In this talk, I will discuss progress on showing hardness of the
Minimum Circuit Size Problem (MCSP). The computational complexity
of MCSP is a longstanding mystery, dating back as far as Levin's
seminal work on NP-completeness in 1973. Over the...
I will describe the construction of a harmonic measure that
reproduces a harmonic function from its Robin boundary data, which
is a combination of the value of the function and its normal
derivative. I shall discuss the surprising fact that this...
Consider a scenario where we are learning a predictor, whose
predictions will be evaluated by their expected loss. What if we do
not know the precise loss at the time of learning, beyond some
generic properties (like convexity)? What if the same...
Let G be an infinite discrete group. Finite dimensional unitary
representations of G are usually quite hard to understand. However,
there are interesting notions of convergence of such
representations as the dimension tends to infinity. One notion
—...
In the late '90s, Eliashberg and Thurston established a
remarkable connection between foliations and contact structures in
dimension three: any co-oriented, aspherical foliation on a closed,
oriented 3-manifold can be approximated by positive and...
The Tree Evaluation Problem has emerged in the past decade as a
leading candidate for separating logspace from polynomial time. In
this talk we will introduce the problem, as well as the context
behind its introduction and conjectured hardness. We...
An interesting feature of General Relativity is the presence of
singularities which can occur in even the simplest examples such as
the Schwarzschild spacetime. However, in this case the singularity
is cloaked behind the event horizon of the black...
A magnetic system is the toy model for the motion of a charged
particle moving on a Riemannian manifold endowed with a magnetic
force. To a magnetic flow we associate an operator, called the
magnetic curvature operator. Such an operator encodes...
Dimitroglou-Rizell-Golovko constructs a family of Legendrians in
prequantization bundles by taking lifts of monotone Lagrangians.
These lifted Legendrians have a Morse-Bott family of Reeb chords.
We construct a version of Legendrian Contact Homology...
