Shamil Asgarli

Office: Room 020, Kassar House

Email: shamil_asgarli@brown.edu

Kassar House, Room 020, Box 1917
151 Thayer Street,
Providence, RI 02912

I am a fifth-year graduate student in the math department at Brown University. My advisor is Brendan Hassett.

Curriculum Viate

Research

Broadly speaking, I am interested in algebraic geometry. Current research interests include algebraic varieties over finite fields, intersection theory of moduli spaces, and birational geometry of the plane.

Here is an example of a problem that interests me: Suppose $S\subseteq\mathbb{P}^2$ is a collection of (reduced) points with coordinates in $\mathbb{F}_q$. Then by Bertini Smoothness Theorem over Finite Fields (due to Bjorn Poonen), there exists a smooth curve $C\subseteq\mathbb{P}^2$ such that $C(\mathbb{F}_q)=S$.

1) What is the minimal degree of such a curve $C$?
2) If $d_0$ is the minimal degree of such a curve, then are there examples in every degree $d\geq d_0$?

Papers

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)  To appear in Transactions of the AMS.
3. Sharp Bertini theorem for plane curves over finite fields. To appear in Canadian Math. Bulletin.
4. Transverse lines to surfaces over finite fields. (with Lian Duan and Kuan-Wen Lai)

Notes on various topics

New: Here are the notes for a course on Diophantine Geometry taught by Joe Silverman in Spring 2019.

This is an expository article on Wedderburn's theorem.
are the notes for Algebraic Geometry I taught by Nathan Pflueger.

Teaching

Here are some of the classes I have TA-ed or taught at Brown.

Fall 2018 - Math 50: Analytic Geometry and Calculus (Instructor)
Spring 2018 - Math 520: Linear Algebra (Instructor).
Fall 2017 - Math 90: Introductory Calculus I (TA).
Spring 2017 - Math 90: Introductory Calculus I (Instructor).
Fall 2016 - Math 100: Introductory Calculus II (TA)
Spring 2016 - Math 200: Intermediate Calculus (for Physics/Engineering) (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.