My current focus is on developing an algebraic geometry of idempotent semirings. An idempotent semirings is a semiring such that \(a + a = a\) for all \(a\). Idempotent semirings have a number of applications in economic theory, the theory of computation and formal languages, algebraic geometry (see tropical geometry).
While my studies are in pure mathematics, I have a background in computer science (particularly in the field of statistical machine translation), and I love to leverage that background into finding applications of algebraic theory.
by William Bernardoni, Robert Kassouf-Short, Robert Cardona, Brian Heller, Justin Curry, David Spivak, Juan A. Fraire
Accepted at the IEEE Aerospace Conference, 2024.
by William Bernardoni, Robert Cardona, Jacob Cleveland, Justin Curry, Robert Green, Brian Heller, Alan Hylton, Tung Lam, Robert Kassouf-Short
Preprint, Submitted to SIAGA
Talks
August 2024
NASA, Glenn Research Center: What routes to Vegas stays in Vegas: Creating contact tables using the Nevada semiring
Talk given on original work in generating time varying, throughput sensitive routing tables for deep space satellite networks using an original algebraic model.
April 2024
Algebra and Combinatorics Seminar, Tulane University: Space, Spectra, and Semiring Systems of Equations
Talk given on original work on systems of equations over idempotent semirings and their applications in both satellite networks and commutative algebra.
September 2023
Developments in Modern Mathematics, University of Göttingen: Applications of Generalized Universal Valuations
Talk given on original work in generalizing valuation theory to a non-commutative setting.
Slides available here.
August 2023
NASA, Glenn Research Center: “Network Storage Analysis via Semiring Geometry”
Talk given on original work on deriving the minimal amount of storage needed in a satellite network to attain the maximum throughput using algebraic and geometric methods.
July 2023
NASA, Glenn Research Center: “Algebraic Path Problem, Semirings, and Contact Graph Routing”
Talk given on original work on developing a semiring which encapsulates Contact Graph Routing, and using it to derive routing plans and storage requirements for a satellite network.
14th Ukraine Algebra Conference, Sumy State Pedagogical University (Virtual): “Applications of Generalized Universal Valuations”
Talk given on original work on generalizing valuation theory to non-commutative settings and deriving classifying objects for non-commutative geometric structures.
November 2022
BUGCAT 2022, Binghampton University: “The Semiring Geometry of Routing Problems”
Talk given on original work in parameterized routing.
August 2022
NASA, Glenn Research Center: “Decompositions in Space: How dynamic satellite configurations affect network optimality”
Talk given on original work in parameterized routing.
NASA, Glenn Research Center: “Tropical Geometry, Matroids, and recent advances in Tropical Ideals”
Survey lecture on various new developments in the field of tropical geometry which could be applicable to the problem of mathematically modelling satellite networks.
Slides available here.
January 2022
Cleveland State University
Week long refresher course on Discrete Math for incoming masters students.
August 2021
Case Western Reserve University
Organized week-long lecture series for incoming PhD students and lectured on Galois Theory as well as the Axiom of Choice.
December 2019
NEURIPS, Reconnaisance Blind Chess Workshop
Invited by JHUAPL to present in competition workshop on methods used in algorithm development for reconnaissance blind chess competition
Replays of my bot's matches can be found here.
Teaching
Case Western Reserve University
Fall 2024
Math 304: Discrete Mathematics
Spring 2023
Math 125: Math and Calculus Applications for Life, Managerial, and Social Sciences I
Fall 2022
Tropical Geometry Seminar
Hosted and lectured for a weekly graduate seminar on Tropical Geometry
Math 224: Elementary Differential Equations
Fall 2021
Math 126: Math and Calculus Applications for Life, Managerial, and Social Sciences II
Summer 2021
Math 120: Elementary Functions and Analytic Geometry
