I am currently a postdoc at AIM (American Institute of Mathematics). My mentor is Brian Conrey. Previously, I recieved my Ph.D. in 2021 from UC Santa Barbara, where my advisor was Yitang Zhang. Before that, I obtained my Masters in 2016 and Bachelor in 2014 from Cal Poly Pomona, and my Associate in 2009 from Orange Coast College.

My primary research interest is in analytic number theory. I am particularly interested in the distributions of the generalized $k$-fold divisor functions in arithmetic progressions, divisor sums, and their connections to bounded gaps between primes, moments of $L$-functions, and random matrix theory.

Generalized divisor functions in arithmetic progressions: I. The $k$-fold divisor function in arithmetic progressions to large moduli,

*J. Number Theory***227**(2021), 30-93. [Journal] [PDF]Explicit Formulas for Enumeration of Lattice Paths: Basketball and the Kernel Method (with C. Banderier, C. Krattenthaler, A. Krinik, D. Kruchinin, V. Kruchinin, and M. Wallner),

*Dev. Math.***58**(2019), Springer, 78-118. [Journal] [PDF]

I have no teaching duties at AIM.

Vector Calculus I, UCSB Math 6A

Differential Equations, UCSB Math 4B

Trigonometry, CPP Math 120

Basic Algebra, CPP Math 11

Transition to Higher Mathematics, UCSB Math 8

Introduction to Linear Algebra, UCSB Math 108A

Introduction to Theory of Complex Variables, UCSB Math 122A

Linear Algebra with Applications, UCSB Math 4A

Differential Equations, UCSB Math 4B

Calculus for Social and Life Sciences I, UCSB Math 34A

Calculus for Social and Life Sciences II, UCSB Math 34B

Early Start Mathematics, CPP ESM 5

- UCSB Mathematics Department Graduate Mentor 2018-2020, organized by the Hypatian Seminar. I provided mentoring to first-year mathemetics graduate students.

Casey Donlan, David Vartanian

Project:*Applications Of Bessel’s Functions*[Poster PDF]Jenny Do, Tien Huynh

Project:*Applications Of Prime Numbers*[Poster PDF]Drew Miller, Ryan Yick

Project:*The Congruent Number Problem*[Poster PDF]Tanner Zuleeg

Project:*Connection Between The Gamma Function And The Hurwitz Zeta Function*[Poster PDF]

The Directed Reading Program is a one-on-one mathematics mentoring program in which graduate students or junior faculty members mentor UCSB undergraduates in reading and research projects.

Weekly seminars on topics in analytic number theory aim towards graduate students. Click for current schedule and more.

Resources for quals for UCSB math grad students.

- dtn@aimath.org
- 600 E Brokaw Rd, San Jose, CA 95112-1006
- by appointment