Commutative and Homological Algebra Market Presentations

Caitlin Davis is a sixth-year graduate student at the University of Wisconsin-Madison, advised by Daniel Erman and Jose Israel Rodriguez. She studies multigraded commutative algebra with a focus on homological questions. In recent work, she studied the nonstandard Koszul property for a class of rational curves in weighted projective space (joint with Ola Sobieska) and for truncations of nonstandard graded polynomial rings (joint with Boyana Martinova). Caitlin has been instructor of record for both Preparatory Algebra and Discrete Math, and has worked on multiple projects aimed at improving outcomes in Preparatory Algebra. She enjoys working with students of all levels through programs such as the Madison Math Circle and the Directed Reading Program.

Pankaj Singh is a PhD student in mathematics at the University of South Carolina, advised by Alex Duncan. His research lies at the intersection of algebraic geometry, arithmetic geometry, and commutative algebra. He studies rationality problems for algebraic tori and toric varieties, as well as the Weak Lefschetz Property for Artinian algebras. In both directions, he is particularly interested in how combinatorial structures arising from toric geometry connect rationality questions with Lefschetz-type phenomena in graded algebras. Pankaj is also passionate about teaching; he enjoys finding clear ways to communicate abstract ideas, and creating an inclusive classroom environment that helps students feel engaged and supported.

Naufil Sakran is a fifth-year graduate student at Tulane University and is expected to complete his Ph.D. by summer 2026. He is working with Mahir Bilen Can. His research interests include semigroups, commutative algebra, algebraic geometry, and Gromov-Witten theory. He is currently working on two projects. His first project is about studying the correspondence between properties of semigroups and algebraic properties of their corresponding k-algebra. In this work, he has introduced the theory of unipotent numerical semigroups, which generalizes classical numerical semigroup theory to the setting of unipotent matrices. His second project is in enumerative geometry, where he has computed the geometric Tevelev degree for rational curves in certain toric varieties. Besides mathematics, he has two kitties and enjoys playing badminton.

Havi Ellers is a fifth year math PhD student at the University of Michigan. She was advised by Mel Hochster prior to his retirement, and is now advised by Karen Smith. She works in positive characteristic, studying the nilpotency of Frobenius on local cohomology modules; in particular, she studies a numerical invariant called the Hartshorne-Speiser-Lyubeznik (HSL) number. In recent work, Havi found an explicit upper bound for the HSL numbers of affine pointed semigroup rings, and has since also found explicit upper bounds for HSL numbers of toric face rings and certain classes of hypersurfaces. Havi is also interested in teaching; she particularly enjoys thinking about how to communicate concepts clearly, how to share the excitement of mathematics with her students, and how to make everyone feel safe in the often stressful environment of introductory math classes. She has been instructor of record for pre-calculus and Calculus 1, and has also coordinated one semester of Calculus 2.

Dipendranath Mahato (aka, Dipen) is a 5th year Graduate Student at Tulane University, working with Tai Huy Ha. His research is centered on Polynomial Interpolation, an active area in Commutative Algebra and Algebraic Geometry, where he tends to find the lowest possible degree of the hypersurface that passes through a given set of points with prescribed multiplicities. Using ideal containment between the symbolic and ordinary power of the defining ideal of points, he recently improved the existing bounds on Demailly's Conjecture. He is also working on Symbolic Rational Powers of Ideals, k-configurations of projective points, and the v-number of several class of ideals. Dipen is a dedicated and effective educator who prioritizes student understanding and a supportive learning environment for all, irrespective of background. Also, he loves mentoring international students on TWOPLES, an online DRP.