Commutative and Homological Algebra Market Presentations

Bek Chase is a 6th year PhD candidate at Purdue University, advised by Giulio Caviglia. Their interests lie primarily in commutative algebra and its connections to combinatorics. More specifically, they are interested in the Lefschetz properties and related notions. In recent work, they have used combinatorial methods to prove the strong Lefschetz property holds for certain modules and codimension three algebras. Bek is also passionate about teaching and has taught numerous math courses at Purdue. They especially enjoy working with students from underrepresented and/or nontraditional backgrounds and prioritize equity and inclusivity as an instructor.

Benjamin Oltsik is a 6th year graduate student at the University of Connecticut, where he works with Mihai Fulger. His research is in commutative algebra; his specific interests include symbolic powers, integral closure, and analytic spread of ideals, particularly for monomial ideals. In his first publication, Benjamin found and proved an asymptotic upper bound of symbolic defect. Benjamin's thesis also details a method for extracting the analytic spread based on the Newton polytope. During his time in graduate school, he taught a variety of classes, including being the lead instructor for a Linear Algebra course in Spring 2024.

Arvind Kumar is a postdoc at New Mexico State University, working with Louiza Fouli and Michael DiPasquale. His primary area of expertise lies in Combinatorial Commutative Algebra. More precisely, he is interested in problems in commutative algebra, which can be translated into the language of combinatorial tools. He previously held postdoctoral appointments at the Chennai Mathematical Institute and the Indian Institute of Technology Delhi in India. Arvind got his PhD at the Indian Institute of Technology Madras under the guidance of A. V. Jayanthan. Arvind Kumar has taught a wide range of undergraduate and graduate classes, he has experience coordinating large courses, and he has supervised undergraduate research projects.