Dr. Ayla Gafni is an Assistant Professor of Mathematics in the Department of Mathematics at the University of Mississippi.
Research Interests
Dr. Ayla Gafni’s research is in Analytic Number Theory, Harmonic Analysis, and Combinatorics.
She is also interested in:
- Problems at the interface between number theory and harmonic analysis
- Hardy-Littlewood circle method
- Distributions of sequences modulo one
- Diophantine approximation on manifolds
- Asymptotic behavior of integer partition functions
Biography
Ayla Gafni completed her PhD at Pennsylvania State University in 2016, under the supervision of Robert C. Vaughan. She held postdoctoral positions at University of Rochester and the Mathematical Sciences Research Institute (MSRI) in Berkeley, California, before joining the UM faculty in 2019. She was a 2020 recipient of the ORAU’s Ralph E. Powe Junior Faculty Enhancement Award.
Dr. Gafni has presented her research at seminars and conferences across the United States, as well as in Canada, UK, Germany, and Australia. She has participated in research workshops at Oberwolfach in Germany, the Heilbronn Institute in the United Kingdom, the Fields Institute and the Banff International Research Station in Canada, and the American Institute of Mathematics in San Jose, California. In Summer 2021, Dr. Gafni participated in the trimester program on Harmonic Analysis and Analytic Number Theory at the Hausdorff Institute of Mathematics in Bonn, Germany. She has collaborated with over 20 mathematicians from across the United States, Canada, UK, India, Germany, and Taiwan.
Publications
Improved bounds on number fields of small degree, (with Theresa C Anderson, Kevin Hughes, Robert J Lemke Oliver, David Lowry-Duda, Frank Thorne, Jiuya Wang, and Ruixiang Zhang), submitted. arXiv:2204.01651 [math.NT]
Uniform distribution and geometric incidence theory, (with Alex Iosevich and Emmett Wyman), submitted. arxiv:2202.05359[math.CO]
Quantitative Hilbert Irreducibility and Almost Prime Values of Polynomial Discriminants, (with Theresa C Anderson, Robert J Lemke Oliver, David Lowry-Duda, George Shakan, and Ruixiang Zhang), International Mathematics Research Notices (2021).
Almost all primes satisfy the Atkin-Serre conjecture and are not extremal, (with Jesse Thorner and Peng-Jie Wong), Research in Number Theory, 7 (2021).
Partitions into Prime Powers, Mathematika, 67 (2021), 468–488.
Connecting the Dots: Maximal polygons on a square grid, (with Sam Chow and Paul Gafni). Mathematics Magazine 94 (2021), 118–124.
Extremal primes of elliptic curves without complex multiplication, (with Chantal David, Amita Malik, Neha Prabhu, and Caroline Turnage-Butterbaugh), Proc. Amer. Math.
Additive energy and the metric Poissonian property, (with Thomas F. Bloom, Sam Chow, and Aled Walker), Mathematika 64 (2018), 679–700.
Power Partitions, Journal of Number Theory, 163 (2016), 19–42.
Longest run of equal parts in a random integer composition, Discrete Mathematics, 338 (2015), 236–247.
Counting rational points near planar curves, Acta Arithmetica, 43 (2014), 91–100.
Courses Taught
- Math 263 Unified Calculus & Analytic Geometry III
- Math 319 Introduction to Linear Algebra
- Math 459 Introduction to Complex Analysis
- Math 655 Theory Functions of Complex Variables I
- Math 656 Theory Functions of Complex Variable II
Education
Ph.D. Mathematics, Pennsylvania State University (2016)