Simons Collaborationon Arithmetic Geometry, Number Theory, and Computation

Adam Logan

Adam Logan graduated from Princeton University in 1995 and received his doctorate from Harvard four years later.  He then held postdoctoral positions at MSRI, UC Berkeley, CRM in Montreal, and the University of Waterloo as well as a tenure-track position at the University of Liverpool before leaving academia, first for finance and then to work for the Government of Canada, where he has been since 2010.  His primary research interests have to do with modularity of varieties of dimension greater than 1 and arithmetic of K3 surfaces, but he is easily persuaded to work on other computational problems involving the arithmetic of geometrically interesting varieties, as illustrated by recent and ongoing work on higher modularity of elliptic curves over function fields, surfaces of maximal Picard rank, Ceresa cycles of plane quartic curves, and modular forms associated to Clifford algebras.  In September 2023 he will join the Collaboration as Senior Research Associate at ICERM.

Jerson Caro

Jerson Caro is a postdoctoral researcher at Boston University. His research area is Number Theory, with an emphasis on arithmetic geometry and algebraic number theory. In general terms, his main interest is in three topics: finiteness of rational points, the rank of elliptic curves, and the arithmetic of number fields. He received his Ph.D. from the Pontificia Universidad Católica de Chile under the supervision of Hector Pasten.

Jun Lau

Jun Bo Lau is a graduate student at University of California, San Diego, working with Kiran Kedlaya. Lau’s research interests lie in explicit methods in arithmetic geometry, more specifically p-adic techniques in modular curves, curves over finite fields and cryptography. He will join the collaboration in August 2023.

Sarah Frei

Sarah Frei is a John Wesley Young Research Instructor at Dartmouth College, specializing in algebraic geometry and arithmetic geometry. Her research interests include arithmetic aspects of moduli spaces, Brauer groups, and rationality. She received her Ph.D. from the University of Oregon in 2019, under the supervision of Nicolas Addington, and was a postdoctoral instructor at Rice University before joining Dartmouth in 2022.

Aashraya Jha

Aashraya Jha is a PhD student at Boston University, working with Jennifer Balakrishnan. He is interested in arithmetic geometry and algebraic number theory, focusing on finding rational points of curves over number fields, properties of modular abelian varieties and Uniform Mordell-Lang.

Grant Molnar

Grant Molnar was awarded his PhD at Dartmouth College in 2023, studying arithmetic statistics under John Voight. He received his BS from BYU Provo in 2016 and his MS from the same university in 2018. Grant has wide-ranging mathematical interests, but possesses a special fascination with algebraic and analytic number theory.

Juanita Duque-Rosero

Juanita Duque-Rosero received her PhD from Dartmouth College in 2023, working with John Voight. Her research interests include number theory and arithmetic geometry, focusing on triangular modular curves and explicit methods for computing rational points. Since July 2023, she has been a research assistant professor at Boston University.

Sachi Hashimoto

Sachi Hashimoto is interested in effective methods in arithmetic geometry and algebraic geometry, and especially in developing methods for determining rational points on curves. She received her PhD in 2022 from Boston University under the supervision of Jennifer Balakrishnan. In July 2023, she started as a Tamarkin Assistant Professor at Brown University. Previously, she was a postdoctoral researcher at the Max Planck Institute for Mathematics in the Sciences in Leipzig.

Oana Padurariu

Oana Padurariu received her PhD at Boston University in 2023 working with Jennifer Balakrishnan. Since July 2023, she has been a postdoctoral fellow at the Max Planck Institute for Mathematics in Bonn. Oana is interested in rational points on varieties (such as Shimura curves and bielliptic curves) and Mazur’s Program B.

Padmavathi Srinivasan

Padmavathi Srinivasan received her PhD in 2016 at MIT under the direction of Bjorn Poonen. She joined the collaboration in Fall 2022 after postdoctoral positions at the Georgia Institute of Technology and the University of Georgia. She is interested in various explicit aspects of families of curves and abelian varieties, and their applications to the study of rational points on curves. In Fall 2023 she will take up a faculty position at Boston University.

Barinder Banwait

Barinder Banwait joined the Collaboration in September 2022. His research into rational points on modular curves includes work on computing pseudoeigenvalues of modular forms as well as determining uniform sets of prime-degree isogenies of elliptic curves. He is also interested in computational aspects of Galois representations of higher dimensional abelian varieties and has contributed to Sage and the LMFDB. Barinder received a BA and MMath from Cambridge University in 2009 and a PhD from Warwick University in 2013 under the supervision of John Cremona. After postdoctoral positions in Bordeaux, Essen, Prayagraj, and Heidelberg, as well as industry positions in Cambridge and London in the Surgical Robotics and Quantitative Finance sectors, he is currently a postdoctoral researcher at Boston University.

Francesca Bianchi

Francesca Bianchi is a postdoc at the University of Groningen. She received her PhD from the University of Oxford in 2019, under the supervision of Jennifer Balakrishnan and Alan Lauder. She is mainly interested in p-adic aspects of (computational) arithmetic geometry, in particular in p-adic heights and p-adic methods to compute rational and integral points on curves.