I'm a senior research scientist at ICERM and Brown University. I'm supported by the Simon's Collaboration on arithmetic geometry, number theory, and computation. I mostly research analytic number theory, computational number theory and geometry, and arithmetic geometry.
Previously, I was a postdoctoral researcher at the University of Warwick. I received my PhD at Brown University with Jeff Hoffstein as my PhD advisor.
See this page for a broad overview of my research.
Publications and Preprints
This is mostly in reverse chronological order. Please note that I upload preprints of all of my papers to the arxiv. If you have trouble accessing one of my papers, email me and I'll send you a copy.

Smitali Bhandari, Twyla Colburn, Patrick Lu, Haran Mouli, Helena Ellis Do Amaral, and David LowryDuda. Königsberg pseudoprimes and Fermat's little theorem for matrices.
(This comes from a PROMYS project for high schoolers). Preprint soon available. 
Chan Ieong Kuan, David LowryDuda, and Alexander Walker. Counting divisors in the outputs of a quadratic polynomial. Preprint soon available.

Theresa C. Anderson, Ayla Gafni, Kevin Hughes, Robert J. Lemke Oliver, David LowryDuda, Frank Thorne, Jiuya Wang, and Ruixiang Zhang. Improved bounds on number fields of small degree. arxiv preprint
Paper discussion page.
Other pages discussing this work: simplified proofs.
Talks discussing this work: May 2022, October 2022. 
Theresa C. Anderson, Ayla Gafni, Robert J. Lemke Oliver, David LowryDuda, George Shakan, and Ruixiang Zhang. Quantitative Hilbert irreducibility and almost prime values of polynomial discriminants. To appear in International Mathematics Research Notices. arxiv preprint.
Paper discussion page. 
David LowryDuda. Sign changes of cusp form coefficients on indices that are sums of two squares. arxiv preprint.

Anupam Datta, Nir Elber, Raymond Feng, David LowryDuda, and Henry Xie. Prime Sums. arxiv preprint.
(This comes from a PROMYS research project for high schoolers). 
Thomas Hulse, Chan Ieong Kuan, David LowryDuda, and Alexander Walker. Arithmetic progressions of squares and multiple Dirichlet series. arxiv preprint.

David LowryDuda, Takashi Taniguchi, and Frank Thorne. Uniform bounds for lattice point counting and partial sums of zeta functions. To appear in Mathematische Zeitschrift. arxiv preprint.

David LowryDuda. Visualizing modular forms. To appear in Arithmetic Geometry, Number Theory, and Computation volume in Simons Symposia series. arxiv preprint.
Springer SharedIt link to published article Talks discussing this work: November 2019 (ICERM), November 2019 (Bowdoin), May 2021, August 2021 
David LowryDuda, with an appendix by Brendan Hassett. Congruent numbers with the same hypotenuse. To appear in Arithmetic Geometry, Number Theory, and Computation volume in Simons Symposia series. arxiv preprint.
Springer SharedIt link to published article 
Alex J. Best, Jonathan Bober, Andy R. Booker, Edgar Costa, John Cremona, Martin Derickx, David LowryDuda, Min Lee, David Roe, Andrew V. Sutherland, and John Voight. Computing classical modular forms. To appear in Arithmetic Geometry, Number Theory, and Computation volume in Simons Symposia. arxiv preprint.
Springer SharedIt link to published article 
Thomas Hulse, Chan Ieong Kuan, David LowryDuda, and Alexander Walker. Triple correlation sums of coefficients of cusp forms. Journal of Number Theory 2020 (2021): 118. arxiv preprint.

Thomas Hulse, Chan Ieong Kuan, David LowryDuda, and Alexander Walker. The Laplace transform of the second moment in the Gauss circle problem. Algebra and Number Theory 15 No. 1 (2021): 127. arxiv preprint.

David LowryDuda and Adam Sakareassen. Towards flying through modular forms. Proceedings of Bridges (2021). arxiv preprint.
Talks discussing this work: August 2021 at Bridges 
David LowryDuda. Nonreal poles and irregularity of distribution. Journal of Number Theory, 217 (2020): 2335. arxiv preprint.

David LowryDuda and Miles Wheeler. Perturbing the mean value theorem: implicit functions, the Morse lemma, and beyond. The American Mathematical Monthly, 128 No. 1 (2020): 5061.
This paper received the Halmos  Ford award for expository excellence.
arxiv preprint.
Paper discussion page
A separate note on choosing functions and making figures for this paper 
Thomas Hulse, Chan Ieong Kuan, David LowryDuda, and Alexander Walker. A shifted problem for the congruent number problem. Ramanujan Journal (2019): 18. arxiv preprint.

Thomas Hulse, Chan Ieong Kuan, David LowryDuda and Alexander Walker. Second moments in the generalized Gauss circle problem. Forum of Mathematics, Sigma, 6 (2018): e24. arxiv preprint.
Paper discussion page. 
Alina Bucur, Edgar Costa, Chantal David, João Guerreiro, and David LowryDuda. Traces, high powers and one level density for families of curves over finite fields. Mathematical Proceedings of the Cambridge Philsophical Society 165 No. 2 (2018): 225248. arxiv preprint.

Thomas Hulse, Chan Ieong Kuan, David LowryDuda, and Alexander Walker. ShortInterval Averages of Sums of Fourier Coefficients of Cusp Forms. Journal of Number Theory, 173 (2017): 394415. arxiv preprint.
Paper discussion page. 
Thomas Hulse, Chan Ieong Kuan, David LowryDuda, and Alexander Walker. SignChanges of Sums of Fourier Coefficients of Cusp Forms. Journal of Number Theory, 177 (2017): 112135. arxiv preprint.
Paper discussion page. 
Thomas Hulse, Chan Ieong Kuan, David LowryDuda, and Alexander Walker. The Second Moment of Sums of Coefficients of Cusp Forms. Journal of Number Theory, 173 (2017): 304331. arxiv preprint.
Paper discussion page. 
Paul Carter and David LowryDuda. On Functions whose MeanValue Abscissas are Midpoints. The American Mathematical Monthly, 124 No. 6 (2017): 535542. arxiv preprint.
Paper discussion page. 
David LowryDuda. On Some Variants of the Gauss Circle Problem. PhD Thesis at Brown University, 2017. arxiv preprint.

David LowryDuda. Unexpected Conjectures about 5 modulo primes, Classroom Capsule in College Math Journal Vol 46 No. 1, January 2015.
Unpublished research notes
In addition to the unpublished notes on this site, I've written the following notes and do not intend to publish them.

David LowryDuda. Visualizing Modular Curves' A short technical note on implementation details for modular curve visualizations (2022). preprint
Discussion page 
David LowryDuda. A Short Note on Gaps between Powers of Consecutive Primes. Unpublished note (2017). arxiv preprint.
Discussion page. 
David LowryDuda. A Friendly Intro to Sieves with a Look Towards Recent Progress on the Twin Primes Conjecture. Unpublished note (2013). arxiv preprint.
Discussion page.