Conference: Monodromy and Its Applications

这次会议将讨论monodromy的一般主题。当一个数学对象在一个空间上平滑地变化时，单值性就发生了，在一个点和附近的每个点上看起来都是一样的，但是在空间中绕一个圈移动会导致对象扭曲。单值性贯穿于整个数学中，特别是在莫比乌斯带中可以看到：每一小块都是一张普通的纸，但是绕着圆运动会导致纸翻转到相反的一边。这次会议将提供一个历史的角度来看，叙述目前的结果，并期待monodromy的未来发展。会议的主题将是monodromy在其所有化身的关键作用：经典和l-adic，本地和全球，算术和几何，它在数论和代数几何的应用，以及它的连接到群论和表示论。近年来，这一领域出现了一些令人兴奋的发展。这些包括有限的完整分类Katz，Rojas-Le 'on和Tiep作为超几何层的单值群出现的（几乎准）简单群，Landesmann和Litt对Putman-Wieland猜想的许多情况的证明，许多数学家在新的设置中计算Tannakian单值群，以及Lawrence和Sawin对Shafarevich猜想的推广的应用，证明了一个相对类似的格罗滕迪克时期猜想的一个家庭的品种巴克和Tsimerman，并证明了无界的concatators猜想的Calegari，Dimitrov和唐。会议将讨论与这些和其他表现形式的monondromy在数学的发展。会议网站https://www.math.princeton.edu/katz80This奖反映了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的支持。

This conference will discuss the general topic of monodromy. Monodromy occurs when a mathematical object varies smoothly over a space, appearing identical at a point and each nearby point, but traveling around a loop in the space causes the object to twist around. Monodromy occurs throughout mathematics and specifically can be seen in the M¨obius strip: each small piece is an ordinary piece of paper, but traveling around the circle causes the paper to flip around to the opposite side. This conference will provide a historical perspective, recount current results, and look forwad to future developments in monodromy.The main theme of the conference will be the key role of monodromy in all its incarnations: classical and l-adic, local and global, arithmetic and geometric, applications of it in number theory and algebraic geometry, and its connections to group theory and representation theory. In recent years there have been a number of exciting developments in this area. These include the complete classification of the finite (almost quasi) simple groups that occur as monodromy groups of hypergeometric sheaves by Katz, Rojas-Le´on and Tiep, the proof of many cases of the Putman-Wieland conjecture by Landesmann and Litt, the calculation of Tannakian monodromy groups in new settings by many mathematicians and their applications to generalizations of Shafarevich’s conjecture by Lawrence and Sawin, the proof of a relative analogue of Grothendieck’s period conjecture for a family of varieties by Bakker and Tsimerman, and the proof of the unbounded denominators conjecture by Calegari, Dimitrov, and Tang. The conference will discuss developments related to these and other manifestations of monondromy in mathematics. Conference website https://www.math.princeton.edu/katz80This 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.