In the previous talks of this series we met the Kneser graph and the character theory of finite groups. In this talk we will revisit these topics, this time through the lens of spectral graph theory. In particular, we will discuss what eigenvalues can tell you about a graph and introduce some other families of […]

We are excited to announce that the University of Colorado, Boulder and Colorado State University, Fort Collins will be hosting Front Range Number Theory Day on October 8th, 2022, at University of Colorado in Boulder. The goal of the FRNTD is to provide a venue for faculty, graduate students, and undergraduates on the Front Range […]

Speaker: Facundo Mémoli from Ohio State University Title: Gromov-like distances between spheres Abstract: Distances between metric spaces such as the Gromov-Hausdorff distance and its Optimal Transport variants are nowadays often invoked in applications related to data classification. Interestingly, the precise value of these distances on pairs of canonical shapes is known only in very limited cases. In […]

Title: Singular Flavors of Compressive Sensing Abstract: About fifteen years ago, a couple of groundbreaking papers revealed the possibility of faithfully recovering high-dimensional signals from far fewer measurements than expected. This realization, coupled with the conception of practical procedures to perform the recovery, gave rise to a vigorous scientific field called compressive sensing. There is […]

This Thursday's Fragment seminar speaker will be our own Clayton Shonkwiler, speaking on Frames, Geometric Invariant Theory, and Optimization.

Department of Mathematics, Texas A&M University Paper Folding: Modeling, Analysis and Simulation The unfolding of a ladybird's wings, the trapping mechanism used by a flytrap, the design of self-deployable space shades, and the constructions of curved origami are diverse examples where strategically placed material defects are leveraged to generate large and robust deformations. With these […]

Advisor:  Dr. Jennifer Committee:  Dr. Margaret Cheney, Dr. Patrick Shipman, Dr. Marlis Rezende Title: An Inverse Problem and Multi-Compartment Lung Model for the Estimation of Lung Airway Resistance throughout the Bronchial Tree Abstract: Mechanical ventilation is a vital treatment for patients with respiratory failure, but mechanically ventilated patients are also at risk of ventilator-induced lung […]

Advisor: Dr. Jeff Achter Committee:  Dr. Rachel Pries, Dr. Jamie Juul, Dr. Indrajit Ray Title: Explicit and quantitative results for abelian varieties over finite fields Abstract: Given an elliptic curve $E$ over a finite field, one may study the number of points of $E$, as well as the number of curves in its isogeny class. […]

Title: Time Integration Methods and Software for Scientific Simulations Abstract: Time-dependent systems are at the heart of numerous scientific applications requiring simulation.  While single rate, fixed step size time integration methods have been used for decades, adaptive step methods and schemes that can efficiently evolve problems with multiple time scales have not yet been fully […]

Polytopes count (introductory talk) Aram Bingham Colorado School of Mines We'll see how many problems in combinatorics can be converted to the problem of counting integral points inside appropriate polytopes. Not only is this conversion a practical advantage in settings where nice, closed formulas for combinatorial quantities aren't available, but phrasing computations as integral point-counting […]

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 […]