Homological mirror symmetry for Milnor fibers of simple singularities
Y Lekili, K Ueda - arXiv preprint arXiv:2004.07374, 2020 - arxiv.org
We prove homological mirror symmetry for Milnor fibers of simple singularities in dimensions
greater than one, which are among the log Fano cases of Conjecture 1.5 in arXiv …
greater than one, which are among the log Fano cases of Conjecture 1.5 in arXiv …
Rabinowitz Fukaya categories and the categorical formal punctured neighborhood of infinity
S Ganatra, Y Gao, S Venkatesh - arXiv preprint arXiv:2212.14863, 2022 - arxiv.org
This paper constructs and studies the Rabinowitz (wrapped) Fukaya category, a categorical
invariant of exact cylindrical Lagrangians in a Liouville manifold whose cohomological …
invariant of exact cylindrical Lagrangians in a Liouville manifold whose cohomological …
Recent progress on SYZ mirror symmetry for some non-compact Calabi-Yau surfaces
TC Collins, YS Lin - arXiv preprint arXiv:2208.14485, 2022 - arxiv.org
We survey the authors recent works, joint with A. Jacob, on Strominger-Yau-Zaslow mirror
symmetry for rational elliptic surfaces and del Pezzo surfaces. We discuss some …
symmetry for rational elliptic surfaces and del Pezzo surfaces. We discuss some …
On the Rouquier dimension of wrapped Fukaya categories and a conjecture of Orlov
S Bai, L Côté - Compositio Mathematica, 2023 - cambridge.org
We study the Rouquier dimension of wrapped Fukaya categories of Liouville manifolds and
pairs, and apply this invariant to various problems in algebraic and symplectic geometry. On …
pairs, and apply this invariant to various problems in algebraic and symplectic geometry. On …
Homological Berglund-H\" ubsch mirror symmetry for curve singularities
M Habermann, J Smith - arXiv preprint arXiv:1903.01351, 2019 - arxiv.org
Given a two-variable invertible polynomial, we show that its category of maximally-graded
matrix factorisations is quasi-equivalent to the Fukaya-Seidel category of its Berglund-H\" …
matrix factorisations is quasi-equivalent to the Fukaya-Seidel category of its Berglund-H\" …
Mirror symmetry for Berglund-H\" ubsch Milnor fibers
B Gammage - arXiv preprint arXiv:2010.15570, 2020 - arxiv.org
We explain how to calculate the Fukaya category of the Milnor fiber of a Berglund-H\" ubsch
invertible polynomial, mostly proving a conjecture of Yank {\i} Lekili and Kazushi Ueda on …
invertible polynomial, mostly proving a conjecture of Yank {\i} Lekili and Kazushi Ueda on …
Derived factorization categories of non‐Thom–Sebastiani‐type sums of potentials
Y Hirano, G Ouchi - Proceedings of the London Mathematical …, 2023 - Wiley Online Library
We first prove semi‐orthogonal decompositions of derived factorization categories arising
from sums of potentials of gauged Landau–Ginzburg models, where the sums are not …
from sums of potentials of gauged Landau–Ginzburg models, where the sums are not …
Homological mirror symmetry for invertible polynomials in two variables
M Habermann - Quantum Topology, 2022 - ems.press
In this paper, we give a proof of homological mirror symmetry for two variable invertible
polynomials, where the symmetry group on the B-side is taken to be maximal. The proof …
polynomials, where the symmetry group on the B-side is taken to be maximal. The proof …
Cluster categories from Fukaya categories
H Bae, W Jeong, J Kim - arXiv preprint arXiv:2209.09442, 2022 - arxiv.org
We show that the derived wrapped Fukaya category $ D^\pi\mathcal {W}(X_ {Q}^{d+ 1}) $,
the derived compact Fukaya category $ D^\pi\mathcal {F}(X_ {Q}^{d+ 1}) $ and the cocore …
the derived compact Fukaya category $ D^\pi\mathcal {F}(X_ {Q}^{d+ 1}) $ and the cocore …