TBA | Geoff Kocks (MIT)

Stop by for snacks and tea with the SHASS community, students, and instructors!HumaniTea is a program partnering with other units in SHASS to gather, share some food and thought, and enrich our shared MIT experience in the process. Once a month, SHASS community members, instructors, and students from diverse fields of studies, backgrounds, and interests can stop in and enjoy a cup of tea or snack.Building 14E-304* *Directions: Third floor of Building 14 from the Lewis Music Library stairs, through the CMS/W doors. Alternatively, take the elevator to the 3rd floor and navigate to the opposite end of the hallway, through third floor and CMS/W doors!

Speaker: Gefei Cai (Peking)Title: Disconnection and non-intersection probabilities of Brownian motion on an annulusAbstract:We derive an exact formula for the probability that a Brownian path on an annulus does not disconnect the two boundary components of the annulus. The leading asymptotic behavior of this probability is governed by the disconnection exponent obtained by Lawler-Schramm-Werner (2001) using the connection to Schramm-Loewner evolution (SLE). The derivation of our formula is based on this connection and the coupling with Liouville quantum gravity (LQG), from which we can exactly compute the conformal moduli of random annular domains defined by SLE curves. Using a similar approach, we also derive exact formulas for the non-intersection probabilities of independent Brownian paths on an annulus, as well as extend the result to the case of Brownian loop soup. Based on joint work with X. Fu, X. Sun, and Z. Xie, and upcoming work with Z. Xie.

Speaker: Jared Weinstein (Boston University)Title: On the splitting conjecture of HopkinsHopkins’ splitting conjecture predicts the structure of a double localization 𝐿𝐾(𝑡) 𝐿𝐾(ℎ) 𝑆 of the sphere spectrum, where 𝐾(ℎ) is Morava 𝐾-theory at a prime 𝑝 and 0 < 𝑡 < ℎ. Perfectoid techniques give powerful evidence for the conjecture while avoiding explicit computation. We show (a) the conjecture is true for (ℎ, 𝑡) = (2, 1) and 𝑝 odd, recovering a difficult result of Shimomura and Yabe, and (b) for ℎ general and 𝑡 = ℎ − 1, the conjecture is true "up to perfection". This is joint work with Lucas Mann, Rin Ray, and Xinyu Zhou.

Marleen Marra (CEPR)