# overview
I have research interests in number theory and arithmetic geometry. I'm interested in elliptic curves and Drinfeld modules, and in particular I work on special values of analytic functions, including L-series, modular forms, and hypergeometric functions, and their connections with periods and logarithms.

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# educationAndTraining[].organization.label
Brown University - (Providence, Rhode Island, United States)

# educationAndTraining[].organization.label
Brown University - (Providence, Rhode Island, United States)

# educationAndTraining[].organization.label
Amherst College - (Amherst Center, Massachusetts, United States)

# publications[].label
Determination of the algebraic relations among special Gamma-values in positive characteristic

# publications[].label
A rapid introduction to Drinfeld modules, $t$-modules, and $t$-motives

# publications[].publisher
European Mathematical Society - EMS - Publishing House GmbH

# publications[].label
Identities for Anderson generating functions for Drinfeld modules

# publications[].label
Special L-values and shtuka functions for Drinfeld modules on elliptic  curves

# publications[].label
A rapid introduction to Drinfeld modules, $t$-modules, and $t$-motives

# publications[].label
Algebraic independence of arithmetic gamma values and Carlitz zeta values

# publications[].label
Effective rigid analytic trivializations for Drinfeld modules

# publications[].label
Algebraic independence of values of Goss L-functions at s=1

# publications[].label
A formula and a congruence for Ramanujan's tau-function

# publications[].label
Convolutions of Goss and Pellarin $L$-series

# publications[].label
Hyperderivative power sums, Vandermonde matrices, and Carlitz multiplication coefficients

# publications[].label
Theta operators, Goss polynomials, and nu-adic modular forms

# publications[].label
Linear independence of Gamma values in positive characteristic

# publications[].label
A Weil-Barsotti formula for Drinfeld modules

# publications[].label
Explicit formulas for Drinfeld modules and their periods

# publications[].label
Theta operators, Goss polynomials, and v-adic modular forms

# publications[].label
Equidistribution of Gross points over rational function fields

# publications[].label
On the torsion of Jacobians of principal modular curves of level 3^n

# publications[].label
Combinatorics of traces of Hecke operators.

# publications[].publisher
Proceedings of the National Academy of Sciences

# publications[].label
A finite field hypergeometric function associated to eigenvalues of a  Siegel eigenform

# publications[].label
Quadratic twists of modular forms and elliptic curves

# publications[].label
Frobenius difference equations and algebraic independence of zeta values in positive equal characteristic

# publications[].label
Extensions of abelian varieties defined over a number field

# publications[].label
Universal norms on abelian varieties over global function fields

# publications[].label
Linear independence of Gamma values in positive characteristic

# publications[].label
Canonical heights on elliptic curves in characteristic p

# publications[].label
Frobenius difference equations and algebraic independence of zeta values  in positive equal characteristic

# publications[].label
Hyperderivatives of periods and quasi-periods for Anderson $t$-modules

# publications[].label
ALGEBRAIC RELATIONS AMONG PERIODS AND LOGARITHMS OF RANK 2 DRINFELD MODULES

# publications[].label
Geometric Gamma values and zeta values in positive characteristic

# publications[].label
A finite field hypergeometric function associated to eigenvalues of a Siegel eigenform

# publications[].label
Hyperderivatives of periods and quasi-periods for Anderson $t$-modules

# publications[].label
A note on log-algebraicity on elliptic curves

# publications[].label
p-adic properties of values of the modular j-function

# publications[].label
Special L-values and shtuka functions for Drinfeld modules on elliptic curves

# publications[].label
Geometric Gamma Values and Zeta Values in Positive Characteristic

# publications[].label
An effective criterion for Eulerian multizeta values in positive  characteristic

# publications[].label
Tannakian duality for Anderson-Drinfeld motives and algebraic  independence of Carlitz logarithms

# publications[].label
Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms

# publications[].label
The de Rham isomorphism for Drinfeld modules over Tate algebras

# publications[].label
Hyperderivative power sums, Vandermonde matrices, and Carlitz  multiplication coefficients

# publications[].label
Extensions of abelian varieties defined over a number field

# publications[].label
Algebraic independence of periods and logarithms of Drinfeld modules  (with an appendix by Brian Conrad)

# publications[].label
Explicit formulas for Drinfeld modules and their periods

# publications[].label
Canonical heights on elliptic curves in characteristic p

# publications[].label
Identities for Anderson generating functions for Drinfeld modules

# publications[].label
Effective rigid analytic trivializations for Drinfeld modules

# publications[].label
An effective criterion for Eulerian multizeta values in positive characteristic

# publications[].publisher
European Mathematical Society - EMS - Publishing House GmbH

# publications[].label
Log-algebraic identities on Drinfeld modules and special L-values

# publications[].label
ALGEBRAIC INDEPENDENCE OF PERIODS AND LOGARITHMS OF DRINFELD MODULES

# publications[].label
Function Field Analogue of Shimura's Conjecture on Period Symbols

# publications[].label
The Mahler measure of a Calabi-Yau threefold and special L-values

# publications[].label
The Mahler measure of a Calabi-Yau threefold and special -values

# publications[].label
Log-algebraic identities on Drinfeld modules and special L-values

# publications[].label
Algebraic independence of arithmetic gamma values and Carlitz zeta  values

# publications[].label
On the torsion of Jacobians of principal modular curves of level 3(n)

# publications[].label
Effective rigid analytic trivializations for Drinfeld modules

# publications[].label
Algebraic independence of periods and logarithms of Drinfeld modules   (with an appendix by Brian Conrad)

# publications[].label
Gaussian hypergeometric functions and traces of Hecke operators

# publications[].label
A Weil-Barsotti formula for Drinfeld modules

# publications[].label
The de Rham isomorphism for Drinfeld modules over Tate algebras

# publications[].label
Algebraic relations among periods and logarithms of rank 2 Drinfeld  modules

# publications[].label
Determination of the algebraic relations among special Gamma-values in  positive characteristic

# publications[].label
A rapid introduction to Drinfeld modules, $t$-modules, and $t$-motives

# publications[].label
Algebraic independence of values of Goss L-functions at s=1

# researcherOn[].label
Arithmetic of Function Fields and Diophantine Geometry

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# researcherOn[].label
NSF-Arithmetic and Transcendence of Values of Special Functions

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# researcherOn[].label
Arithmetic and Transcendence of Values of Special Functions

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# researcherOn[].awardedBy.label
Qatar National Research Fund - (Doha, Qatar)

# streetAddress
Texas A&M University; Mathematics; 3368 TAMU

# etdChairOf[].label
Lutes, Brad Aubrey (2010-10). Special Values of the Goss L-function and Special Polynomials. Doctoral Dissertation.

# etdChairOf[].label
Fuselier, Jenny G. (2009-05). Hypergeometric functions over finite fields and relations to modular forms and elliptic curves. Doctoral Dissertation.

# etdChairOf[].label
Samart, Detchat (2014-08). Mahler Measures of Hypergeometric Families of Calabi-Yau Varieties. Doctoral Dissertation.

# etdChairOf[].label
Vega Veglio, Maria V. (2010-07). Hypergeometric functions over finite fields and their relations to algebraic curves.. Doctoral Dissertation.