In this talk, I will describe the construction of contact
structures on higher-dimensional spheres with exotic fillability
properties. These can then me implemented on more general manifolds
via connected sum, yielding a host of exotic higher...
Filtered Lagrangian Floer homology gives rise to a barcode
associated to a pair of Lagrangians. It is well-known that
the lengths of the finite bars and the spectral distance are lower
bounds of the Lagrangian Hofer metric. In this talk we are...
Enumerative mirror symmetry is a correspondence between closed
Gromov-Witten invariants of a space X, and period integrals of a
family Y. One of the predictions of Homological Mirror Symmetry is
that the closed Gromov-Witten invariants can be...
Powerful homology invariants of knots in 3-manifolds have
emerged from both the gauge-theoretic and the symplectic kinds of
Floer theory: on the gauge-theoretic side is the instanton knot
homology of Kronheimer-Mrowka, and on the symplectic the...
Solitons are particle-like solutions to dispersive evolution
equations whose shapes persist as time evolves. In some situations,
these solitons appear due to the balance between nonlinear effects
and dispersion, in other situations their existence...
It is an open question as to whether the prime numbers contain
the sum A+B of two infinite sets of natural numbers A, B (although
results of this type are known assuming the Hardy-Littlewood prime
tuples conjecture). Using the Maynard sieve and the...
The four dimensional ellipsoid embedding function of a toric
symplectic manifold M measures when a symplectic ellipsoid embeds
into M. It generalizes the Gromov width and ball packing numbers.
This function can have a property called an infinite...
The Lefschetz property is central in the theory of projective
varieties, detailing a fundamental property of their Chow rings,
essentially saying that the multiplication with a geometrically
motivated class is of full rank.