Nick Sheridan

Institute for Advanced Study; Member, School of Mathematics

April 14, 2014

Nick Sheridan

Institute for Advanced Study; Member, School of Mathematics

April 14, 2014

Nick Sheridan

Institute for Advanced Study; Member, School of Mathematics

March 10, 2014

Nick Sheridan

Institute for Advanced Study; Member, School of Mathematics

March 3, 2014

Nick Sheridan

Institute for Advanced Study; Member, School of Mathematics

February 24, 2014

Juan Maldacena

Institute for Advanced Study; Faculty, School of Natural Science

February 20, 2014

Nathan Seiberg

Institute for Advanced Study; Faculty, School of Natural Science

February 20, 2014

Edward Witten

Institute for Advanced Study; Faculty, School of Natural Science

February 20, 2014

Peter Scholze

University of Bonn

February 14, 2014

One of the most studied objects in mathematics is the modular curve, which is the quotient of hyperbolic 2-space by the action of \(\mathrm{SL}_2(\mathbb Z)\). It is naturally the home of modular forms, but it also admits an algebraic structure. The interplay of these structures lies at the heart of the Langlands correspondence for \(\mathrm{GL}_2/\mathbb Q\), connecting modular forms with Galois representations. The natural generalizations of the modular curve to higher dimension are the arithmetic locally symmetric spaces.

Peter Scholze

University of Bonn

February 12, 2014

One of the most studied objects in mathematics is the modular curve, which is the quotient of hyperbolic 2-space by the action of \(\mathrm{SL}_2(\mathbb Z)\). It is naturally the home of modular forms, but it also admits an algebraic structure. The interplay of these structures lies at the heart of the Langlands correspondence for \(\mathrm{GL}_2/\mathbb Q\), connecting modular forms with Galois representations. The natural generalizations of the modular curve to higher dimension are the arithmetic locally symmetric spaces.

Nick Sheridan

Institute for Advanced Study; Member, School of Mathematics

February 10, 2014