Tuesday, December 4, 2018
12/04/2018 - 4:00pm
Abstract: New, more effective cancer therapies have upended traditional randomized controlled trials. For targeted therapies and immunotherapies, single-arm trials made up heterogeneous groups of patients have become common. This change has motivated the development of new techniques for identifying patient subtypes based individual-level features. In this talk, we will present a framework based on a latent-space construction to characterize patients by their subtype, increase the predictive response rate, and construct counterfactuals to distinguish the effect of a drug from that of the subtype. Applications based on real trials will be included to illustrate these points. This is joint work with Brian Hobbs at the Cleveland Clinic.
12/04/2018 - 4:15pm
The study of eigenvarieties began with Coleman and Mazur, who constructed the first eigencurve, a rigid analytic space parametrizing $p$-adic modular Hecke eigenforms. Since then various authors have constructed eigenvarieties for automorphic forms on many other groups. We will give bounds on the eigenvalues of the $U_p$ Hecke operator appearing in Chenevier’s eigenvarieties for definite unitary groups. These bounds generalize ones of Liu-Wan-Xiao for dimension $2$, which they used to prove a conjecture of Coleman-Mazur-Buzzard-Kilford in that setting, to all dimensions. We will then discuss the ideas of the proof, which goes through the classification of automorphic representations that are principal series at $p$, and a geometric consequence.