Seminars archive
Upcoming Seminars   No upcoming seminars currently scheduled.  Past Seminars   Colloquium Randomized Block Coordinate Gradient Methods for a Class of Structured Nonlinear Programming Zhaosong Lu, Simon Fraser University   Seminar: Algebra Something special... Ken Ono, Emory   Seminar: Algebra More examples of nonrational adjoint groups Nivedita Bhaskhar, Emory University   Seminar: Computer Science Hierarchy and Structure: Nonparametric models for space, language, and relations Alex Smola, Google/CMU   Defense: Dissertation Computational Methods for Centrality Measurements in Complex Networks Christine Klymko, Emory University   Seminar: Computer Science Scalable and PrivacyPreserving Searchable Cloud Data Services Ming Li, Utah State University   Seminar: Combinatorics On Erdos' conjecture on the number of edges in 5cycles Zoltan Furedi, Renyi Institute of Mathematics, Budapest, Hungary   Seminar: Algebra Degree 3 cohomological invariants and quadratic splitting of hermitian forms JeanPierre Tignol, Université Catholique de Louvain   Seminar: Combinatorics 3Coloring and 3ListColoring Graphs on Surfaces Luke Postle, Emory University   Seminar: Algebra The distribution of 2Selmer ranks and additive functions Robert Lemke Oliver, Stanford University Venue: Mathematics and Science Center, Room W306 Show abstract The problem of determining the distribution of the 2Selmer ranks of quadratic twists of an elliptic curve has received a great deal of recent attention, both in works conjecturing distributions and in those providing solutions; in both cases, the nature of the twotorsion of the elliptic curve plays a cruical role. In particular, if $E/\mathbb{Q}$ has full twotorsion, the distribution is known, due to work of HeathBrown, SwinnertonDyer, and Kane, and if $E$ possesses no twotorsion, then, again, the distribution is known, due to work of Klagsbrun, Mazur, and Rubin, though with the caveat that one arranges discriminants in a nonstandard way. In stark contrast to these two cases, we show that if $K$ is a number field and $E/K$ is an elliptic curve with partial twotorsion, then no limiting distribution on 2Selmer ranks exists. We do so by showing that, for any fixed integer $r$, at least half of the twists of $E$ have 2Selmer rank greater than $r$, and we establish an analogous result for simultaneous twists, either for multiple elliptic curves twisted by the same discriminant or for a single elliptic curve twisted by a tuple of discriminants. These results depend upon connecting the 2Selmer rank of twists to the values of an additive function and then establishing results analogous to the classical Erd\H{o}sKac theorem. This work is joint with Zev Klagsbrun. 
