**Graduate Student**

** **

** Office**: Room 020, Kassar House

**Email:** shamil_asgarli@brown.edu

** Mailing Address**: Department
of Mathematics

020 Kassar House

Box 1917

151 Thayer Street

Providence, RI 02912

** **

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

Broadly speaking, I am interested in algebraic geometry. My current research is in equivariant intersection theory. In particular, I would like to understand the integral Chow rings of various moduli spaces (equipped with a group action).

Another subject that I find appealing is the study algebraic curves/surfaces defined over finite fields. 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)

3. Sharp Bertini theorem for
plane curves over finite fields. To appear in Canadian Math.
Bulletin.

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

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)

Giovanni Inchiostro and I are the organizers for the Algebraic Geometry seminar at Brown University for Spring 2018.

Dori Bejleri, Giovanni Inchiostro and I are the organizers for the Baby Algebraic Geometry seminar at Brown University for Spring 2018

This is an expository article
on Wedderburn's
theorem.

Here
are the notes for Algebraic Geometry I (taught by Nathan
Pflueger).