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 […]

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 […]