The honest answer to the question is that I actually do not
know. I will therefore rather talk about several famous examples
that are widely called "h-principle results" and try to explain
some of the ideas behind the ones I am most familiar with.
We consider the problem of computing a Gradient Descent solution
of a continuously differentiable function f on a bounded convex
domain, i.e., finding a "point where Gradient Descent terminates".
Equivalently, this corresponds to computing a so...
Knots associated to overtwisted manifolds are less explored.
There are two types of knots in an overtwisted manifold – loose and
non-loose. Non-loose knots are knots with tight complements whereas
loose knots have overtwisted complements. While we...
In this talk we consider the links of simple singularities,
which are contactomoprhic to S3/G for finite subgroups G of
SU(2,C). We explain how to compute the cylindrical contact homology
of S3/G by means of perturbing the canonical contact form by...
Recent years have seen the appearance of a plethora of possible
metrics on spaces of Lagrangian submanifolds. Indeed, on top of the
better-known Lagrangian Hofer metric and spectral norm, Biran,
Cornea, and Shelukhin have constructed families of so...
We consider the standard L-function attached to a cuspidal
automorphic representation of a general linear group. We present a
proof of a subconvex bound in the t-aspect. More generally, we
address the spectral aspect in the case of uniform parameter...
The defocusing Non Linear Schrödinger equation iut=Δu−u|u|p−1 is
a classical model of mathematical physics. For energy subcritical
non linearities, Ginibre and Velo proved in the ’80s that all
solutions are global in time and asymptotically behave...
The query model is one of the most basic computational
models. In contrast to the Turing machine model, fundamental
questions regarding the power of randomness and quantum computing
are relatively well-understood. For example, it is
well-known...
In the last forty years, the study of singularity formation has
mostly concerned model problems and focusing non linearities. In
this second lecture, we will try to give a unified overview on the
known mechanisms of singularity formation, with in...
