Shamil Asgarli

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

Papers and preprints

1. A New Proof of Warning's Second Theorem. The American Mathematical Monthly Vol. 125, No. 6 (2018), 549--553.
2. 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.
3. Sharp Bertini theorem for plane curves over finite fields. Canadian Math. Bulletin. Vol. 62 (2), 2019 p. 223--230.
4. Transverse lines to surfaces over finite fields. (with Lian Duan and Kuan-Wen Lai) manuscripta mathematica (165) pages 135--157 (2021) Erratum
5. On the proportion of transverse-free plane curves. (with Brian Freidin) Finite Fields and Their Applications. Vol 72, June 2021
6. A Bertini type theorem for pencils over finite fields. (with Dragos Ghioca) Finite Fields and Their Applications. Vol 77, Jan 2022
7. Bijective Cremona transformations of the plane. (with Kuan-Wen Lai, Masahiro Nakahara, Susanna Zimmermann) Selecta Mathematica, New Series 28, 53 (2022)
8. 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.
9. Smoothness in pencils of hypersurfaces over finite fields. (with Dragos Ghioca) Bulletin of the Australian Mathematical Society
(2022), p. 1-10.
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.
11. Linear families of smooth hypersurfaces over finitely generated fields. (with Dragos Ghioca and Zinovy Reichstein) to appear in Finite Fields and Their Applications
12. Transverse linear subspaces to hypersurfaces over finite fields. (with Lian Duan and Kuan-Wen Lai)
13. The subspace structure of maximum cliques in pseudo-Paley graphs from unions of cyclotomic classes. (with Chi Hoi Yip)
14. Frobenius nonclassical hypersurfaces. (with Lian Duan and Kuan-Wen Lai)
15. Blocking sets arising from plane curves over finite fields. (with Dragos Ghioca and Chi Hoi Yip)
16. Most plane curves over finite fields are not blocking. (with Dragos Ghioca and Chi Hoi Yip)
17. Proportion of blocking curves in a pencil. (with Dragos Ghioca and Chi Hoi Yip)
18. Existence of pencils with nonblocking hypersurfaces. (with Dragos Ghioca and Chi Hoi Yip)
19. Tangent-filling plane curves over finite fields. (with Dragos Ghioca)

Expository notes and other documents

Teaching at Santa Clara University

Teaching at UBC (past)

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

Teaching at Brown (past)

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

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