Commutative and Homological Algebra Market Presentations

Anirban Bhaduri is a sixth-year graduate student at the University of South Carolina, advised by Matthew Ballard. His research interests are studying derived categories arising from algebraic geometry, representation theory and noncommutative algebra. In recent work, he has studied Orlov spectra of weighted projective lines, generation and Rouquier dimension for noncommutative schemes, and dimension theory for noncommutative curves. He is interested in understanding noncommutative schemes through derived categories over noncommutative algebras like quivers. Anirban has been instructor of record for courses such as College Algebra and Business Calculus and has served as a mentor in USC's Peer Mentoring Program. He enjoys engaging students at all levels and is committed to creating supportive and inclusive classroom environments.

Reid Buchanan is a Ph.D. student at Oklahoma State University advised by Jeff Mermin. He studies combinatorial commutative algebra, specifically homological information of monomial ideals such as their free resolutions. He is currently focusing on understanding when and how the minimal resolution of a monomial ideal in \(k[x_1,\ldots,x_n]\) depends on the characteristic of k. Most recently, he has found a way to construct ideals with characteristic-dependent projective dimension using small numbers of generators relative to the literature. Reid has also demonstrated a combinatorial duality between lex ideals and quotients, and studied when a Morse resolution admits a DG-algebra structure. As an instructor-of-record for multiple Calculus I and precalculus classes, Reid enjoys finding ways to develop a more comfortable environment for his students to learn mathematics, emphasizing a visual and intuitive approach to support practice with exercises.

Vignesh Jagathese is a 5th year PhD student at the University of Illinois at Chicago, advised by Kevin Tucker. His research lies at the intersection of commutative algebra and algebraic geometry where he studies singularities in positive and mixed characteristic. He is particularly interested in the study of quasi-F-splittings, a weakening of Frobenius splitting that allows for mild arithmetic supersingularity, and using commutative algebra to understand their number-theoretic and geometric properties. He has extended these notions to arbitrary excellent rings and, with Jack J. Garzella, computed the F-pure threshold of any quasi-F-split hypersurface. As part of a six-author collaboration, he also introduced the mixed-characteristic analogue of the F-pure threshold, the plus-pure threshold, showing it recovers the F-pure threshold over sufficiently ramified DVRs. He plans to build on these connections to address fundamental questions in arithmetic and birational geometry.

Thiago Holleben is a fourth-year graduate student at Dalhousie University working with Sara Faridi. He works in combinatorics, commutative algebra, and their interactions, with his research in combinatorics often motivated by enumerative and topological questions about simplicial complexes homeomorphic to spheres. His work in commutative algebra focuses on studying expected and extremal behaviour of squarefree monomial ideals, for example in terms of Lefschetz properties and algebraic invariants arising from powers of ideals. He is also interested in providing a friendly and welcoming environment to students when teaching. He has been instructor of record for Calculus II twice, once for the general course and once for engineering students.

Vinh Anh Pham is a PhD candidate in Mathematics at Tulane University, advised by Huy Tài Hà. His research lies at the intersection of commutative algebra and combinatorics, focusing on how convex geometric and combinatorial structures such as Newton polyhedra, Newton-Okounkov bodies, and p-bodies encode algebraic invariants of ideals. He has developed a Volume = Multiplicity formula for Newton non-degenerate ideals, studied asymptotic invariants of p-families of ideals in positive characteristic, and collaborates on projects involving Newton non-degenerate binomial ideals and extensions of F-volumes to filtrations. Equally committed to teaching, Vinh promotes student-centered learning that builds intuition, connects abstract concepts to real-world meaning, and fosters inclusive classrooms where students gain confidence and critical reasoning skills. His dedication as an educator was recognized with the 2025 Tulane Mathematics Department Excellence in Teaching Award.

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.