WINRS, Mid-Atlantic Region:
WINRS, Mid-Atlantic Region:
Algebra and Combinatorics Session:
• Tori Akin (Duke University):
• Sahana Balasubramanya (UNC, Greensboro):
• Talia Fernos (UNC, Greensboro):
• Rebecca Goldin (George Mason University):
• Patricia Hersh (NC State):
• Bakul Sathaye (Wake Forest University):
Algebraic Geometry, Commutative Algebra and Number Theory Session:
• Candace Bethea (University of South Carolina):
• Emily Bergman (University of Delaware):
• Ela Celikbas (University of West Virginia):
• Alicia Lamarche (University of South Carolina):
• Rebecca R.G. (George Mason University):
• Ashley Wheeler (James Madison University):
Analysis, PDE and Probability Session:
• Dale Frymark (will be at Sydney-Hampton College)
• Constanze Liaw (University of Delaware)
• Jessica Kelly (Christopher Newport University)
• Benjamin Peter Russo (University of Connecticut)
• Katie Quertermous (James Madison University)
Applied Mathematics and Biomathematics Session:
• Lauren Childs (Virginia Tech):
• Maria-Veronica Ciocanel (Mathematical Biosciences Institute at The Ohio State University):
• Samantha Erwin (North Carolina State University):
• Katharine Gurski (Howard University):
• Katie Newhall (University of North Carolina at Chapel Hill):
• Leah Shaw (William & Mary):
Geometry Session:
• Danielle O’Donnol (Marymount University):
• Svetlana Katok (Penn State University):
• Heather Russel (University of Richmond):
• Radmila Sazdanovic (North Carolina State University):
• Lisa Traynor (Bryn Mawr):
History of Mathematics Session:
• Amy Ackerburg-Hastings (Smithsonian, National Museum of American History):
• Della Dumbaugh (University of Richmond):
• Nancy Hall (University of Delaware):
• Karen Parshall (University of Virginia):
• Brit Shields (University of Pennsylvania):
• Ying Wu (University of Richmond):
Topology Session:
• Rebecca Fields (James Madison University):
• Sarah Yaekel (University of Maryland):
Elizabeth DENNE (Washington & Lee University):
TBA
Jack LOVE (George Mason University):
TBA
Axel SAENX (University of Virginia): Computations and Simulations on Interacting Particle Systems from Integrable Probability.
In integrable probability, a recent field of mathematics with high activity since the turn of the century, one takes models that may arise in statistical mechanics with an extremely large number of particles (to be integrable) and introduces random variables to the evolution equations (to be a probability). The introduction of the random variables into the evolution equations is very precise and it carries much structure from sources such as algebraic combinatorics or representation theory. Then, one is able to obtain exact formulas that may be manipulated to analyze the models. Otherwise, the analysis of the model becomes intractable from the point of view of the formulas. The goal of the talk is to build basic intuition on models from integrable probability. I will introduce the totally asymmetric exclusion process (TASEP), which is related to random growth models. In particular, this introduction will rely on computations and simulations that run on the computer language Mathematica. The talk is based in part on a project from the summer 2018 UVa Math REU by Cedric Harper (UVa), Eric Keener (JMU), Fernanda Yepez-Lopez (UVa), and Ethan C. Zell (UVa) in which the students used simulations to analyze more general interacting particle systems.
• Basil Arafat (University of Richmond)
• Iva Bilanovic (George Washington University)
• Andrea Carracedo Rodriguez (Virginia Tech)
• Alex Chandler (North Carolina State University)
• Irina Georgeana Ilioaea (Georgia State University)
• Lauren Hux (Virginia Commonwealth University)
• Rebecca Jayne (Hampden-Sydney College)
• Jiahua Jiang (Virginia Tech)
• Ratna Khatri (George Mason University)
• Sarah Minucci (Virginia Commonwealth University)
• Katrina Morgan (University of North Carolina at Chapel Hill)
• Angela Reynolds (Virginia Commonwealth University)
• Rachel Rupnow (Virginia Tech)
• Kaitlyn Serbin (Virginia Tech)
• Marcella Torres (Virginia Commonwealth University)
• Melody Walker (Virginia Tech)
Emily Riehl (Johns Hopkins University): Categorifying cardinal arithmetic.
In this interactive talk we’ll prove, with help from the audience, the distributivity of multiplication over addition — a x (b + c) = a x b + a x c — not via the usual methods but by diving deeper into the question of what cardinal numbers really mean. The first deep idea is categorification, where we understand cardinal numbers as describing sizes of sets. The second step involves the Yoneda lemma, which tells us that any set can be characterized by the collection of functions for which it serves as the domain. The third deep idea describes operations + and x on sets via their universal properties, that is, by characterizing the functions whose inputs are drawn from the sets so-construted. The final step involves the notion of adjunction, in this case an operation known as “currying” in computer science. In an epilogue, we will discover that the proof just described applies in vastly more general contexts and try to understand why one would want to bother describing mathematical objects in this abstract fashion.
Kim Sellers (Georgetown University): Making Statistics that Count!
Discrete data (particularly counts) introduce an added layer of complexity to any sort of statistical analysis. While their is historically a classical distribution (namely the Poisson distribution) used to describe and/or model such data, constraining qualities bring its use into question. This talk will introduce alternative models, particularly one with which I have worked heavily to advance the field of discrete or count data modeling.