Commutative and Homological Algebra Market Presentations

Josh Pollitz is an NSF postdoc at the University of Utah, working with Srikanth Iyengar. He received his PhD from the University of Nebraska-Lincoln in 2019 under the supervision of Luchezar Avramov and Mark Walker. Josh's research interests are in commutative algebra, especially applying homological techniques to acquire ring and module theoretic data. He has had successes applying triangulated category techniques, certain notions of cohomological support, Hochschild cohomology and certain graded Lie algebras associated to rings or maps. As an educator, Josh has taught a variety of courses at all levels of undergraduate mathematics. He puts an emphasis on group work and creating a dynamic and welcoming learning environment.

Luigi Ferraro is a postdoc at Texas Tech University, working with Lars Christensen. He received his PhD from the University of Nebraska-Lincoln in 2017 under the supervision of Luchezar Avramov and Srikanth Iyengar. His research in commutative algebra has focused on the structure of the stable cohomology of a local ring, on the Castelnuovo-Mumford regularity of graded modules, on the rigidity of Ext and Tor, on the intersection theorems, on grade 3 perfect ideals and on the homotopy Lie algebra of local rings. His research in noncommutative algebra has focused on studying actions of groups and, more generally, actions of Hopf algebras on noncommutative rings and on the study of the homological properties of quotients of skew polyomial rings. As a teacher, Luigi has taught many classes at the undergraduate level, and the first year graduate course of Algebra. His teaching style is to emphasize critical thinking by engaging the students with activities, giving in-class problem sets to work on in groups, and encouraging the students to meet him outside of class in office hours.

Rachel Diethorn is a Lecturer at Yale University. She earned her Ph.D. from Syracuse University in 2020 under the supervision of Claudia Miller. Rachel's research interests are in commutative algebra, especially on its homological aspects. She is particularly interested in resolutions, their constructions and their applications, and Koszul homology. In one of her recent publications, Rachel describes the Koszul homology algebra structure of the quotient by the edge ideal of a forest. Rachel has recently developed a new interest in differential operators; in collaboration with Jeffries, Miller, Packauskas, Pollitz, Rahmati, and Vassiliadou she constructs the minimal free resolutions of the modules of differential operators in low order over rings that define surfaces with mild singularities. Rachel is also an experienced and passionate teacher; she has seven years of experience as the instructor of record for a variety of undergraduate courses and has advised several undergraduate research projects for math majors. In each course she teaches, Rachel is committed to creating a dynamic and student-centered classroom that invites active learning.

Delio Jaramillo-Velez is a PhD candidate at CINVESTAV, Mexico City. His advisor is Rafael H. Villarreal. He was a master student at CIMAT under the supervision of Luis Núñez-Betancour and Manuel González Villa. He focuses on Commutative algebra and Coding theory; his research interests include evaluation codes, edge ideals, binomial edge ideals, and singularities in prime characteristic. He has described the v-number of an edge ideal in a combinatorial way, and he has found a necessary condition for the Cohen-Macaulayness of the second symbolic power of an edge ideal. Delio has taught several undergraduate courses. He believes that everyone can have joyful mathematical experiences, and he likes to encourage students to discuss and share their ideas with their classmates.

Jake Kettinger is a PhD candidate at the University of Nebraska-Lincoln. His advisor is Brian Harbourne and he completed his master's degree at UNL. Jake focuses on algebraic geometry. His research interests include geproci configurations of points in projective space, unexpected varieties, superabundance of varieties, and fields of positive characteristic. He has found new configurations of geproci sets in prime characteristic of a kind that does not exist in characteristic 0, and is applying quasi-elliptic fibrations to the study of geproci sets in characteristic 2. As an educator, Jake has taught a variety of courses aimed at undergraduate students with diverse backgrounds in math, including education majors. He believes that mathematics is for everyone, and that students learn best when they see math as a collaborative effort instead of a skill passed down from a single authority.

Joshua Rice is a Ph.D. candidate at Iowa State University working under Dr. Jason McCullough. Joshua's research interests are in commutative algebra and algebraic geometry. In particular, he is interested in homological and numerical invariants coordinate rings. He has found a class of Koszul rings, which arise as the coordinate ring of a generic collection of lines in projective space. As a mathematics teacher, Joshua believes that mathematics is a pathway to upward mobility for those who have been educationally disenfranchised. As such, Joshua spends much of his time teaching mathematics to veterans of Iowa State University and has taught students for the ISU 4U promise program.

Cheng Meng is a PhD candidate at Purdue University. His advisors are Giulio Caviglia and Linquan Ma. Cheng's research interests are in commutative algebra and its interactions with algebraic geometry, homological algebra and combinatorics. He works on problems regarding the graded-irreducibility of graded modules, generic initial ideals, Boij-Soderberg theory for local cohomology tables, Lech's conjecture on multiplicities of flat local extension of Noetherian local rings, and singularities in prime characteristic. He has proved a new case of Lech's conjecture, and has found a way to decompose local cohomology tables of almost Cohen-Macaulay modules. As an instructor, he has taught an undergraduate class on calculus and was one of the official tutors in the ICTP summer school Graduate Course on Tight Closure of Ideals and its Applications.

Hannah Klawa is a PhD candidate at George Mason University and her advisor is Neil Epstein. Her research is in commutative ring theory and her dissertation work has revolved around questions involving flat overrings. Most of her work falls into two categories: the preservation of properties of overrings in pullback constructions and graded analogs of domains defined in terms of properties that hold for the overrings of the domain. Hannah has taught several undergraduate math courses in addition to working as a teaching assistant running recitations and assisting with implementing active learning activities in a graduate linear analysis course. She has also co-written an educational research article with a group of faculty and graduate students at George Mason University.