Expander graphs arising from finite groups Martin Kassabov Cornell University Informally, expander graphs are  graphs which can not be easily disconnected.  In the case of bounded degree, this property is equivalent to a spectral gap in the Laplacian matrix of the graph. Margulis was the first to find an explicit construction of expander graphs, relating […]

TITLE: The Kuramoto model and Synchronization ABSTRACT: Synchronization occurs in many natural and technological systems, from cardiac pacemaker cells to coupled lasers. In the synchronized state, the individual cells or lasers coordinate the timing of their oscillations, but they do not move through space. A complementary form of self-organization occurs among swarming insects, flocking birds, […]

Advisor:  Dr. Jeff Achter Committee:  Dr. Rachel Pries, Dr. Alexander Hulpke, Dr. Maria Gillespie, Dr. Shrideep Pallickara Title: Counting the Size of an Isogeny Class of Drinfeld Modules over Finite Fields via Frobenius Distribution Abstract: Drinfeld modules are the function field analogue to elliptic curves. Two Drinfeld modules are isogenous if and only if they […]

Advisor:  Dr. Rachel Pries Committee:  Dr. Jeff Achter, Dr. Mark Shoemaker, Dr. Maria Rugenstein Title: Relative oriented class groups of quadratic extensions Abstract: Perhaps the most beautiful development in the theory of binary quadratic forms was the work of Gauss in his Disquisitiones Arithmeticae in which he described the underlying group structure of binary quadratic […]

Advisor:  Dr. Margaret CheneyCo-Advisor:Dr. Raghu Raj Committee:  Dr. Emily King, Dr. Mahmood Azimi-Sadjadi Title: Deep Compound Gaussian Prior for Linear Inverse Problems Abstract: Linear inverse problems are common in a variety of areas including compressive sensing and image reconstruction, which have applications in radar, sonar, medical, and tomographic imaging. Model-based and data-driven methods are two […]

The singular locus of regular Hessenberg varieties Martha Precup Washington University in St. Louis Hessenberg varieties are subvarieties of the flag variety with important connections to representation theory, algebraic geometry, and combinatorics. Like Schubert varieties, the structure of Hessenberg varieties can be studied using the combinatorics of the symmetric group. In this talk, we will […]

Workshop series with Robin Wilson and Nina White presenting on Groupwork, Equity, and Student Buy-In in. The workshop will be roughly 55 minutes in length followed by time for questions and answers. Workshop held remotely https://converse.zoom.us/j/92396141820

Advisor:  Dr. Henry Adams Committee:  Dr. Chris Peterson, Dr. Amit Patel, Dr. Asa Ben-Hur Title: Persistence and Metric Thickenings Abstract: This talk will cover multiple related topics in applied topology.  Persistent homology, the main tool of applied topology, is based on the algebraic theory of persistence modules.  This theory has developed over roughly the last […]