Shamil Asgarli

Office: Room 020, Kassar House

Email: shamil_asgarli@brown.edu

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

Research Interests
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 every degree $d\geq d_0$?

Papers

A New Proof of Warning's Second Theorem. To appear in the American Mathematical Monthly.
The Picard Group of the Moduli of Smooth Complete Intersections of Two Quadrics (with Giovanni Inchiostro)

Teaching
Here are some of the classes I have TA-ed or taught at Brown.
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 Fall 2017.
Notes on various topics

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