Conference: Monodromy and Its Applications

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/katz80 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.