Commutative and Homological Algebra Market Presentations

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.

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.