External Speakers

Monday, Oct. 11, Seminar 4:00-4:50 PM and Student Fireside Chat 4:50-5:20 PM

Dr. Pratima Hebbar (Duke University), seminar on dynamical systems, stochastics and asymptotics

Seminar title:

Modeling cell growth with Branching Processes

Abstract:

In this talk, I will first introduce Galton-Watson Branching Processes and discuss some well-known results about their long-time behavior. Then, I will consider a stochastic model for the evolution of a cell population, where the number of cells grow according to a supercritical continuous-time Galton-Watson process. In addition, the mass of each cell grows in time according to a deterministic function. At the moment of branching, the total mass of the parent cell is divided among two child cells. Each child receives a random proportion of the mass of its parent cell. In a recent paper, we consider different types of growth functions, which depend on both the mass and time, and derive the long-time asymptotics of the distribution of the mass of a typical cell. I will discuss the proofs of these results as well as present numerical simulations of this model.

Biographical Sketch:

Dr. Pratima Hebbar is an Assistant Research Professor at the Department of Mathematics at Duke University. She received her Ph.D. at the University of Maryland, College Park in 2019. Her research work is in the field of Probability, Partial Differential Equations and Dynamical Systems.

Friday, Mar. 19, 4-5 PM Eastern and Student Fireside Chat 5-5:30 PM

Cindy Orozco Bohorquez (Stanford University), seminar on robust point set registration

Title: Understanding robustness of point-set registration on the n-sphere

Seminar co-hosted with Department of Mathematics Colloquium

Abstract: Point-set registration is a classical image processing problem that looks for the optimal

transformation between two sets of points. It is used in satellite communication and reconstruction of objects in computer graphics. One of its biggest challenges is the noise associated with each dataset, which can vary between precision error up to total corruption of portions of the dataset. In this work, our motivation is to understand the recovery power of different loss functions when the data has a large proportion of outliers. We focus on recovering the optimal rotation between two point-clouds that belong to a n-dimensional sphere. In this talk, we will first discuss why traditional approaches using linear algebra fail in recovering the ground truth rotation. After, we will discuss how using least-unsquared loss solves these challenges if the right domain of optimization is chosen. As a result, we will demonstrate, under a specific probabilistic model, that least-unsquared loss makes exact recovery possible regardless of the corruption level and the optimization algorithm if we have enough samples.

Tuesday, Mar. 23, Seminar 11-11:50 AM and Student Fireside Chat 11:50 AM-12:15 PM

Dr. Beth Malmskog (Colorado College), seminar on mathematics of gerrymandering

Title: Mathematics, Context, and Fair Redistricting: How Mathematics Can Detect and Prevent Gerrymandering in Colorado and Beyond

Seminar co-hosted with Virginia Tech's Women and Minority Artists and Scholars Lecture Series (WMASLS)

Abstract: Gerrymandering is the process of manipulating the boundaries of electoral districts for political gain. This is considered by many to be deeply unfair, but it has been common practice in states across the country for more than 200 years. This talk will introduce ensemble analysis, a relatively new mathematical tool to detect partisan bias in map drawing, and describe how this perspective has become central to the national conversation about fair redistricting. I will share the work our group is doing in Colorado and discuss how the same techniques can apply in every state.