IISER Mohali, Knowledge city, Sector 81, SAS Nagar, Manauli PO 140306

Explicit isogenies of prime degree over quadratic fields

Dr. Barinder Banwait (HRI, Allahabad)

Zoom Link

Location Online
Abstract:
We begin the talk by illustrating some of the motivation for studying elliptic curves, including the congruent number problem which the ancient Greeks considered, as well as modern-day cryptography. We then recall Mazur's theorem on rational isogenies of prime degree, and present our algorithmic work which provides, conditional upon the Generalised Riemann Hypothesis, a method to extend Mazur's theorem to quadratic fields, yielding the first examples of the determination of prime degree isogenies since Mazur's work in the 70s. A live-demo of the Sage and PARI/GP implementations of the algorithm will be given.

Meeting ID: 947 0910 0636
Passcode: 971375
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