Shamil Asgarli

Graduate Student


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     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

    


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

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.


Teaching
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


Notes on various topics

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