Arithmetic Geometry, Number Theory, and Computation

Jennifer Balakrishnan is Clare Boothe Luce Associate Professor of Mathematics and Statistics at Boston University. She holds a Ph.D. in Mathematics from the Massachusetts Institute of Technology.Noam Elkies is Professor of Mathematics at Harvard University. He holds a Ph.D. in Mathematics from Harvard University.Brendan Hassett is Professor of Mathematics at Brown University and Director of the Institute for Computational and Experimental Research in Mathematics. He holds a Ph.D. in Mathematics from Harvard University.Bjorn Poonen is Distinguished Professor in Science at the Massachusetts Institute of Technology. He holds a Ph.D. in Mathematics from the University of California at Berkeley.Andrew Sutherland is Principal Research Scientist at the Massachusetts Institute of Technology. He holds a Ph.D. in Mathematics from the Massachusetts Institute of Technology.John Voight is Professor of Mathematics at Dartmouth College. He holds a Ph.D. in Mathematics from the University of California at Berkeley.

• A robust implementation for solving the S-unit equation and several application (C. Rasmussen).- Computing classical modular forms for arbitrary congruence subgroups (E. Assaf).- Square root time Coleman integration on superelliptic curves (A. Best).- Computing classical modular forms ( A. Sutherland).- Elliptic curves with good reduction outside of the first six primes (B. Matschke).- Efficient computation of BSD invariants in genus 2 (R. van Bommel).- Restrictions on Weil polynomials of Jacobians of hyperelliptic curves (E. Costa).- Zen and the art of database maintenance (D. Roe).- Effective obstructions to lifting Tate classes from positive characteristic (E. Costa).- Conjecture: 100% of elliptic surfaces over Q have rank zero (A. Cowan).- On rational Bianchi newforms and abelian surfaces with quaternionic multiplication (J. Voight).- A database of Hilbert modular forms (J. Voight).- Isogeny classes of Abelian Varieties over Finite Fields in the LMFDB (D. Roe).- Computing rational points on genus 3 hyperelliptic curves (S. Hashimoto).- Curves with sharp Chabauty-Coleman bound (S. Gajović).- Chabauty-Coleman computations on rank 1 Picard curves (S. Hashimoto).- Linear dependence among Hecke eigenvalues (D. Kim).- Congruent number triangles with the same hypotenuse (D. Lowry-Duda).- Visualizing modular forms (D. Lowry-Duda).- A Prym variety with everywhere good reduction over Q(√ 61) ( J. Voight).- The S-integral points on the projective line minus three points via étale covers and Skolem's method (B. Poonen).