Math Colloquium: Summer Research Student Talks

Analyzing Network Topology for DDoS Mitigation Using the Abelian Sandpile Model - Bhavana Panchumarthi and Monroe Stephenson

Using the Abelian Sandpile model, we have created a new toy model that can optimize the DDoS mitigation strategy of blackholing. The model captures the phenomenon of how much data is lost given a distinct server that is DDoSed, taking into account internal deletion and external rejection. Though useful for DDoS mitigation, the underlying mathematics that the model presents are also deeply profound. In particular, the properties of the matrix that is formed by setting the i-th coordinate to denote the designated black hole and the j-th coordinate to denote the attacked server.

Random Matrix Theory and the Exterior Algebra - Jonathan Li

This research project uses standard statistical modeling procedures to investigate the dynamics and stochastic behavior of a certain class of random algebraic objects when subjected to perturbation and expansion, in order to determine precise conditions on the object parameters to ensure a particular inverse problem can be solved. A thorough description of these conditions may yield answer to an outstanding question in the field of random matrix theory: can the algebraically-reduced formulas for the three classic β-ensembles studied by Dyson, Mehta, et. al be extended to a more general class of β-ensembles? The presentation will go over our intriguing process of developing theorems through Monte Carlo simulation methods and the fascinating discoveries that we found about these bizarre algebraic objects.

The Enumeration of Transfer Systems - Evan Franchere, Usman Hafeez, Peter Marcus, Weihang Qin, and Riley Waugh

Transfer systems are combinatorial gadgets that keep track of “multiplicative structure” on “equivariant ring spectra”. Classifying and enumerating transfer systems has an immediate homotopical payoff. In this talk, we discuss the enumeration of transfer systems on an assortment of  finite Abelian groups. We also present a concrete involution on such transfer systems obtained through a bijection with weak factorization systems.

Thursday, October 8, 2020 at 4:45pm to 5:30pm

Virtual Event
Event Type

Lecture

Audience

Faculty, Students, Staff

Department
Division of Mathematical and Natural Sciences, Mathematics
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