University of Utah
Department of Mathematics
155 S 1400 E RM 233
Salt Lake City, UT, 84112-0090
Office: JWB 209
I am a postdoctoral research assistant professor at the University of Utah. In 2019, I received my PhD at the University of Nebraska-Lincoln where my advisors were Lucho Avramov and Mark Walker. My research interests are primarily in the homological aspects of commutative algebra. I am also interested in DG homological algebra, triangulated categories, and representation theory. You can find my CV here. Currently, at Utah, I am working closely with Srikanth Iyengar, my postdoc mentor, and Benjamin Briggs.
Here's a little bit more about me: I spent most of my formative years in the San Francisco bay area and the suburbs of Seattle. I have also spent a good deal of time in Oregon and Nebraska, while pursuing my PhD. Some of my hobbies are biking, rock climbing, hiking, napping, and hanging out with my cats. Also, I am an avid movie-goer and love to talk about films!
Publications, Preprints, Notes, and Current Projects
Here is a list of my research papers:
PhD Thesis (2019): "The derived category of a locally complete intersection ring" NOTE: This is an expanded version of the the Advances paper with the same title (Digital Commons PDF)
- "Cohomological supports over derived complete intersections and local rings" submitted. (arXiv version)
- "Equivariant isomorphisms of Ext and Tor modules" To appear in Journal of Algebra (2020). (arXiv version)
- "The derived category of a locally complete intersection ring", Advances in Mathematics (2019). (arXiv version)
Currently, I am involved in the following projects:
- Ben Briggs and I are studying the growth of graded Ext and Tor modules over complete intersections. This completes a study that was initiated in the beautiful and far-reaching work of Avramov and Buchweitz, in [AB,2000]. A preprint is being prepared.
Ben Briggs, Srikanth Iyegnar, Janina Letz and I characterize when a morphism of commutative noetherian rings is a complete intersection in terms of ascent properties of proxy-small objects. This extends work in , above. A preprint is being prepared.
- Luigi Ferraro, W. Frank Moore and I are studying the Hochschild cohomology over certain quotients of a skew polynomial ring. These quotients are shown to possess many of the homological properties of complete intersections. Furthermore, we introduce a theory of support varieties in this setting. A preprint is being prepared.
- Srikanth Iyegnar, Billy Sanders and I extend results in [DS,2017] by showing that the support variety of "finite" derived tensor products correspond to the join of certain support varieties over a complete intersection ring.
We provide new arguments, even in the known cases, which complement the arguments in [DS,2017]. We plan to prepare a preprint shortly but some work is still in progress.
Ben Briggs, Eloísa Grifo and I are studying a derived category characterization of complete intersection rings in terms of proxy-small modules and quotient rings. This is still very much work in progress.
I am passionate about education and strive to make my classrooms a dynmaic and fun learning enviroment. Below are the couses I have taught as the instructor of record. Current students, please see the Canvas course webpage:
- University of Utah:
- Math 3210: Foundations of Analysis, Spring 2020 (Syllabus)
- Math 2200: Discrete Mathematics, Fall 2019 (Syllabus)
- University of Nebraska:
- Math 314: Linear Algebra, Spring 2019
- Math 208: Calculus III, Fall 2017 and Fall 2018
- Math 802P: Numbers, Geometry, and Algebraic Thinking II for K-3 Math Specialists, Summer 2017 (class for in-service K-3 teachers in or around Omaha, NE)
- Math 302: Mathematical Modeling, Spring 2017 (class for pre-service math teachers at UNL)
- Math 300: Mathematics Matters, Fall 2016 (class for pre-service math teachers at UNL)
- Math 104: Applied Calculus, Summer 2015 and Spring 2016
- Math 203: Contemporary Mathematics, Fall 2015
- Math 101: College Algebra, Fall 2014 and Spring 2015
Recent and Upcoming Conferences and Talks
- WARTHOG 2020 University of Oregon, July 21-25, 2020 (Participant).
- AMS Special Session: DG Methods in Commutative Algebra and Representation Theory, CSU Fresno, May 2-3, 2020 (Co-organizer along with Ben Briggs and Janina Letz)
- URICA: "Upcoming Researchers in Commutative Algebra", conference for graduate students and postdocts, University of Nebraska, April 25-26, 2020 (Speaker)
- Algebra Seminar, University of Texas at Arlington, April 2020 (Speaker, 50 minute talk)
- AMS Special Session: Homological Methods in Algebra, University of Florida, November 2-3, 2019 (Speaker, 20 minute talk)
- KUMUNU, University of Nebraska, September 21-22, 2019
- Commutative Algebra Seminar, University of Genoa, July 8, 2019 (Speaker, 60 minute talk)
Some Conference Photos (A "Where's Waldo?" of sorts)
I am interested in collecting more of these! If you have a conference photo that you and I both attended, that is not above, could you please send it to me? Thanks, I greatly appreciate it.