COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Number Theory Seminar > Average Ranks of Elliptic Curves After p-Extension

## Average Ranks of Elliptic Curves After p-ExtensionAdd to your list(s) Download to your calendar using vCal - Ross Paterson (University of Bristol)
- Tuesday 25 October 2022, 14:30-15:30
- Centre for Mathematical Sciences, MR13.
If you have a question about this talk, please contact Rong Zhou. As E varies among elliptic curves defined over the rational numbers, a theorem of Bhargava and Shankar shows that the average rank of the Mordell—Weil group E(Q) is bounded. If we now fix a number field K, is the same true of E(K)? I will report on progress on this question, answering it in the affirmative for certain choices of K. This progress follows from a statistical study of certain local invariants of elliptic curves, which loosely describe the failure of Galois descent for the associated p-Selmer groups. Time permitting, we will also discuss upper and lower bounds for the average dimension of 2-Selmer groups over multi-quadratic extensions. This talk is part of the Number Theory Seminar series. ## This talk is included in these lists:- All CMS events
- All Talks (aka the CURE list)
- CMS Events
- Centre for Mathematical Sciences, MR13
- DPMMS Lists
- DPMMS Pure Maths Seminar
- DPMMS info aggregator
- DPMMS lists
- Hanchen DaDaDash
- Interested Talks
- Number Theory Seminar
- School of Physical Sciences
- bld31
Note that ex-directory lists are not shown. |
## Other listsCUID Type the title of a new list here The Believing Brain: Neuroscience of Belief panel discussion## Other talksCan we use network analysis to predict violence? The Expressive Power of CSP Quantifiers Base Editing and Prime Editing: Precise Gene Correction Without Double-Strand DNA Breaks Joined Up Thinking Ocean/sea-ice interactions at the floe scale: regimes of sea-ice floe melt Discussion Panel |