Shamil Asgarli

Graduate Student


     Office: Room 020, Kaphotossar House

     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.

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)
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.
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.

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

Giovanni Inchiostro and I are the organizers for the Baby Algebraic Geometry seminar at Brown University for Fall 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).