Suzana Serboi

I completed my PhD in Mathematics under the supervision of Martin Weissman and I'm a Lecturer in the Mathematics and in the Statistics Departments at UC Santa Cruz. Before coming to UC Santa Cruz, I received a M.S. in Mathematics from University of South Florida, a M.S. in Cryptograpy and a B.S. in Math and Computer Science from University of Bucharest.

I’m currently teaching:

MATH 103A Complex Analysis: Spring 2025 - in person at UC Santa Cruz (28 students)
MATH 2 College Algebra: Spring 2025 - in person at UC Santa Cruz (75 students)
MATH 2A Differential Equations - asyncronous online at De Anza College (93 students)

selected publications

PNAS
Arithmetic of arithmetic Coxeter groups

Suzana Milea, Christopher D. Shelley, and Martin H. Weissman

PNAS, Jan 2019

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In the 1990s, J.H. Conway published a combinatorial-geometric method for analyzing integer-valued binary quadratic forms (BQFs). Using a visualization he named the "topograph," Conway revisited the reduction of BQFs and the solution of quadratic Diophantine equations such as Pell’s equation. It appears that the crux of his method is the coincidence between the arithmetic group PGL2(Z) and the Coxeter group of type (3, ∞). There are many arithmetic Coxeter groups, and each may have unforeseen applications to arithmetic. We introduce Conway’s topograph, and generalizations to other arithmetic Coxeter groups. This includes a study of "arithmetic flags" and variants of binary quadratic forms.
@article{10.1073/pnas.1809537115, title = {Arithmetic of arithmetic Coxeter groups}, author = {Milea, Suzana and Shelley, Christopher D. and Weissman, Martin H.}, journal = {PNAS}, volume = {116}, issue = {2}, pages = {442-449}, year = {2019}, month = jan, publisher = {American Physical Society,}, doi = {10.1073/pnas.1809537115}, url = {https://doi.org/10.1073/pnas.1809537115}, dimensions = {true}, }
thesis
Generalizations of Conway’s Topograph arising from Arithmetic Coxeter Groups

Suzana Milea

escholarship.org, Jan 2020

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Conway’s topograph can be used in the study of binary quadratic forms (BQFs) to replace tedious algebraic computations with straightforward geometric arguments. The crux of his method is the isomorphism between the arithmetic group PGL2(Z) and the Coxeter group (3, ∞). We introduce the arithmetic groups called dilinear groups and construct generalizations of Conway’s topograph called dilinear topographs. Then we use them to study variants of BQFs, called binary quadratic diforms (BQDs). The payoff can be seen in the last chapter in our investigation of minimum value bounds for diforms and pairs of BQFs.
@article{PhDThesis, title = {Generalizations of Conway's Topograph arising from Arithmetic Coxeter Groups}, author = {Milea, Suzana}, year = {2020}, journal = {escholarship.org}, url = {https://escholarship.org/content/qt50j5g6nf/qt50j5g6nf.pdf}, }