An introduction to topological combinatorics The chromatic number of a graph is the number of vertex colors needed so that adjacent vertices have different colors. In 1955, Kneser made a conjecture about the chromatic number of a certain family of graphs (now called Kneser graphs). This conjecture remained unproven for 23 years until Lovász gave […]

Title:Defining Persistence Diagrams for Cohomology of a Cofiltration Indexed Over a Finite Lattice Advisor: Dr. Amit Patel Committee: Dr. Mark Shoemaker, Dr. Dustin Tucker Persistent homology and cohomology are important tools in topological data analysis, allowing us to track how homological features change as we move through a filtration of a space. Original work in […]

The Buzz about BHZ: The Life and Times of Brauer's Height Zero Conjecture Mandi Schaeffer Fry Metropolitan State University of Denver In 1955, Richard Brauer, often regarded as the founder of modular representation theory, made one of the first of the so-called ``local-global'' conjectures in character theory and opened the door to an entire area […]

Advisor: Dr. Maria Gillespie Committee: Dr. Alexander Hulpke, Dr. Mark Shoemaker, Dr. Sudipto Ghosh Title: Generalized RSK for enumerating projective maps from $n$-pointed curves A recent result of Farkas and Lian in enumerative geometry arose in the study of linear series on curves. The theory of Schubert calculus leads to a natural combinatorial interpretation of […]

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. […]