Josh Pollitz
Picture from Genova Talk

Contact Info

University of Utah
Department of Mathematics
Office: JWB 130
Email: pollitz@math.utah.edu

General Info

I am an NSF postdoctoral research fellow 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 enjoy thinking about DG homological algebra, triangulated categories, growth of resolutions and relations between commutative algebra and representation theory. You can find my CV here. At Utah, I discuss maths with my postdoc mentor Srikanth Iyengar and the rest of Utah CA community.

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 Nebraska and Oregon, while pursuing my PhD. Some of my hobbies are biking, hiking, rock climbing, and cat-time.

Publications, Preprints, Notes, and Current Projects

 Here is a list of my published and accepted papers:
  1. Constructing non-proxy small test modules for the complete intersection property with Ben Briggs and Eloísa Grifo
    Nagoya Math. J. (2021): arXiv version, journal version
  2. Cohomological supports over derived complete intersections and local rings
    Math. Z. (2021): arXiv version, journal version
  3. Locally complete intersection maps and the proxy small property with Ben Briggs, Srikanth Iyengar, and Janina Letz
    Int. Math. Res. Not. IMRN (2021): arXiv version, journal version
  4. Duality and symmetry of complexity over complete intersections via exterior homology with Jian Liu
    Proc. Amer. Math. Soc. (2021): arXiv version, journal version
  5. Equivariant isomorphisms of Ext and Tor modules
    J. Algebra (2020): arXiv version, journal version
  6. The derived category of a locally complete intersection ring
    Adv. Math. (2019): arXiv version, journal version
Below are preprints submitted for publication:
  1. The homotopy Lie algebra of a Tor-independent tensor product with Luigi Ferraro, Mohsen Gheibi, Dave Jorgensen and Nicholas Packauskas
    arXiv version
  2. A comparison of dg algebra resolutions with prime residual characteristic with Michael DeBellevue
    arXiv version
  3. Exceptional complete intersection maps of local rings with Srikanth Iyengar, Janina Letz, and Jian Liu
    arXiv version
  4. Support varieties over skew complete intersections via derived braided Hochschild cohomology with Luigi Ferraro and W. Frank Moore
    arXiv version
  5. A partial converse ghost lemma for the derived category of a commutative noetherian ring with Jian Liu
    arXiv version
The following are in preparation and preprints will appear "soon":
  1. Cohomological jump loci for a deformation with Ben Briggs and Daniel McCormick.
  2. Joins of cohomological supports with Srikanth Iyengar and Billy Sanders.
Other writings: Below is an incomplete list of some of my current collaborations (feel free to inquire via email about any of the projects below if you are interested in hearing more):
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: Independent reading coures
Recent and Upcoming Conferences and Talks
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.