Nathan Kaplan

Nathan Kaplan is a Professor in the Department of Mathematics at the University of California, Irvine, where he conducts research in number theory, algebraic geometry, and combinatorics. His work spans rational points on varieties over finite fields, arithmetic statistics, coding theory, and the study of numerical semigroups. He is actively involved in the mathematical community, organizing seminars and conferences including the UC Irvine Number Theory Seminar and the Southern California Number Theory Day.

Dr. Kaplan received his PhD from Harvard University in 2013 under the direction of Noam Elkies. Following his doctorate, he was a postdoctoral researcher at Yale University from 2013-2015 before joining the faculty at UC Irvine.

His research interests focus on the intersection of number theory and algebraic geometry, with particular attention to problems involving rational points on varieties over finite fields, arithmetic statistics, and coding theory. He has made significant contributions to the study of numerical semigroups, cokernels of random p-adic and integer matrices, and quadratic forms and lattices. His work often bridges theoretical mathematics with applications in coding theory and cryptography.

Analysis of his recent publications shows a strong trend toward combinatorial aspects of number theory, particularly in the study of numerical semigroups and their properties. He frequently collaborates with researchers across institutions, with recent work spanning algebraic geometry, combinatorics, and coding theory. His publications demonstrate expertise in both theoretical developments and computational aspects of number theory.

Dr. Kaplan is deeply committed to undergraduate research and mentoring. He has experience as a mentor for undergraduate research projects through programs including SUMRY (a research program for Yale undergraduates), the University of Minnesota-Duluth REU program, and the Trinity University REU program. He actively encourages undergraduates to apply for summer research opportunities and has organized numerous outreach activities.

He is an organizer of the UC Irvine Number Theory Seminar and the Southern California Number Theory Day conference series. In 2018, he co-organized the Conference on Open Questions in Cryptography and Number Theory in honor of Alice Silverberg's 60th Birthday.

Dr. Kaplan has given numerous talks at mathematical venues including the Museum of Mathematics' Math Encounters series, where he presented "Error-Correcting Codes: The Mathematics of Communication" in July 2022. He has also spoken at the Yale Undergraduate Math Society, the UCI Math Circle, and various other outreach events.