The Category of Sets and Constructing Combinatorial Data Structures. Abstract: Set theory is the foundation of modern mathematics, but the commonly used foundations are poorly suited for the everyday reasoning of mathematicians. They are also poorly suited for implementation in software. This talk will present an axiomatization of Set Theory due to Lawvere (1964) as […]
Miklos Bona: Combinatorics of Genome Rearrangements We will discuss a few biologically motivated sorting algorithms in which we model genomes by permutations. We define various notions of evolutionary distance, and discuss some open problems. Best, Miklos Bona
A talk on counting the number of primes in different patterns. Click for slides Click for YouTube link (talk starts at 5:30)
Title: Branching processes in epidemiology Abstract: I will give a brief intro to the probability generating functions and use the PGFs to study the Galton-Watson branching process. Specifically, I will explicitly calculate the mean and the variance of the G-W BP in time as well as the probability of ultimate extinction of the process. Then […]
Modeling Virus Dynamics – Dr. Rong Abstract: Mathematical models, combined with experimental data, have made significant contributions to our understanding of virus dynamics. In this talk, I will introduce some models developed to study virus infections (HIV, hepatitis, influenza, and the recent coronavirus), drug treatment, and immune responses. Model formulation, mathematical analysis, and validation by […]
By: Dr. Meera Sitharam Abstract: Given a triangulation of points in the plane, a flip deletes an edge e whose removal leaves a convex quadrilateral and replaces e by the opposite diagonal of the quadrilateral. In the topological setting, a triangulation of a closed surface is an equivalence class permitting points to be moved freely […]
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By Dr. Bartosova Abstract: The notoriously known pigeonhole principle will set us off on a tour through different areas of mathematics, where we can encounter different manifestations of the Ramsey-like behavior.
By Cooper O’Kuhn Abstract: The Mondrian Puzzle is a problem dealing with tessellations of rectangles inside of a square of integer length. In juxtaposition to the geometric nature of this problem, the Mondrian Puzzle has seen the most advancements through applications of number-theoretic and combinatorial arguments. As well as being a great opportunity for research, […]
Abstract: It is well known that there are numerous ties between different fields of mathematics and physics, and the study of partial differential equations (PDE) is usually crucial for many important discoveries in various seemingly unrelated fields. While it is too much a task to give even a glimpse of the influence of PDE, I […]
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By: Dr. Luca Di Cerbo Abstract: In this talk, I will introduce the classification problem for compact 3-manifolds and pictorially describe its recent resolution by the mysterious and reclusive Russian mathematician Grigori Perelman. Among other things, Perelman’s work implies the celebrated Poincare’ conjecture (stated back in 1904).
Read more "UMS Talk – Grigori Perelman and the Saga of 3-Manifolds"