BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Antoine Leudière (University of Calgary) DTSTART:20250313T190000Z DTEND:20250313T200000Z DTSTAMP:20260423T005832Z UID:ANTS/13 DESCRIPTION:Title: El liptic curves\, Drinfeld modules\, and computations\nby Antoine Leudi ère (University of Calgary) as part of Calgary Algebra and Number Theory Seminar\n\nLecture held in MS 337.\n\nAbstract\nWe will talk about Drinfel d modules\, and how they compare to elliptic curves for algorithms and com putations.\n\nDrinfeld modules can be seen as function field analogues of elliptic curves. They were introduced in the 1970's by Vladimir Drinfeld\, to create an explicit class field theory of function fields. They were in strumental to prove the Langlands program for GL2 of a function field\, or the function field analogue of the Riemann hypothesis.\n\nElliptic curves \, to the surprise of many theoretical number theorists\, became a fundame ntal computational tool\, especially in the context of cryptography (ellip tic curve Diffie-Hellman\, isogeny-based post-quantum cryptography) and co mputer algebra (ECM method).\n\nDespite a rather abstract definition\, Dri nfeld modules offer a lot of computational advantages over elliptic curves : one can benefit from function field arithmetics\, and from objects calle d Ore polynomials and Anderson motives.\n\nWe will use two examples to hig hlight the practicality of Drinfeld modules computations\, and mention som e applications.\n LOCATION:https://researchseminars.org/talk/ANTS/13/ END:VEVENT END:VCALENDAR