Spring 2018 Graduate Student Seminar



Meeting Tuesdays at 3:00pm in room WXLR A202.

Date Speaker Title & Abstract (click the title to expand)
01/30 Lauren Crider

Situations in which the volume of collected data overtaxes capacity to communicate and store it for centralized processing are increasingly common in applications -- in particular when the data are measurements made by high-bandwidth sensors. When the objective of data collection is to support a binary hypothesis test, one well-studied approach is to perform a set of tests each of which uses only part of the data; e.g., each node in a distributed sensor network processes its data separately and transmits only its “local” decision to a central location to a central node that synthesizes a “global” decision. The first part of this presentation will review the basics of statistical hypothesis testing and apply these to develop rules for synthesizing a global decision from the collection of local decisions. The second part will discuss some ongoing research on polling of the local decision makers by the central node.

02/06 Joseph Wells

Beginning in the 1920's, Dehn and Nielsen studied a homeomorphism invariant of manifolds called the mapping class group, which is closely related to the fundamental group. Especially in the past 50 years, the study of mapping class groups has been a very active area of research for their rich geometric and dynamic properties. In this talk, I'll give an introduction to mapping class groups and the Neilsen-Thurston classification of automorphisms of closed, oriented surfaces.

02/13

02/20 Mela Hardin

Abstract Interacting particle systems is a field of probability theory devoted to the rigorous analysis of certain types of models that arise in other fields such as statistical physics, biology, and economics. These systems are motivated by the voter model for the dynamics of opinions. A one-dimensional voter model is a stochastic process where individuals are located on the integer line who at any time can have one of two opinions denoted by 0 or 1. These individuals update their opinion at a constant rate of one based on the opinion of their two neighbors chosen uniformly at random. In my research with Drs. Lanchier and Scarlatos, we introduce an opinion graph – a finite connected graph in which the vertices represent the set of opinions. This allows for more than two opinions in the model. In addition, we also introduce a confidence threshold that dictates whether an individual interacting with a neighbor move one step towards the opinion of the other individual on the opinion graph. The main question about the general opinion model is whether the system fluctuates and clusters, leading the population to a global consensus, or fixates in a fragmented configuration. My talk will mostly focus on the background and the mathematical tools we use in this research.

02/27 Brady Gilg

Abstract TBD

03/13 David Polletta

Abstract TBD

03/20 Dylan Weber

Abstract TBD

03/27 Mario Giacomazzo

Abstract TBD

04/03 Camille Moyer

Abstract TBD

04/10

04/17 Mary Cook

Abstract TBD

04/24