## About Me

I am a third year PhD student in Mathematics and an NSF Graduate Research Fellow at the University of Pennsylvania. I am co-advised by Mona Merling and Kirsten Wickelgren. Previously I was an undergraduate at Johns Hopkins University. I am interested in algebraic topology, particularly $\textbf{A}^1$-homotopy theory and equivariant homotopy theory. My CV is here.

tbraz at math.upenn.edu

I co-founded the Penn chapter of the Directed Reading Program with Mona Merling, which I now co-organize with George Wang. We were recently featured in an article in Omnia.

### Papers and Preprints:

**Bézoutians and the $\mathbb{A}^1$-degree**, with S. McKean, S. Pauli,

30 pages, 2021. Submitted.**Sums of distinct residues of Lucas polynomials over $\mathbb{F}_p$**, with J. Harrington, M. Litman, T.H.W. Wong,

18 pages, 2021. Preprint.**Homotopy Mackey functors of equivariant algebraic $K$-theory**,

39 pages, 2021. Submitted.**An introduction to $\mathbb{A}^1$-enumerative geometry**,

33 pages, 2020. To appear in*Springer Lecture Notes in Mathematics*.**A note on semilinearization and twisted group rings**,

*Communications in Algebra*, 2021.**The trace of the local $\mathbb{A}^1$-degree**, with R. Burklund, S. McKean, M. Montoro, M. Opie,

*Homology, Homotopy and Applications*23(1):243-255, 2021.**Zeros of newform Eisenstein series on $\Gamma_0(N)$**, with V. Jakicic,

*J. Number Theory*(190):109-130, 2018.**On consecutive $n$th roots of unity modulo $q$**, with J. Harrington, S. Kannan, M. Litman,

J. Number Theory (174):494-504, 2017.

### Other writing:

- Constructing the Unstable Motivic Homotopy Category using $(\infty,1)$-Categories, arXiv:1810.00094.
- The Generalized Poincaré Conjecture Using $s$-Cobordism, for the Penn Grad Student Seminar, Fall 2018.

### Conference and course notes:

*Disclaimer:*Any errors found in these notes should be attributed to me, not the original lecturer. If you find any typos or have suggestions, please feel free to contact me.

- School on Motives and Stacks, September 2019, minicourses by Hoskins, Østvæer, Rydh. Notes available upon request.
- European Autumn School in Topology, September 2019, minicourses by Barthel, Salvatore. Notes available upon request.
- PIMS Workshop on Arithmetic Topology, June 2019, minicourses by Ellenberg, Farb, Galatius, Ho, Vakil/Landesman, Wickelgren.
- An Introduction to $\textbf{A}^1$-homotopy theory from an infinity-categorical viewpoint, June 2018, (notes from lectures of Strunkland and Tamme, Homotopy Theory Summer Berlin 2018).