I'll discuss spectral gaps in the following contexts:
- d-regular graphs
- locally symmetric spaces e.g. hyperbolic manifolds
- finite dimensional unitary representations of discrete groups
e.g. free groups, surface groups
Toric integrable systems, also known as symplectic toric
manifolds, arise as examples in different contexts within geometry
and related areas. Semitoric integrable systems are a
generalization of toric integrable systems in dimension four. In
this...
For the past 25 years, Legendrian contact homology has played a
key role in contact topology. I'll discuss a package of new
invariants for Legendrian knots and links that builds on Legendrian
contact homology and is derived from rational symplectic...
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 celebrated...
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 finite...
I will discuss two methods for diagnosing ’t Hooft anomalies of
internal symmetries in 2+1d lattice systems. Anomalous symmetries
of this kind arise naturally at the boundary of 3+1D
symmetry-protected topological phases, and are known to be...
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 celebrated...
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 finite...
