About Me

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.

Publications

1. 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]

2. 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]

Preprints

1. Generalized divisor functions in arithmetic progressions: II. Variance of the ternary divisor function in arithmetic progressions (2021), 22 pages. [PDF]

2. A note on the zeros of the derivative of the Riemann zeta function near the critical line (2020), 6 pages. [PDF]

Current Teaching

I have no teaching duties at AIM.

Past Teaching

As Instructor of Record

• Vector Calculus I, UCSB Math 6A

• Differential Equations, UCSB Math 4B

• Trigonometry, CPP Math 120

• Basic Algebra, CPP Math 11

As Teaching Assistant

• 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

Mentoring

Graduate Mentoring

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

Undergraduate Mentoring

• 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]

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