Josh Pollitz
Contact Info
University of Utah
Department of Mathematics
155 S 1400 E RM 233
Salt Lake City, UT, 841120090
USA
Office: JWB 209
Email:
pollitz@math.utah.edu
General Info
I am a postdoctoral research assistant professor at the University of Utah. In 2019, I received my PhD at the University of NebraskaLincoln 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 moviegoer and love to talk about films!
Publications, Preprints, Notes, and Current Projects
Here is a list of my research papers:
 "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)
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)
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 farreaching 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 proxysmall objects. This extends work in [1], 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 proxysmall modules and quotient rings. This is still very much work in progress.
Teaching
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 K3 Math Specialists, Summer 2017 (class for inservice K3 teachers in or around Omaha, NE)
 Math 302: Mathematical Modeling, Spring 2017 (class for preservice math teachers at UNL)
 Math 300: Mathematics Matters, Fall 2016 (class for preservice 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 2125, 2020 (Participant).
 AMS Special Session: DG Methods in Commutative Algebra and Representation Theory, CSU Fresno, May 23, 2020 (Coorganizer along with Ben Briggs and Janina Letz)
 URICA: "Upcoming Researchers in Commutative Algebra", conference for graduate students and postdocts, University of Nebraska, April 2526, 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 23, 2019 (Speaker, 20 minute talk)
 KUMUNU, University of Nebraska, September 2122, 2019
(Participant)
 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.