Number theory seminar tomorrow: Barinder Banwait

[Isabel Vogt]

Hi everyone,

Our speaker tomorrow is Barinder Banwait from Harish-Chandra Research Institute.  His title is "Explicit isogenies of prime degree over quadratic fields".  As usual, come prepared to ask a lot of questions!

Zoom link. Meeting ID: 995 4255 2693 Passcode: C401, Tuesday 10am - 10:55am 
Gather.town for lunch, Tuesday 12:30 - 1:30pm

Seminar calendar

Abstract: Let K be a quadratic field which is not an imaginary quadratic field of class number one. We describe an algorithm to compute a superset of the set of primes p for which there exists an elliptic curve over K admitting a K-rational p-isogeny. Combining this algorithm with recent work on the determination of quadratic points on low-genus modular curves, we determine - conditional upon the Generalised Riemann Hypothesis - the above set of isogeny primes for several quadratic fields, providing the first such examples after Mazur's 1978 determination for K = Q. We will give a live demo of the Sage and PARI/GP implementations of the algorithm.

See you tomorrow!

Isabel

[Isabel Vogt]

Hi everyone,

Attached are Barinder's slides from today -- see those of you who can make it at lunch soon.

Best,

Isabel