**Graduate Student**

**Email:** shamil_asgarli@brown.edu

** Mailing Address**: Department
of Mathematics

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.

**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

**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.

Here 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.