# Mathematics

I recieved my PhD in mathematics at the University of Colorado Boulder under David Grant.

My mathematical interests are in arithmetic geometry. More specifically, I study elliptic curves, genus-two curves, abelian surfaces, curves of higher genus, higher-dimensional abelian varieties, p-adic numbers, theta functions, and modular forms.

Papers# p-Adic Numbers

For each prime integer p, there is a whole set of numbers, alternative to the real numbers, which are well-suited to a version of calculus that somehow still remembers discrete properties around p.

# Elliptic Curves

Elliptic curves are geometric objects with profound connections to many areas of mathematics.

# Modular Forms

Modular forms are a certain class of geometric function. As complex functions, they encode classifying information about elliptic curves. At the same time, their power series coefficients exibit deep patterns in the integers.

# Higher Genus Curves

Elliptic curves are just the start of the theory of algebraic curves, being the curves of genus one. Their higher-genus cousins form a furtile playground in which to enrich our understanding of everything we know from elliptic curves.

# Abelian Varieties

Abelian varieties are yet another way to extend the essence of elliptic curves, but as geometric spaces of higher dimension.

# Theta Functions

Theta functions are a class of geometric function that encode some of both the modular information of modular forms and the geometric information of abelian varieties.

# Papers

A collection of my papers are listed below:

Title | Coauthors | Link |
---|---|---|

Twisted Kronecker theta functions and p-adic interpolation | Y. Choie | Submitted |

Twisted Kronecker series and periods of modular forms on $\Gamma_0(\mathbb{N})$ | Y. Choie | Submitted |

Universal p-adic sigma and Weierstrass zeta functions | D. Grant | Journal arXiv |

Perfectoid covers of abelian varieties | D. Gvirtz, B. Heuer, D. Shchedrina, K. Shimizu, P. Wear, Z. Yao | Journal arXiv |

Constants in Titchmarsh divisor problems for elliptic curves | R. Bell, A.C. Cojocaru, A. Cowan, N. Jones, V. Matei, G. Smith, I. Vogt | Journal arXiv |

On Generalizations of p-Adic Weierstrass Sigma and Zeta Functions | self | Thesis |