I am a third-year graduate student at the University of Georgia. I earned my undergraduate degree in Mathematics at the University of California, San Diego, where my undergraduate research was in homotopy theory and spectral sequences with Justin Roberts. I am broadly interested in moduli and classification problems, algebraic, homological, and homotopical invariants, and topics in the Langlands program.
You can find a copy of my CV here. (last updated Fall 2021).
In Spring 2022, I am teaching Math 2250 (Calculus), and co-organizing the UGA graduate student seminar with Arvind Suresh. See UGA GSS.
Qualifying Exams: See https://quals.dzackgarza.com/ for a wiki of qualifying exam resources, topics, and review guides, along with worked problems and solutions.
Current Course Notes
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Cohomology in Representation Theory (Dan Nakano, Spring 2022)
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Commutative Algebra (Daniel Litt, Spring 2022)
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Contact Topology (Peter Lambert-Cole, Spring 2022)
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Functional Analysis (Weiwei Hu, Spring 2022)
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Sheaf Cohomology (Valery Alexeev, Spring 2022)
Talks
You can find more links and details on my talks page.
- Betz-Cohen’s “Graph Moduli Spaces and Cohomology Operations”: The Equivariant Invariants. (UGA Reading Group, November 2021)
- Computing Volumes of Moduli Spaces (Mock AMS Conference, UGA August 2021)
- Slides: to be posted!
- Grothendieck’s “On the de Rham Cohomology of Algebraic Varieties” (CRAAG, UGA, July 2021)
- The Adams Spectral Sequence. (Stable Homotopy Theory Seminar)
- McDuff-Salamon “$J\dash$holomorphic Curve and Symplectic Topology” Seminar
(Symplectic Reading Seminar, UGA, June 2021)
- Talk 1: Sufficient conditions for regularity
- Talk 2: Examples of regularity, constrained curves
- Stable Homotopy Theory (UGA GSS, March 2021)
- Homotopy Groups of Spectra (Stable Homotopy Theory Seminar)
- Interesting Topological Spaces in Algebraic Geometry (Mock AMS, UGA, July 2020)
- Zeta Functions and The Weil Conjectures (CRAAG, UGA, April 2020)
- Homotopy Groups of Spheres (UGA GSS, April 2020)
Recent Notes
For older notes, see my writing page.
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Notes from the MSRI workshop on Chern-Simons and Other Topological Field Theories:
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Notes from the IAS/PCMI Graduate Summer School on Motivic Homotopy:
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Notes from the MIT Talbot Workshop: Viva Talbot!:
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Jeremy Hahn, “Methods and Mysteries in the Construction of Ring Spectra”
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Tasos Mouliunos, “Perspectives of Nonabelian Hodge Theory”
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Projects
Topological Snake
A visualization of what the game ‘Snake’ would look like in various topologies.
