64 citations · 346 across the 27 of their papers we have counts for
25 papers · 1 filter
Rigidity, flexibility, and a sign error
Yanki Lekili, Nick Sheridan
The documents [OAI26a, OAI26b, OAI26c] claimed to prove cases of the Hodge conjecture via homological mirror symmetry, before being withdrawn by OpenAI. We discuss the source of th…
Kodaira fibres and wrapped Floer cohomology
Yanki Lekili
Let be a singular fibre of a relatively minimal complex elliptic fibration with smooth total space, and let be a nonvanishing holomorphic two-form near . We show that a…
Curves on surfaces and moduli of associative algebras
Yanki Lekili
Given an immersion of a circle in a punctured surface , we give an explicit (and finite) computation of the -algebra associated with this curve when viewed as an objec…
Deformations of Kalck--Karmazyn algebras via Mirror Symmetry
Yanki Lekili, Jenia Tevelev
As observed by Kawamata, a -Gorenstein smoothing of a Wahl singularity gives rise to a one-parameter flat degeneration of a matrix algebra. A similar result holds for a…
Noncommutative crepant resolutions of singularities via Fukaya categories
Jonathan David Evans, Yanki Lekili
We compute the wrapped Fukaya category of a cylinder relative to a divisor of points, proving a mirror equivalence with the ca…
Equivariant Fukaya categories at singular values
Yanki Lekili, Ed Segal
Given a Hamiltonian torus action on a symplectic manifold, Teleman and Fukaya have proposed that the Fukaya category of each symplectic quotient should be equivalent to an equivari…
Symplectic cohomology of compound Du Val singularities
Jonathan David Evans, Yanki Lekili
We compute symplectic cohomology for Milnor fibres of certain compound Du Val singularities that admit small resolution by using homological mirror symmetry. Our computations sugge…
A symplectic look at the Fargues-Fontaine curve
Yanki Lekili, David Treumann
This paper discusses homological mirror symmetry for the Fargues-Fontaine curve of equal characteristic.
The symplectic geometry of higher Auslander algebras: Symmetric products of disks
Tobias Dyckerhoff, Gustavo Jasso, Yanki Lekili
We show that the perfect derived categories of Iyama's -dimensional Auslander algebras of type are equivalent to the partially wrapped Fukaya categories of the -…
Homological mirror symmetry for higher dimensional pairs of pants
Yanki Lekili, Alexander Polishchuk
Using Auroux's description of Fukaya categories of symmetric products of punctured surfaces, we compute the partially wrapped Fukaya category of the complement of generic hyp…
Derived equivalences of gentle algebras via Fukaya categories
Yanki Lekili, Alexander Polishchuk
Following the approach of Haiden-Katzarkov-Kontsevich arXiv:1409.8611, to any homologically smooth graded gentle algebra we associate a triple , where is…
Auslander orders over nodal stacky curves and partially wrapped Fukaya categories
Yanki Lekili, Alexander Polishchuk
It follows from the work of Burban and Drozd arXiv:0905.1231 that for nodal curves , the derived category of modules over the Auslander order provides a categori…
Fukaya categories of plumbings and multiplicative preprojective algebras
Tolga Etgü, Yanki Lekili
Given an arbitrary graph and non-negative integers for each vertex of , let be the Weinstein -manifold obtained by plumbing copies of according t…
Duality between Lagrangian and Legendrian invariants
Tobias Ekholm, Yanki Lekili
Consider a pair , of a Weinstein manifold with an exact Lagrangian submanifold , with ideal contact boundary , where is a contact manifold and …
Associative Yang-Baxter equation and Fukaya categories of square-tiled surfaces
Yanki Lekili, Alexander Polishchuk
We show that all strongly non-degenerate trigonometric solutions of the associative Yang-Baxter equation (AYBE) can be obtained from triple Massey products in the Fukaya category o…
Arithmetic mirror symmetry for genus 1 curves with marked points
Yanki Lekili, Alexander Polishchuk
We establish a -linear derived equivalence between the relative Fukaya category of the 2-torus with distinct marked points and the derived catego…
Generating the Fukaya categories of Hamiltonian G-manifolds
Jonathan David Evans, Yanki Lekili
Let be a compact Lie group and be a field of characteristic such that does not have -torsion. We show that a free Lagrangian orbit of a Ham…
Koszul duality patterns in Floer theory
Tolga Etgü, Yanki Lekili
We study symplectic invariants of the open symplectic manifolds obtained by plumbing cotangent bundles of 2-spheres according to a plumbing tree . For any tree , we cal…
Floer cohomology of the Chiang Lagrangian
Jonathan David Evans, Yanki Lekili
We study holomorphic discs with boundary on a Lagrangian submanifold in a Kaehler manifold admitting a Hamiltonian action of a group which has as an orbit. We prove var…
Floer cohomology of -equivariant Lagrangian branes
Yanki Lekili, James Pascaleff
Building on Seidel-Solomon's fundamental work, we define the notion of a -equivariant Lagrangian brane in an exact symplectic manifold where $\mathfrak{g} \subset…
Arithmetic mirror symmetry for the 2-torus
Yanki Lekili, Timothy Perutz
This paper explores a refinement of homological mirror symmetry which relates exact symplectic topology to arithmetic algebraic geometry. We establish a derived equivalence of the…
The symplectic topology of some rational homology balls
Yanki Lekili, Maksim Maydanskiy
We study the symplectic topology of some finite algebraic quotients of the An Milnor fibre which are diffeomorphic to the rational homology balls that appear in Fintushel and Stern…
Fukaya categories of the torus and Dehn surgery
Yanki Lekili, Timothy Perutz
This paper is a companion to the authors' forthcoming work extending Heegaard Floer theory from closed 3-manifolds to compact 3-manifolds with two boundary components via quilted F…
Geometric composition in quilted Floer theory
Yanki Lekili, Max Lipyanskiy
We prove that Floer cohomology of cyclic Lagrangian correspondences is invariant under transverse and embedded composition of Lagrangians under a general set of assumptions. In the…