Commutative and Homological Algebra Market Presentations

Sara Mueller is a sixth-year Ph.D. student at the University of Nebraska-Lincoln, advised by Tom Marley. Her research focuses in homological algebra, specifically in homological dimension theory. In particular, she studies the Cohen-Macaulayness of modules with finite G- and CI- dimensions. Sara has served as the instructor of record for a wide variety of courses, from Intermediate and College Algebra to an Introduction to Proofs course. She loves sharing her passion for mathematics with undergraduate students through teaching, leading undergraduate research projects, and mentorship in AWM.

Manav Batavia is a graduate student in his fifth year at Purdue University, advised by Linquan Ma and Uli Walther. A central theme in his research is the study of local cohomology modules and the numerical invariants which govern their behaviour, particularly cohomological dimension and arithmetic rank. He established a universal sharp upper bound on cohomological dimension in the unramified mixed characteristic, and over multiple collaborative projects, computed the arithmetic rank of several generic residual intersections and nullcone ideals. He created and co-organizes Ideal Conversations, the student commutative algebra seminar at Purdue. Earlier in 2026, he was awarded the Certificate of Merit for outstanding classroom instruction at Purdue.

Anne Fayolle is a fifth-year Ph.D. student at the University of Utah, advised by Karl Schwede. Her research focuses on singularities, with an emphasis on methods in positive and mixed characteristic. She has used perfectoid rings to introduce a mixed-characteristic analogue of log canonical centers and centers of F-purity, and she is currently interested in developing a more general theory of perfectoid purity. In positive characteristic, she has studied the behavior of singularities under finite covers by relating them to tame ramification. She is now exploring applications of these ideas to the study of foliations in positive characteristic. Anne also really enjoys teaching and has taught a wide range of courses, from foundational introductory classes through calculus.

Kory Pollicove is a 6th year PhD student at Syracuse University, advised by Josh Pollitz. Kory works in homological algebra with a focus on structures on free resolutions (such as DG and A-infinity), Koszul duality, and cohomological operations. In particular, he is interested in using the techniques of Koszul duality to construct universal resolutions and systems of higher homotopies in settings that are not Koszul in the classical sense. Kory is also a devoted educator, passionate about conveying the wonder of mathematics to his students through active discussion and group work, and has mentoring experience through a directed reading program. He currently co-organizes a graduate-level learning seminar.

Dorian Kalir is a sixth-year graduate student at Syracuse University, advised by Josh Pollitz. His research uses homological, derived-categorical, and operadic methods to study algebraic structures on free resolutions and invariants of modules over local rings. In particular, he is interested in extending phenomena witnessed over complete intersection and Golod rings to more general rings and dg algebras. As an educator, he is passionate about creating welcoming and interactive classrooms and incorporates inquiry-based learning into his teaching. He has served as instructor of record for a variety of calculus courses, co-organized a weekly learning seminar for graduate students, and is excited to supervise an undergraduate directed reading program in Fall 26.

Anna Brosowsky is a postdoc at the University of Nebraska-Lincoln, working with Jack Jeffries. She got her Ph.D. in 2024 at the University of Michigan, where she was advised by Karen Smith. Her work is in commutative algebra and algebraic geometry, with a particular focus on singularities in prime characteristic. Recent and ongoing projects include computing the limit F-signature for 3 weighted points in P^2 (with Coskun, Pande, and Tucker) and investigating how operations on a Cartier algebra alter the corresponding test ideal (with Lee and Smith). She has taught a variety of courses, from Calculus 1 to a topics course for PhD students. These include two different project-based courses where students apply their mathematical skills to a question of interest, culminating in a presentation and report.

Olivia Strahan is a postdoc at University of New Mexico, working with Janet Vassilev. She got her PhD from University of Michigan in 2025, where her advisor was Karen E. Smith. Olivia's research is in mixed-characteristic combinatorial commutative algebra. In recent work with Mel Hochster, Olivia develops the theory of "t-Stanley-Reisner rings," the algebraic invariants of which can be described in terms of topology. This connection is particularly nuanced in the mixed characteristic setting. Her ongoing projects include characteristic dependency in discrete Morse theory (with Janet Vassilev) and development of an appropriate analogue of D-module theory for t-Stanley-Reisner rings (with Lance Miller). She has a wide range of teaching experience, including course coordination and instructorship for calculus, linear algebra with applications, and discrete structures.

Jake Kettinger (left) is a postdoc at Colorado State University, working with Chris Peterson. His primary area of expertise lies in Algebraic Geometry and Commutative Algebra and their intersection with Combinatorics, Number Theory, and Discrete Dynamical Systems. More precisely, he is interested in configurations of points, lines, and planes in projective space and their blowups, and various algebraic objects arising therefrom, such as groupoids, symmetry groups, and symbolic powers of ideals. His interest in the connections between Algebraic Geometry, Number Theory, and Dynamics lies in studying the dynamics of the iterated Hesse derivative on cubic curves, and in generalizing the concept of Lattès maps to higher genus curves. Jake Kettinger got his PhD at the University of Nebraska‐Lincoln under the guidance of Brian Harbourne. Jake has taught a wide range of undergraduate classes, including Number Theory, Data Science, Combinatorics, Differential Equations, and Linear Algebra; he also has experience using Active Learning strategies and implementing Standards-Based Grading in small courses, and experience coordinating large courses.