A function f:𝔽n2→𝔽n2 is linear if f(x+y)=f(x)+f(y) for all pairs
(x,y).
Suppose f is "a bit linear" -- say, f(x+y)=f(x)+f(y) for 1% of
pairs(x,y). Must f agree with a truly linear function a
positive proportion of the time? How large a
proportion...
I will discuss a recursive formula for the homotopy type of the
space of Legendrian embeddings of sufficiently positive cables with
the maximal Thurston-Bennequin invariant. Via this formula, we
identify infinitely many new components within the...
Lagrangian cobordisms induce exact triangles in the Fukaya
category. But how many exact triangles can be recovered by
Lagrangian cobordisms? One way to measure this is by comparing the
Lagrangian cobordism group to the Grothendieck group of the...
In the talk, I will introduce a distance-like function on the
zero section of the cotangent bundle using symplectic embeddings of
standard balls inside an open neighborhood of the zero section. I
will provide some examples which illustrate the...
Given a lagrangian link with k components it is possible to
define an associated Hofer norm on the braid group with k strands.
In this talk we are going to detail this definition, and explain
how it is possible to prove non degeneracy if k=2 and...
Floer homotopy type refines the Floer homology by associating a
(stable) homotopy type to an Hamiltonian, whose homology gives the
Hamiltonian Floer homology. In particular, one expects the existing
structures on the latter to lift as well, such as...
We consider 2D quantum materials (non-magnetic and constant
magnetic field cases), modeled by a continuum Schroedinger
operator, whose potential is a sum of translates of an atomic well,
centered on the vertices of a discrete subset of the plane...
I will discuss how to build small symplectic caps for contact
manifolds as a step in building small closed symplectic
4-manifolds. As an application of the construction, I will give
explicit handlebody descriptions of symplectic embeddings of...
I'll explain joint work in progress with Abbondandolo and Kang
concerning the Clarke dual action functional of convex domains and
pseudoholomorphic planes. In dimension 4, I'll explain applications
to the knot types of periodic Reeb orbits.
A recent line of work has shown a surprising connection between
multicalibration, a multi-group fairness notion, and
omniprediction, a learning paradigm that provides simultaneous loss
minimization guarantees for a large family of loss functions...
