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。工作坊的日常安排将包括一系列的教学讲座，以及来自主要研究人员的关于开放问题和当前结果的演讲。将有四门小型课程，由专家就他们自己的研究主题授课，包括讲座和问题讨论。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性问题。在数学和物理的各个领域，Hitchin系统正受到越来越多的研究者的关注。这个研究生暑期学校回应了围绕希格斯束的令人兴奋的发展和兴趣，它们的光谱数据和希钦模空间，以及它们在弦理论中的实现。科学目标是向年轻的研究人员介绍该领域的重要基础知识和最新发展。所涵盖的主题将包括：1)希格斯束及其膜的模空间和希格斯模空间上相干束的等变特性（包括与朗兰兹对偶的联系）2)弦理论中希格斯系统的表现（包括M-和f -理论紧化中的t膜解）3)希格斯模空间的几何，包括希格斯模空间中的极限和几何结构；以及模空间两端与Calabi-Yau三倍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理论（包括弦对偶）中的作用。会议的网站可在http://scgp.stonybrook.edu/archives/25133.This上找到。奖项反映了NSF的法定使命，并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，被认为值得支持。

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.