Abstract: The goal of this lecture series is to give you a
glimpse into the Langlands program, a central topic at the
intersection of algebraic number theory, algebraic geometry and
representation theory. In the first lecture, we will look at
a...
Abstract: Geometry and representation theory are intertwined in
deep and foundational ways. One of the most important instances of
this relationship was uncovered in the 1970s by Deligne and
Lusztig: the representation theory of matrix groups over...
Abstract: The theory of elliptic curves with complex
multiplication has yielded some striking arithmetic applications,
ranging from (cases of) Hilbert’s Twelfth Problem to the Birch and
Swinnerton-Dyer Conjecture. These applications rely on the...
Shimura varieties are an important geometric object in the
Langlands program, because the Hecke (adelic group) action allows
us to view various cohomology groups as Hecke modules. Moreover,
the cohomology admits an integral structure when the...
Abstract: The goal of this lecture series is to give you a
glimpse into the Langlands program, a central topic at the
intersection of algebraic number theory, algebraic geometry and
representation theory. In the first lecture, we will look at
a...
Abstract: Geometry and representation theory are intertwined in
deep and foundational ways. One of the most important instances of
this relationship was uncovered in the 1970s by Deligne and
Lusztig: the representation theory of matrix groups over...
Abstract: An explicit understanding of the category of all
(smooth, complex) representations of p-adic groups provides an
important tool not just within representation theory. It also has
applications to number theory and other areas, and in...
Abstract: The goal of this lecture series is to give you a
glimpse into the Langlands program, a central topic at the
intersection of algebraic number theory, algebraic geometry and
representation theory. In the first lecture, we will look at
a...
Abstract: Geometry and representation theory are intertwined in
deep and foundational ways. One of the most important instances of
this relationship was uncovered in the 1970s by Deligne and
Lusztig: the representation theory of matrix groups over...