Tuesday, November 19, 2019
Time  Items 

All day 

4pm 
11/19/2019  4:00pm Abstract: Informed by physiology, the waveshape oscillatory model for biomedical time series asserts that cycles lie on or near a lowdimensional manifold. Recovering this manifold provides insight into the dynamics of the underlying system. I present a manifold learning framework for biomedical time series analysis, and I provide a guarantee on the dynamical information which can be recovered using this framework. We will discuss several applications in the analysis of electrocardiograms and blood pressure monitoring. Timepermitting, we will examine further approaches to biomedical time series analysis which fuse traditional signal processing with modern mathematics. Location:
LOM 215
11/19/2019  4:15pm When geometric structures on surfaces are determined by the lengths of curves, it is natural to ask which curves’ lengths do we really need to know? It is a classical result of Fricke that a hyperbolic metric on a surface is determined by its marked simple length spectrum. More recently, Duchin–Leininger–Rafi proved that a flat metric induced by a unitnorm quadratic differential is also determined by its marked simple length spectrum. In this talk, I will describe a generalization of the notion of simple curves to that of qsimple curves, for any positive integer q, and show that the lengths of qsimple curves suffice to determine a nonpositively curved Euclidean cone metric induced by a qdifferential metric. Location:
DL 431
11/19/2019  4:15pm Abstract: We describe a Breuil–Mezard type conjecture that relates structure of mod l fibers of deformation rings of the Galois group of a local field K (which has residue characteristic p different from l) to deformations of smooth mod l representations of GL_n(K). These conjectures are centered around the compatibility between inertial local Langlands and its mod l version. We sketch a proof of a weaker version of the conjecture, when K is a local function field, using the Taylor–Wiles–Kisin patching method. If time permits, we will report on some progress on variants for the conjecture for inner forms. Location:
LOM 205

5pm 
11/19/2019  5:00pm Abstract: A matroid is a combinatorial object generalizing the idea of “linear independence” of a set in vector spaces. One example of a matroid is the edge set of a finite graph together with all forests in the graph. Such matroids can be used to prove the correctness of various greedy algorithms for finding spanning trees of a finite graph. Besides this instance of matroids, I want to share with you some invariants of general matroids and their incarnations in geometry that connect combinatorics, graph theory and algebra.
Location:
LOM 206
