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5:00 – 5:20: Raymond Ying, with “Set Cut-out Classification”
Abstract. Given a notion of a family of sets “cutting out” another set, we will prove a surprising classification of the growth rates of the cardinality of these cut-outs. Specifically, we classify them as either exponential or polynomial growth.
5:25 – 5:45: Andrew Mowry, with “Group Theory in Chemistry”
Abstract. In my talk, I plan to highlight a physical application of group theory – that being molecular symmetry. I will describe what symmetry operations on 3D molecules look like (some aren’t straightforward), and how chemists use these to classify compounds into “point groups”. Then I will gloss over how each symmetry operation has a 3 by 3 matrix representation, and how the trace of these give way to character tables – a tool used to describe properties of compounds with specific symmetry. The purpose of this is to provide a unique perspective to how something as abstract as group theory can have an immediate and important use to other academic disciplines.
5:50 – 6:10: Andersen Wall, with “Sheaf Theory and Applications”
Abstract. This talk will start with an introduction to basic sheaf and category theory that is necessary for analyzing some application. We can use sheafs to represent various optimization problems including different constraint satisfaction problems (CSPs). Various example of these types of problems will be covered as well as a solver to some CSPs.
6:10 – 6:40: Pizza break!
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6:40 – 7:00: James Meier, with “Baseball Break”
Abstract. I intend to cover the posted solution to the Baseball Break Biweekly Brainteaser. I also intend to cover an alternate such solution.
7:05 – 7:25: Julian Carvajal, with “Fractional Dimensions and the Hausdorff Measure”
Abstract. The Hausdorff dimension is the standard dimension given to fractals and will be the main focus. In order to define it, I will introduce the Lebesgue measure and the closely related Hausdorff measure. I will also mention other notions of dimension and if time permits, applications of Hausdorff measure/dimension. Ideal knowledge: some real analysis, no measure theory.
7:30 – 7:50: Penelope Beall, with “Schubert Polynomials as Generating Polynomials”
Abstract. Schubert polynomials form a basis for the polynomial ring in countably many variables. They are a generalization of Schur polynomials and represent Schubert classes in the cohomology ring of the flag variety. In this talk, we will explore a few ways to compute Schubert polynomials. This will involve turning a permutation into a collection of combinatorial objects, turning each object into a monomial, and then taking the sum of the monomials to finally obtain the Schubert polynomial for the original permutation. Relevant combinatorial objects include pipe dreams, bumpless pipe dreams, and diagrams obtained by Kohnert moves.