
Travis Scholl
Thu Oct 11, 2018
3:00 pm
In this talk we will focus on constructing "superisolated abelian varieties". These are abelian varieties that have isogeny class which contains a single isomorphism class. Their motivation comes from security concerns in elliptic and hyperelliptic curve cryptography. Using a theorem of Honda and Tate, we transfer the problem of finding...

Jacob Tsimerman
Thu Oct 4, 2018
3:00 pm
The class group is a natural abelian group one can associate to a number field, and it is natural to ask how it varies in families. Cohen and Lenstra famously proposed a model for families of quadratic fields based on random matrices of large rank, and this was later generalized by CohenMartinet. However, their model was observed by Malle to have...

Zev Klagsbrun
Thu May 31, 2018
3:00 pm
We determine the average size of the ΦSelmer group in any quadratic twist family of abelian varieties having an isogeny Φ of degree 3 over any number field. This has several applications towards the rank statistics in such families of quadratic twists. For example, it yields the first known quadratic twist families of absolutely...

Vadim Ponomarenko
Thu May 24, 2018
3:00 pm
Since Fermat characterized (without proof) those integers represented by the quadratic form x^2+y^2, number theorists have been extending these results. Recently a paper appeared in Journal of Number Theory answering the question for x^2 ± xy ± y^2. It turns out that this was not news (although JNT refuses to...

Daqing Wan
Thu May 17, 2018
3:00 pm
Given a global function field K of characteristic p>0, the fundamental arithmetic invariants include the genus, the class number, the prank and more generally the slope sequence of the zeta function of K. In this expository lecture, we explore possible stability of these invariants in a padic Lie tower of K. Strong stability is expected when...

Weiyan Chen
Tue Apr 17, 2018
3:00 pm
It is a classical topic dating back to Maclaurin (1698–1746) to study certain special points on smooth cubic plane curves, such as the 9 inflection points (Maclaurin and Hesse), the 27 sextatic points (Cayley), and the 72 points "of type 9" (Gattazzo). Motivated by these algebrogeometric constructions, we ask the following...

Bryden Cais
Thu Apr 12, 2018
3:00 pm
Let Y > X be a branched Gcovering of curves over a field k. The genus of X and the genus of Y are related by the famous Hurwitz genus formula. When k is perfect of characteristic p and G is a pgroup, one also has the DeuringShafarevich formula which relates the prank of X to that of Y. In this talk, we will discuss...