The degree mantra states that any non-zero univariate polynomial
of degree at most d has at most d roots (counted with
multiplicity). A generalization of this to the multivariate
setting, proved by Dvir-Kopparty-Saraf-Sudan asserts that over
any...
In this short talk, I will introduce the notion of n-morphisms
between two A-infinity algebras. These higher morphisms are such
that 0-morphisms correspond to standard A-infinity morphisms and
1-morphisms correspond to A-infinity homotopies. Their...
A generalization of the cartesian product and the free sum of
two convex domains is the p-product operation. We investigate the
behavior of symplectic capacities with respect to symplectic
p-products, and we give applications related to Viterbo's...
In this talk, I will present two results relating the
qualitative dynamics of non-degenerate Hamiltonian isotopies on
surfaces to the structure of their Floer complexes.
The first will be a topological characterization of those Floer
chains...
Clifford Geertz once quipped: “It is difficult to see what is
always there. Whoever discovered water, it was not a fish.” In the
same way, seeing familiar environments can prove challenging. Those
of us who live our lives in a given space become...
If a monomorphism of abstract groups H↪G induces an isomorphism
of profinite completions, then (G,H) is called a Grothendieck pair,
recalling the fact that Grothendieck asked about the existence of
such pairs with G and H finitely presented and...
The classification of geometric structures on manifolds
naturally leads to actions of automorphism groups, (such as mapping
class groups of surfaces) on "character varieties" (spaces of
equivalence classes of representations of surface groups).
Reproducibility is vital to ensuring scientific conclusions are
reliable, but failures of reproducibility have been a major issue
in nearly all scientific areas of study in recent decades. A key
issue underlying the reproducibility crisis is the...
A compact four dimensional completely integrable system f:M→R2
is semitoric if it has only non-degenerate singularities, without
hyperbolic blocks, and one of the components of generates a circle
action. Semitoric systems have been extensively...
