University of Utah
Department of Mathematics
Office: JWB 130
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:
Below are preprints submitted for publication:
- 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
- Cohomological supports over derived complete intersections and local rings
Math. Z. (2021): arXiv version, journal version
- 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
- Duality and symmetry of complexity over complete intersections via exterior homology with Jian Liu
Proc. Amer. Math. Soc. (2021): arXiv version, journal version
- Equivariant isomorphisms of Ext and Tor modules
J. Algebra (2020): arXiv version, journal version
- The derived category of a locally complete intersection ring
Adv. Math. (2019): arXiv version, journal version
The following are in preparation and preprints will appear "soon":
- The homotopy Lie algebra of a Tor-independent tensor product with Luigi Ferraro, Mohsen Gheibi, Dave Jorgensen and Nicholas Packauskas
- A comparison of dg algebra resolutions with prime residual characteristic with Michael DeBellevue
- Exceptional complete intersection maps of local rings with Srikanth Iyengar, Janina Letz, and Jian Liu
- Support varieties over skew complete intersections via derived braided Hochschild cohomology with Luigi Ferraro and W. Frank Moore
- A partial converse ghost lemma for the derived category of a commutative noetherian ring with Jian Liu
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):
- Cohomological jump loci for a deformation with Ben Briggs and Daniel McCormick.
- Joins of cohomological supports with Srikanth Iyengar and Billy Sanders.
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
- 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 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
- 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
Recent and Upcoming Conferences and Talks
- JMM AMS Special Session: Commutative Algebra, Seattle, WA, January 6-7, 2022
- IIT Bombay Virtual Commutative Algebra Seminar, October 29, 2021.
- 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 9-10,2021.
- UC Riverside Commutative Algebra Seminar, May 7, 2021. (GoodNotes from talk)
- AMS Special Session: Differential Graded Methods in Commutative Algebra, Georgia Tech, March 13-14, 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 10-11, 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.