arXiv subjects

Sara Venkatesh

Publications and source records attributed to Sara Venkatesh.

5 recordsLinked to original sources

arXiv2025

Semi-orthogonality in Fukaya-Seidel mirrors to blowups of abelian varieties

We prove evidence of Kontsevich's homological mirror symmetry conjecture (HMS) for a blow-up of an abelian surface times the complex plane, on the complex side, and its symplectic Landau-Ginzburg mirror. Specifically, the first author proved evidence of HMS for a 1-parameter family of genus 2 curves on the complex side, as a hypersurface in an abelian surface. The generalized SYZ mirror to the hypersurface is then the SYZ mirror to the Landau-Ginzburg model given by the blow-up of the abelian surface times the complex plane, along the hypersurface times zero, with superpotential given by projection to the complex plane. The mirror to the blow-up - without the superpotential - is obtained by removing a generic smooth fiber from the generalized SYZ mirror superpotential. We prove a categorical HMS result for the latter pair, between categories expected to split-generate. To do so, we equip the punctured superpotential with a Fukaya category which involves both partial and full wrapping in the base of the symplectic Landau-Ginzburg model due to the removal of a generic fiber. Semi-orthogonality appears in the categorical invariants on both sides of HMS.

math.SG↗

arXiv2022

Rabinowitz Fukaya categories and the categorical formal punctured neighborhood of infinity

This paper constructs and studies the Rabinowitz (wrapped) Fukaya category, a categorical invariant of exact cylindrical Lagrangians in a Liouville manifold whose cohomological morphisms, ``Rabinowitz wrapped Floer homology groups" measure the failure of wrapped Floer cohomology to satisfy Poincare duality (and in particular vanish for any pair with at least one compact Lagrangian). Our main result, answering a conjecture of Abouzaid, relates the Rabinowitz and usual wrapped Fukaya category by way of a general construction introduced by Efimov, the categorical formal punctured neighborhood of infinity. As an application, we show how Rabinowitz Fukaya categories can be fit into - and in particular often computed in terms of - mirror symmetry.

math.SG↗

arXiv2021

Periodic leaf-wise intersection points from Lagrangians

We investigate leaf-wise intersection points on hypersurfaces of contact type in monotone symplectic manifolds. We show that monotone Floer-essential Lagrangians detect periodic leaf-wise intersection points in hypersurfaces of contact type whose Reeb flow is Zoll. Examples include the prequantization bundles appearing in monotone toric negative line bundles. Generalizing, we prove the existence of leaf-wise intersection points for certain annulus subbundles in weak+-monotone negative line bundles, not necessarily toric. The proofs combine reduced symplectic cohomology with the original methods employed by Albers-Frauenfelder to prove global existence results of this kind.

math.SG↗

arXiv2020

The quantitative nature of reduced Floer theory

We study the reduced symplectic cohomology of disk subbundles in negative symplectic line bundles. We show that this cohomology theory "sees" the spectrum of a quantum action on quantum cohomology. Precisely, quantum cohomology decomposes into generalized eigenspaces of the action of the first Chern class by quantum cup product. The reduced symplectic cohomology of a disk bundle of radius $R$ sees all eigenspaces whose eigenvalues have size less than $R$, up to rescaling by a fixed constant. Similarly, we show that the reduced symplectic cohomology of an annulus subbundle between radii $R_1$ and $R_2$ captures all eigenspaces whose eigenvalues have size between $R_1$ and $R_2$, up to a rescaling. We show how local closed-string mirror symmetry statements follow from these computations.

math.SG↗

arXiv2017

Rabinowitz Floer homology and mirror symmetry

We define a quantitative invariant of Liouville cobordisms with monotone filling through an action-completed symplectic cohomology theory. We illustrate the non-trivial nature of this invariant by computing it for annulus subbundles of the tautological bundle over $\mathbb{C} P^1$ and give further conjectural computations based on mirror symmetry. We prove a non-vanishing result in the presence of Lagrangian submanifolds with non-vanishing Floer homology.

math.SG↗