Research
My primary interests are in commutative and homological algebra, especially monomial ideals, Betti numbers, and combinatorial and topological methods in algebra. I am also interested in noncommutative algebra, algebraic combinatorics, representation theory, and combinatorics on words.
Publication
Noah Ripke and Phillip Yoon.
“Characteristic Independence of Betti Numbers of Monomial Ideals in Five Variables.”
Journal of Pure and Applied Algebra 230 (2026), 108354.
Current Research
Characteristic dependence of Betti numbers of monomial ideals
During the CSU Chico REU/RET in Mathematics, under the supervision of Dr. Guillermo Alesandroni, I worked with Noah Ripke on characteristic dependence of Betti numbers of monomial ideals. We proved that the multigraded, graded, and total Betti numbers of every monomial ideal in five variables are independent of the characteristic, using squarefree reductions, Hochster’s formula, and simplicial topology. I am now investigating the corresponding questions in higher numbers of variables.
Growth of algebras and combinatorics on words
In ongoing joint work with Dr. Be’eri Greenfeld, we study growth and ideal structure in monomial algebras through combinatorics on words. We constructed a finitely generated monomial algebra of quadratic growth with no largest nilpotent ideal, giving a negative answer to a question of L’vov. We are developing these results into a joint manuscript.
Previous Research
Solvable lattice models and quantum superalgebras
Through Polymath Jr., under the mentorship of Dr. Benjamin Brubaker, I worked on solvable lattice models related to quantum superalgebras. I studied rank-three examples, Bruhat-order vanishing conditions, and explicit recurrence computations. I presented this work jointly at the 2026 Joint Mathematics Meetings.