About this Event
SPEAKER: Jan Vonk (Institute for Advanced Study)
TITLE: "Rigid Cocycles and their Arithmetic"
ABSTRACT: In the early 20th century, Hecke studied the diagonal restrictions of Eisenstein series over real quadratic fields. An infamous sign error caused him to miss an important feature, which later lead to highly influential developments in the theory of complex multiplication (CM) initiated by Gross and Zagier in their famous work on Heegner points on elliptic curves. In this talk, we will explore what happens when we replace the imaginary quadratic fields in CM theory with real quadratic fields, and propose a framework for a tentative 'RM theory', based on the notion of rigid meromorphic cocycles, introduced in joint work with Henri Darmon. I will discuss several of their arithmetic properties, and their apparent relevance in the study of explicit class field theory of real quadratic fields, the construction of rational points on elliptic curves, and the theory of Borcherds lifts. This concerns various joint works, with Henri Darmon, Alice Pozzi, and Yingkun Li.
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Bjorn Poonen is inviting you to a scheduled Zoom meeting.
Topic: MIT number theory seminar
Time: Apr 28, 2020 04:30 PM Eastern Time (US and Canada)
Every week on Tue, until May 5, 2020, 3 occurrence(s)
Apr 28, 2020 04:30 PM
May 5, 2020 04:30 PM
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