Starting Fall 2022, I am an assistant professor in the Department of Mathematics and Computer Science at Santa Clara University. Previously, I was a postdoctoral fellow at the University of British Columbia with Dragos Ghioca and Zinovy Reichstein as my mentors.

I received my PhD from Brown University (May 2019) under the supervision of Brendan Hassett.

I am interested in algebraic geometry and arithmetic geometry, with recent foray into algebraic graph theory. Much of my work has focused on geometry and combinatorics over finite fields, but I am also interested in problems in characteristic 0.

Email: sasgarli@scu.edu

- A New Proof of Warning's Second Theorem.
*The American Mathematical Monthly*Vol. 125, No. 6 (2018), 549--553. - The Picard group of the moduli of smooth complete intersections of two
quadrics. (with Giovanni
Inchiostro)
*Trans. Amer. Math. Soc.*, Vol. 372, No. 5 (2019) p. 3319--3346. - Sharp Bertini theorem for plane curves over finite fields.
*Canadian Math. Bulletin.*Vol. 62 (2), 2019 p. 223--230. - Transverse lines to surfaces over finite fields. (with Lian
Duan and Kuan-Wen Lai)
*manuscripta mathematica*(165) pages 135--157 (2021) Erratum - On the proportion of transverse-free plane curves. (with Brian Freidin)
*Finite Fields and Their Applications.*Vol 72, June 2021 - A Bertini type theorem for pencils over finite fields. (with Dragos Ghioca)
*Finite Fields and Their Applications.*Vol 77, Jan 2022 - Bijective Cremona transformations of the plane. (with Kuan-Wen Lai, Masahiro Nakahara, Susanna Zimmermann)
*Selecta Mathematica, New Series***28**, 53 (2022) - Van Lint-MacWilliams' conjecture and maximum cliques in Cayley graphs
over finite fields. (with Chi Hoi Yip)
*Journal of Combinatorial Theory, Series A*Vol. 192 (2022), Paper No. 105667. - Smoothness in pencils of hypersurfaces over finite fields. (with Dragos Ghioca)
*Bulletin of the Australian Mathematical Society* (2022), p. 1-10.
- The EKR-module property of pseudo-Paley graphs of square order. (with Sergey Goryainov, Huiqiu Lin, and Chi Hoi Yip)
*Electron. J. Combin.*29 (2022), no. 4, Paper No. P4.33, 19 pp. - Linear families of smooth hypersurfaces over finitely generated fields. (with Dragos Ghioca and Zinovy Reichstein) to appear in
*Finite Fields and Their Applications* - Transverse linear subspaces to hypersurfaces over finite fields. (with Lian Duan and Kuan-Wen Lai)
- The subspace structure of maximum cliques in pseudo-Paley graphs from unions of cyclotomic classes. (with Chi Hoi Yip)
- Frobenius nonclassical hypersurfaces. (with Lian Duan and Kuan-Wen Lai)
- Blocking sets arising from plane curves over finite fields. (with Dragos Ghioca and Chi Hoi Yip)
- Most plane curves over finite fields are not blocking. (with Dragos Ghioca and Chi Hoi Yip)
- Proportion of blocking curves in a pencil. (with Dragos Ghioca and Chi Hoi Yip)
- Existence of pencils with nonblocking hypersurfaces. (with Dragos Ghioca and Chi Hoi Yip)
- Tangent-filling plane curves over finite fields. (with Dragos Ghioca)

Course notes on Diophantine Geometry (taught by Joe Silverman)

Spring 2023

Math 112: Abstract Algebra II

Spring 2023

Math 175: Number Theory

Winter 2023

Math 178: Cryptography (2 sections)

Here are some of the classes I taught at the University of British Columbia (as a postdoctoral fellow):

Summer 2021

Math 312: Introduction to Number Theory

Spring 2021

Math 103: Integral Calculus with Applications to Life Sciences

Summer 2020

Math 316: Partial Differential Equations

Spring 2020

Math 103: Integral Calculus with Applications to Life Sciences

Fall 2019

Math 190: Calculus Survey

Here are some of the classes I TA-ed or taught at Brown (as a graduate student):

Spring 2018

Math 520: Linear Algebra (Instructor)

Fall 2018

Math 50: Analytic Geometry and Calculus (Instructor)

Spring 2017

Math 90: Introductory Calculus I (Instructor)

Fall 2017

Math 90: Introductory Calculus I (TA)

Spring 2016

Math 200: Intermediate Calculus (for Physics/Engineering) (TA)

Fall 2016

Math 100: Introductory Calculus II (TA)

Fall 2015

Math 100: Introductory Calculus II (TA)

I completed the Certificate I: Reflective Teaching Program through the Sheridan Center for Teaching and Learning.