Guilherme Zeus
Dantas e Moura
Master of Mathematics Student
Department of Combinatorics & Optimization
University of Waterloo
200 University Ave W, Waterloo, Ontario, Canada N2L 3G1
Office: MC 6311
Email:
zdantase@uwaterloo.ca
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zeus@guilhermezeus.com
I am a first-year graduate student pursuing a Master of Mathematics degree in the Department of Combinatorics & Optimization at the University of Waterloo. I am working on permuted-basement non-symmetric Macdonald polynomials, under the supervision of Olya Mandelshtam.
Before Waterloo, I completed my Bachelor of Science degree at Haverford College, with majors in Mathematics and Linguistics. As a high school student, I was an IMO medalist. My Erdős number is two.
My research interests are in combinatorics, in particular, algebraic combinatorics. Non-research interests include math olympiads, board games, linguistics, and Linux.
Remark on my surname. My family name is “Dantas e Moura”, so the correct initial for my surname is “D”, not “M”. Accordingly, in alphabetical lists sorted by surname, I should be listed as “Dantas e Moura, Guilherme Zeus”. Some automatic citation generators may incorrectly identify “Moura” as my last name. This is incorrect and should be manually corrected to reflect the full family name “Dantas e Moura”.
Recent Publications (all)
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Probabilistic Entry Swapping Bijections for Non-Attacking Fillings (2025)
Abstract
Non-attacking fillings are combinatorial objects central to the theory of Macdonald polynomials. A probabilistic bijection for partition-shaped non-attacking fillings was introduced by Mandelshtam (2024) to prove a compact formula for symmetric Macdonald polynomials. In this work, we generalize this probabilistic bijection to composition-shaped non-attacking fillings. As an application, we provide a bijective proof to extend a symmetry theorem for permuted-basement Macdonald polynomials established by Alexandersson (2019), proving a version with fewer assumptions.
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Cluster monomials in graph Laurent phenomenon algebras (2024)
To appear in Algebraic CombinatoricsAbstract
Laurent Phenomenon algebras, first introduced by Lam and Pylyavskyy, are a generalization of cluster algebras that still possess many salient features of cluster algebras. Graph Laurent Phenomenon algebras, defined by Lam and Pylyavskyy, are a subclass of Laurent Phenomenon algebras whose structure is given by the data of a directed graph. The main result of this paper is that the cluster monomials of a graph Laurent Phenomenon algebra form a linear basis, conjectured by Lam and Pylyavskyy and analogous to a result for cluster algebras by Caldero and Keller.
Recent and Upcoming Activities (all)
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I attend the weekly Algebraic and Enumerative Combinatorics Seminar at the University of Waterloo.