Search Research Symposium Abstracts

A $p$-adic analytic Brauer group

The Brauer group of a local field plays a central role in class field theory. On one hand, the Brauer group of a field $K$ classifies central simple algebras, up to Morita equivalence. On the other hand, the Brauer group $\mathrm{Br}(K)$ is identified with the Galois cohomology $H^2(\mathrm{Gal}_K, \overline{K}^\times)$. In this talk, we introduce a [Read More...]

Presenter: Deewang Bhamidipati, UC Santa Cruz
Authors: Deewang Bhamidipati
Symposium Year: 2023
Session: Rethinking Number Theory [Organized by Deewang Bhamidipati, Eva Goedhart, and Amita Malik]
Presentation Time: September 30, 2023; 10:35 am

A Dedekind-Rademacher homomorphism for Bianchi groups*

We construct a generalization of the Dedekind-Rademacher homomorphism to congruence subgroups of $\mathrm{SL}_2(\mathbb C)$, and derive some of its basic properties. These results have applications of this work including special values of L-functions and Sharifi's Conjectures. Time permitting, we may also discuss an extension of this work to the [Read More...]

Presenter: Kim Klinger-Logan, Kansas State University
Authors: Kim klinger-Logan, Kalani Thalagoda, Tung Nguyen, Tian An Wong
Symposium Year: 2022
Session: Rethinking Number Theory
Presentation Time: June 18, 2022; 3:45 pm

A definition of fractional k-dimensional measure

I will introduce a fractional notion of k-dimensional measure, with 0≤k<n, that depends on a parameter σ that lies between 0 and 1. When k=n−1 this coincides with the fractional notions of area and perimeter, and when k=1 this coincides with the fractional notion of length. We will see that, when multiplied by the factor 1−σ, this σ-measure [Read More...]

Presenter: Cornelia Mihaila, Saint Michael's College
Authors: Cornelia Mihaila, Brian Seguin
Symposium Year: 2023
Session: Advances in Partial Differential Equations and Applications [Organized by Maya Chhetri, Nsoki Mavinga and Irina Mitrea]
Presentation Time: September 30, 2023; 2:25 pm

A discussion of future directions and challenges facing researchers in mathematical biology today

The session will conclude with a discussion that looks to the future of the field. Emerging motivation for new work in mathematical biology will be discussed, including healthcare challenges and an explosion of available data. We will discuss the advantages of current approaches, including their ability to develop large-scale predictions, patient-specific [Read More...]

Presenter: Rayanne Luke, George Mason University
Authors: Rayanne Luke, Sarah Strikwerda, and Prajakta Bedekar
Symposium Year: 2023
Session: Early Career Researchers in Mathematical Biology and Differential Equations [Organized by Rayanne Luke, Sarah Strikwerda, and Prajakta Bedekar]
Presentation Time: October 2, 2023; 9:45 am

A Graph Theoretic Approach to Regularity of Toric Ideals

One measure of the complexity of an ideal is its regularity, which may be difficult to compute with algebraic tools. To study the regularity of certain toric ideals (prime ideals generated by differences of monomials) with quadratic initial ideals, we instead make use of correspondences between the initial ideals and graphs. Moreover, a key theorem by [Read More...]

Presenter: Beth Anne Castellano, Lafayette College
Authors: Beth Anne Castellano, Marcella Manivel
Symposium Year: 2022
Session: Poster Presentation
Presentation Time: June 17, 2022; 2:45 pm

A Graph Theory Based Approach to Modeling Dynamic Wind Turbine Yaw

Yaw control has shown great potential as a method for increasing the power output of wind farms but there have been relatively few efforts to model the dynamic behavior of an array of dynamically yawing turbines. When a turbine is dynamically yawed, the wake created by that turbine is deflected and its shape changes, which also affects the dynamics of [Read More...]

Presenter: Genevieve M Starke, Johns Hopkins University
Authors: Genevieve M. Starke, Charles Meneveau, Jennifer R. King, and Dennice F. Gayme
Symposium Year: 2022
Session: Systems and Control
Presentation Time: June 18, 2022; 4:35 pm

A graph-theoretic approach to analyzing decoding failures of BIKE

We present experimental findings on the decoding failure rate (DFR) of BIKE, a fourth-round candidate in the NIST Post-Quantum Standardization process, at the 20-bit security level using graph-theoretic approaches. We select parameters according to BIKE design principles and conduct a series of experiments using Rust to generate significantly more decoding [Read More...]

Presenter: Angela Robinson, PhD, NIST
Authors: Sarah Arpin, Tyler Raven Billingsley, Daniel Rayor Hast, Jun Bo Lau, Ray Perlner, Angela Robinson
Symposium Year: 2023
Session: Rethinking Number Theory [Organized by Deewang Bhamidipati, Eva Goedhart, and Amita Malik]
Presentation Time: October 1, 2023; 2:25 pm

A mathematical model of inflammatory-stress-cardiovascular dynamics in response to an endotoxin challenge

A pathogenic, surgical, or wound-related threat to the body enacts a complex immune response that, when successful, eradicates the threat and returns the body to homeostasis. Two subsystems that play a key role in regulating inflammation from the immune response include the hypothalamic-pituitary-adrenal (HPA) axis and the cardiovascular system. The dynamics [Read More...]

Presenter: Kristen A Windoloski, North Carolina State University
Symposium Year: 2022
Session: Poster Presentation
Presentation Time: June 18, 2022; 2:00 pm

A mathematical model of microtubule assembly and polarity in dendrites

In neurons, the microtubule cytoskeleton is responsible for long-range and long-term intracellular transport of mRNAs and proteins. Microtubules, comprised of tubulin dimers, are defined by their polarity and their highly dynamic assembly process, where each end of the microtubule can grow and depolymerize by stochastically switching between states of [Read More...]

Presenter: Anna C. Nelson, Duke University
Authors: Anna C. Nelson, Maria-Veronica Ciocanel, Scott McKinley, and Melissa Rolls
Symposium Year: 2022
Session: Poster Presentation
Presentation Time: June 18, 2022; 2:00 pm

A Mathematical Model of Particle Deposition in the Human Lung

Respiratory syncytial virus (RSV) is the leading respiratory disease in infants and young children. Jet nebulizers, which deliver aerosolized drugs to the lung, are commonly used to treat RSV. However, they are ineffective at delivering drug to the lower pediatric lung. A combination of factors leads to this inefficiency, including smaller airways, lower [Read More...]

Presenter: Jordana O'Brien, Rochester Institute of Technology
Authors: Jordana O'Brien, Kara Maki, Jennifer O'Neil
Symposium Year: 2023
Session: Early Career Researchers in Mathematical Biology and Differential Equations [Organized by Rayanne Luke, Sarah Strikwerda, and Prajakta Bedekar]
Presentation Time: October 1, 2023; 9:45 am

A mathematical model of phenotypic plasticity for Arizona Tiger Salamanders

Phenotypic plasticity is the ability of an organism to change its phenotype in response to changes in the environment. General mathematical descriptions of the phenomenon rely on an abstract measure of “viability”. In the case of the Arizona Tiger Salamander, the organism has a point in its development when, upon maturing, it may take two very different [Read More...]

Presenter: Maeve Lewis McCarthy, Murray State University
Authors: Maeve L. McCarthy, Dorothy I. Wallace
Symposium Year: 2023
Session: Exploring the Intersection of Mathematics and Ecology: Research Applications and Findings [Organized by Lakmali Weerasena and Maeve McCarthy]
Presentation Time: September 30, 2023; 10:10 am

A mathematical model of platelet aggregation and fibrin polymerization

The formation of a blood clot involves complex biophysical and biochemical processes that occur under flow. In the event of an injury, platelets become active and weakly aggregate to form a plug at the injury site. Activated platelets express binding sites for procoagulant species, and platelet surface-bound complexes convert zymogen prothrombin into enzyme [Read More...]

Presenter: Anna C. Nelson, Duke University
Authors: Anna C. Nelson, Aaron L. Fogelson
Symposium Year: 2022
Session: Recent Advances in Mathematical Biology
Presentation Time: June 19, 2022; 8:50 am

A mathematical modeling exploration of data assimilation for simple model fitting

Data Assimilation (DA) techniques, such as Kalman filtering, have historically been employed in engineering applications, but are rarely used by mathematical modelers or taught to mathematics students. However, because of DA's fusing of mechanistic modeling with machine-learning approaches, it holds great potential for strengthening the predictive power of [Read More...]

Presenter: Christina Catlett, Scripps College
Authors: Christina Catlett, Lisette de Pillis, An Dela, Christina J. Edholm, Daniel Shenker, Blerta Shtylla, Rachel Wander, Maya Watanabe
Symposium Year: 2022
Session: Recent Developments in Ecological and Epidemiological Modeling
Presentation Time: June 17, 2022; 10:15 am