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.
Below are preprints submitted for publication:
Below are my published articles:
- Cohomological jump loci and duality in local algebra with Ben Briggs and Daniel McCormick
- Cohomological supports of tensor products of modules over commutative rings with Srikanth Iyengar and William Sanders
- 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
- A partial converse ghost lemma for the derived category of a commutative noetherian ring with Jian Liu
- 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):
- Constructing non-proxy 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
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
- 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 6-7, 2022 Cancelled due to COVID-19
- 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 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.