Josh Pollitz
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 NebraskaLincoln 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 cattime.
Research
Below are preprints submitted for publication:
 Cohomological jump loci and duality in local algebra with Ben Briggs and Daniel McCormick
arXiv version
 Cohomological supports of tensor products of modules over commutative rings with Srikanth Iyengar and William Sanders
Submitted
 The homotopy Lie algebra of a Torindependent tensor product with Luigi Ferraro, Mohsen Gheibi, Dave Jorgensen and Nicholas Packauskas
arXiv version
 A comparison of dg algebra resolutions with prime residual characteristic with Michael DeBellevue
arXiv version
 A partial converse ghost lemma for the derived category of a commutative noetherian ring with Jian Liu
arXiv version
Below are my published articles:
 Exceptional complete intersection maps of local rings with Srikanth Iyengar, Janina Letz, and Jian Liu
Pacific Journal of Mathematics (to appear): arXiv version  Support varieties over skew complete intersections via derived braided Hochschild cohomology with Luigi Ferraro and W. Frank Moore
Journal of Algebra (2022):
arXiv version,
journal version
 Constructing nonproxy small test modules for the complete intersection property with Ben Briggs and Eloísa Grifo
Nagoya Mathematical Journal (2021): arXiv version, journal version
 Cohomological supports over derived complete intersections and local rings
Mathematische Zeitschrift (2021): arXiv version, journal version
 Locally complete intersection maps and the proxy small property with Ben Briggs, Srikanth Iyengar, and Janina Letz
International Mathematics Research Notices IMRN (2021): arXiv version, journal version
 Duality and symmetry of complexity over complete intersections via exterior homology with Jian Liu
Proceedings of the American Mathematical Society (2021): arXiv version, journal version
 Equivariant isomorphisms of Ext and Tor modules
Journal of Algebra (2020): arXiv version, journal version
 The derived category of a locally complete intersection ring
Advances in Mathematics (2019): arXiv version, journal version
 PhD Thesis (2019), Digital Commons PDF
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 4400: Introduction to Number Theory, Fall 2021
 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
Independent reading coures
 Fall 2020, two students:
 One student covered the first two chapters of Bruns and Herzog's Cohen Macaulay rings plus miscellaneous sections of Avramov's Infinite free resolutions.
 The second student covered several chapters of Atiyah and MacDonald's Introduction to commutative algebra.
 Spring 2021, two students:
 One student is completing the last four chapters of Atiyah and MacDonald's Introduction to commutative algebra as well as the first chapter of Bruns and Herzog's Cohen Macaulay rings.
 The second student will be working through Atiyah and MacDonald's Introduction to commutative algebra.
 Summer 2021, four students:
 One student is working through sections of Avramov's Infinite free resolutions.
 The other students are working through Atiyah and MacDonald's Introduction to commutative algebra
 Fall 2021, three students:
 Covering various sections of Atiyah and MacDonald's Introduction to commutative algebra.
 Spring 2022, one student:
 Covering first three chapters of Atiyah and MacDonald's Introduction to commutative algebra.
Recent and Upcoming Conferences and Talks
 University of Minnesota Commutative Algebra Seminar, April 28, 2022
 Syracuse University Algebra Seminar, April 22, 2022
 MSRI Eisenbud Seminar: Commutative Algebra and Algebraic Geometry, February 10, 2022
JMM AMS Special Session: Commutative Algebra, Seattle, WA, January 67, 2022 Cancelled due to COVID19
 IIT Bombay Virtual Commutative Algebra Seminar, October 29, 2021. (Video)
 University of Arkansas Commutative Algebra Seminar, October 22, 2021.
 University of Nebraska Commutative Algebra Seminar, October 13, 2021.

AMS Special Session: Commutative Algebra, Creighton University, October 910,2021.
 UC Riverside Commutative Algebra Seminar, May 7, 2021. (GoodNotes from talk)
 AMS Special Session: Differential Graded Methods in Commutative Algebra, Georgia Tech, March 1314, 2021.
 Texas Tech University Algebra and Number Theory Seminar, March 3, 2021.
 Algebra Seminar, University of Texas at Arlington, October 16, 2020. (GoodNotes from talk)
 AMS Special Session: Homological Commutative Algebra, University of Tenessee, October 1011, 2020. (GoodNotes from 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.