的有才华的初级研究人员，向该领域的领导者学习。研讨会的日常日程安排将包括一系列教学讲座以及领先研究人员关于开放问题和当前结果的演讲。将有四个小型课程，由专家就接近他们自己的研究主题，包括讲座和问题会议的组合。在下午，还将有该领域专家的高级研究讲座，让年轻的参与者了解该领域最新的开放问题。希钦系统正在受到数学和物理各个领域研究人员越来越多的关注。这个研究生暑期学校响应围绕希格斯束，他们的光谱数据和希钦模空间，以及他们在弦理论中的实现令人兴奋的发展和兴趣。科学目标是向年轻研究人员介绍该领域的重要基础和最新发展。涵盖的主题包括：1）通过Hitchin纤维化和Hitchin模空间上相干层的等变特征，得到了Higgs丛及其膜的模空间（包括与朗兰兹对偶的链接）2）希钦系统在弦理论中的出现（包括M-和F-理论的解释中的T-膜解）3）希钦模空间的几何，包括希钦纤维化中的极限和几何结构，以及模空间的端点与Calabi-Yau三重Donaldson-Thomas不变量的代数研究的关系。4）Hitchin和Calabi-Yau可积系统之间的联系及其在弦论中的作用会议网站可在www.example.com上获得。http://scgp.stonybrook.edu/archives/25133.This奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估来支持。

The summer school "Graduate Summer School on the Mathematics and Physics of Hitchin Systems" will take place on May 27th-31st, 2019 at the Simons Center for Geometry and Physics. The goal of the summer school is to promote and facilitate interdisciplinary research in this rapidly developing field within mathematics and physics. The event will bring together talented junior researchers from a diverse range of institutions and backgrounds to learn from leaders in the field. The daily schedule of the workshop will feature a series of pedagogical lectures as well as talks from leading researchers on open questions and current results. There will be four mini-courses by experts on topics close to their own research, including a mix of lectures and problem sessions. During the afternoons, there will also be advanced research talks by experts in the field, exposing young participants to the most current open questions in the area.Hitchin systems are receiving ever increasing attention from researchers in diverse areas of mathematics and physics. This Graduate Summer School responds to the exciting developments and interest around Higgs bundles, their spectral data and the Hitchin moduli space, as well as their realizations within string theory. The scientific goal is to introduce young researchers to important fundamentals and recent developments in the field. Topics covered will include:1) The moduli space of Higgs bundles and its branes through the Hitchin fibration and equivariant characters of coherent sheaves on the Hitchin moduli space (including links to Langlands duality)2) Appearances of Hitchin systems within string theory (including T-brane solutions within compactications of M- and F-theory)3) The geometry of the Hitchin moduli space, including limits and geometric structures within the Hitchin fibration, and the relation of ends of the moduli space to the algebraic study of Donaldson-Thomas invariants of Calabi-Yau threefolds.4) Links between Hitchin and Calabi-Yau integrable systems and their role in string theory (including string dualities).The conference website is available at http://scgp.stonybrook.edu/archives/25133.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.