Commutative and Homological Algebra Market Presentations

Justin Fong is a graduate student at Purdue University working under Uli Walther. His research interest is in commutative algebra and its occasional intersection with combinatorics. His current work is in the positive characteristic setting where he is computing values of the F-pure threshold (a numerical invariant analogous to the log canonical threshold in characteristic zero, which is a measurement of the singularity of an ideal) for various types of rings, such as the coordinate rings of flag varieties, Schubert varieties, and ladder determinantal rings. He has worked as a teaching assistant for many calculus courses in the past in both his master's program at San Francisco State University and at Purdue.

Sean Grate is a fifth-year graduate student at Auburn University working with Hal Schenck on problems in commutative algebra and algebraic geometry amenable to computational methods. He has worked on projects on Lefschetz properties, showing that Betti tables can sometimes serve as an indicator for failure of the weak Lefschetz property, as well as Castelnuovo-Mumford regularity of toric surfaces, providing combinatorial bounds on the regularity. Sean has also been working in algebraic combinatorics studying the combinatorics of the stable Tamari lattice and the unimodality of some of its statistics. While teaching, he employs research-backed methodologies to provide effective instruction in a stimulating and inviting active learning environment for his students.

Adam LaClair is a graduate student at Purdue University with a focus on commutative algebra, combinatorics, and the mathematical connections between these two fields. In his research, Adam has studied free resolutions of ideals, Koszul algebras, symbolic powers, F-singularities, and binomial edge ideals. Adam has served as a teaching assistant for a variety of courses and is currently the instructor of record for Calculus I. His teaching style emphasizes active student involvement and collaborative problem-solving, providing real-time feedback to enhance their learning experience.

Olivia Strahan is a sixth year graduate student at University of Michigan. She was advised by Mel Hochster prior to his retirement, and is currently working with Karen Smith. Her research is in commutative algebra. In particular, she developed the idea of p-monomials in order to define and study combinatorial classes of mixed characteristic rings. She has regularly taught introductory math courses as a GSI; in addition, she mentored two semesters of an undergraduate directed reading course, and she worked as a teaching assistant for the MMSS Graph Theory summer camp.

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.

Eamon Quinlan-Gallego is an NSF postdoc in the Department of Mathematics of the University of Utah. Before that, he was a graduate student at University of Michigan, where his advisor was Karen Smith. He is interested in rings of differential operators and their applications to commutative algebra and algebraic geometry. In particular, he has been studying positive-characteristic analogues of Bernstein-Sato polynomials.

Peter McDonald is a Lecturer at the University of Illinois Chicago. He completed his PhD in 2024 at the University of Utah under the supervision of Srikanth Iyengar and Karl Schwede and he is primarily interested in using homological and homotopical techniques to study singularities in commutative algebra and algebraic geometry. His thesis was focused on two distinct problems: developing a new characterization of the multiplier ideal to give a derived splinter characterization of klt singularities and studying homological properties of the relative Frobenius. He is currently working to use these results to study closure operations in characteristic zero and he has also recently developed an interest in the McKay correspondence. He is a dedicated teacher, having taught calculus, statistics, and linear algebra to a wide variety of students, and has also been highly involved in service to the profession through mentorship, conference organization, and volunteering with the Association for Women in Mathematics.

Jake Kettinger (right) is a postdoc at Colorado State University, working with Chris Peterson. His primary area of expertise lies in Algebraic Geometry and its intersection with Combinatorics. More precisely, he is interested in configurations of points, lines, and planes in projective space, which can be understood in the language of Design Theory. He is also interested in the connections between Algebraic Geometry and Number Theory and Dynamics by studying the dynamics of the iterated Hesse derivative on cubic curves. Jake got his PhD at the University of Nebraska‐Lincoln under the guidance of Brian Harbourne. Jake Kettinger has taught a wide range of undergraduate classes, and he has experience using Active Learning strategies and implementing Standards-Based Grading in small courses, and experience coordinating large courses.

Kyle Maddox is a Visiting Assistant Professor at the University of Arkansas, working with Lance E. Miller. His area of expertise is in prime characteristic methods and F-singularities, particularly F-nilpotent singularities. He was previously a Visiting Assistant Professor at the University of Kansas, working with Hailong Dao, and prior to that he received his Ph.D. from the University of Missouri-Columbia under the supervision of Ian Aberbach. In recent joint work, Kyle showed that F-nilpotent rings are always geometrically unibranched, and this property characterizes F-nilpotent curves. He is also a dedicated and passionate teacher, having taught a wide variety of both introductory and major-specific courses. Finally, Kyle is engaged in a number of service projects, including serving on his department's Institutional Excellence/DEI committee.

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.