Seminars archive
Upcoming Seminars   No upcoming seminars currently scheduled.  Past Seminars   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.   Seminar: Combinatorics Set families with a forbidden induced subposet Tao Jiang, Miami university   Seminar: Combinatorics The minimum number of nonnegative edges in hypergraphs Hao Huang, Institute for Advanced Study and DIMACS   Seminar: Algebra Unramified Brauer classes on cyclic covers of the projective plane Andrew Obus, University of Virginia   Defense: Dissertation Characterization of Quasiconformal Mapping and Extremal Length Decomposition and Its Application Wenfei Zou, Emory University   SOUTHEAST GEOMETRY SEMINAR (SGS XXIII) ., .   Seminar: Combinatorics Thresholds for Random Geometric kSAT Will Perkins, Georgia Tech   Seminar: Combinatorics Some problems in AntiRamsey Theory Sogol Jahanbekam, The University of Colorado, Denver   Seminar: Numerical Analysis and Scientific Computing Regularization by Krylov Subspace Methods Silvia Gazzola, University of Padova   Seminar: Combinatorics Progressions with a pseudorandom step Elad AignerHorev, Hamburg University 
