19 citations · 55 across the 9 of their papers we have counts for
9 papers
Relating categorical dimensions in topology and symplectic geometry
Andrew Hanlon, Jeff Hicks, Oleg Lazarev
We study several notions of dimension for (pre-)triangulated categories naturally arising from topology and symplectic geometry. We prove new bounds on these dimensions and raise s…
Reverse isoperimetric inequalities for Lagrangian intersection Floer theory
Jean-Philippe Chassé, Jeff Hicks, Yoon Jae Nick Nho
We extend Groman and Solomon's reverse isoperimetric inequality to pseudoholomorphic curves with punctures at the boundary and whose boundary components lie in a collection of Lagr…
Resolutions of toric subvarieties by line bundles and applications
Andrew Hanlon, Jeff Hicks, Oleg Lazarev
Given any toric subvariety of a smooth toric variety of codimension , we construct a length resolution of by line bundles on . Furthermore, these l…
Some cute applications of Lagrangian cobordisms towards examples in quantitative symplectic geometry
Jeff Hicks, Cheuk Yu Mak
We provide some constructions using Lagrangian cobordisms that improve known examples for some symplectic squeezing problems. Additionally, we prove a flexibility result that Lagra…
Lagrangian cobordisms and Lagrangian surgery
Jeff Hicks
Lagrangian -surgery modifies an immersed Lagrangian submanifold by topological -surgery while removing a self-intersection. Associated to a -surgery is a Lagrangian surger…
Aspects of functoriality in homological mirror symmetry for toric varieties
Andrew Hanlon, Jeff Hicks
We study homological mirror symmetry for toric varieties, exploring the relationship between various Fukaya-Seidel categories which have been employed for constructing the mirror t…
Tropical Lagrangians in toric del-Pezzo surfaces
Jeff Hicks
We look at how one can construct from the data of a dimer model a Lagrangian submanifold in whose valuation projection approximates a tropical hypersurface. Each…
Wall-crossing from Lagrangian Cobordisms
Jeff Hicks
Biran and Cornea showed that monotone Lagrangian cobordisms give an equivalence of objects in the Fukaya category. However, there are currently no known non-trivial examples of mon…
Tropical Lagrangian Hypersurfaces are Unobstructed
Jeff Hicks
We produce for each tropical hypersurface a Lagrangian whose moment map projection is a tropical amoeba of . When…