Email: hqd4bz (at) virginia (dot) edu
Office: Kerchof 401
Office Hours: MW 3:30 - 4:30; Thursday 1:00 - 2:00
I am a fifth-year graduate student at the University of Virginia. My thesis advisor is Andrew Obus. My research interests are arithmetic geometry, algebraic number theory, and Galois theory. In particular, I am working on the lifting problem for curves and deformations of wildly ramified covers. Before graduate school, I used to work as a mechanical engineer for a year.
I am on the job market, looking for a postdoctoral position. Here are my CV and my research statement.
1. Connectedness of the Moduli space of Artin-Schreier curves of fixed genus, 2017. Submitted. In this paper, we show that the moduli space of Artin-Schreier covers (Z/p-covers over a field of positive characteristic) of a given genus g is connected when g is sufficiently large.
2. Deformations of Artin-Schreier covers, 2018. In preparation.
1. The refined cyclic local lifting problem for curves. We are studying whether local cyclic extensions are liftable in towers. In particular, we aim to answer the following question. Given a local G-extension k[[z]]/k[[t]] with G cyclic and a lift R[[S]]/R[[T]] of a subextension k[[s]]/k[[t]] to characteristic zero, is there a lift of k[[z]]/k[[t]] to characteristic zero that containing R[[S]]/R[[T]] as a subextension? One can learn more about the lifting problem from this paper written by Andrew Obus. So far, we are able to answer the question for most of the cases when k has characteristic 2. In particular, the answer is yes when k=2 and G=Z/4xZ/m where m is odd.
2. Equicharacteristic deformations of Artin-Schreier-Witt covers . Let R=k[[t]] where char k=p>0. Given an order p^n-automorphism of a formal disc over R. One can derive the minimal semi-stable model for which the specializations of fixed points are distinct and lie in the smooth locus of the special fiber. The description leads to a combinatorial object which resembles a Hurwitz tree in mixed characteristic (0,p), which we give the same name. The existence of a Hurwitz tree is necessary for the existence of a p^n-automorphism whose ramification data fitted into the Hurwitz tree. In the case of n=1, we can prove that the conditions imposed by the Hurwitz tree's structure are also sufficient. That helps us improve our results about the connectedness of the moduli of Artin-Schreier covers. We are working on extending our results for the case n>1, and studying the ring of versal deformations of Artin-Schreier-Witt covers.
Instructor of Record:
2017 Fall, Math 1310, Calculus I
2017 Spring, Math 1210 Applied Calculus I
2016 Fall, Math 1210 Applied Calculus I
2016 Spring, Math 1220 Applied Calculus II
2015 Fall, Math 1210 Applied Calculus I
2017 Summer, Math 1320, Calculus II
2015 Summer, Math 1310, Calculus I
2015 Spring, Math 5656, Number Theory and Math 1330, Calculus III
2014 Fall, Math 1310, Calculus I (2 sections)
I got a Bachelor in Mechanical Engineering and worked as a mechanical engineer for a year in Vietnam. Below are some of the simulation videos I made for my projects back in College.
1. Metal Clip Machine, 2009
2. Automatic Sorting System 1, 2009
3. Automatic Sorting System 2, 2009
My bachelor thesis (in Vietnamese) was about designing and constructing a model of pipe conveyor. Here are the drawings and some photos of the real model.