1 citations · 3 across the 13 of their papers we have counts for
14 papers
On intrinsic homological mirror symmetry for toric degenerations
Shaoyun Bai, Sebastian Haney
This paper studies the Floer-theoretic aspects of homological mirror symmetry inspired by proposals of Perutz and Siebert and the Gross--Siebert intrinsic mirror symmetry program.…
A proof of the Arnold-Givental conjecture
Shaoyun Bai, Egor Shelukhin, Yi Wang +1
We prove the Arnold-Givental conjecture in full generality: given a closed symplectic manifold , an anti-symplectic involution with fixed point set $L={\rm F…
Quantum Steenrod powers and Hamiltonian maps
Shaoyun Bai, Egor Shelukhin, Nicholas Wilkins +1
We prove a series of new results in Hamiltonian dynamics on a general closed symplectic manifold , including: 1. If admits a Hamiltonian diffeomorphism which is either…
Integral Hamiltonian Floer theory: Foundations
Shaoyun Bai, Guangbo Xu
Continuing our previous work on the integral Arnold conjecture, we establish the foundation of Hamiltonian Floer theory over integer coefficients on any compact symplectic manifold…
Bordism and resolution of singularities
Mohammed Abouzaid, Shaoyun Bai
We adapt algorithms for resolving the singularities of complex algebraic varieties to prove that the natural map of homology theories from complex bordism to the bordism theory of…
Cohomological splitting over rationally connected bases
Shaoyun Bai, Daniel Pomerleano, Guangbo Xu
We prove a cohomological splitting result for Hamiltonian fibrations over enumeratively rationally connected symplectic manifolds As a key application, we prove that the cohomology…
Equivariant formality in complex-oriented theories
Shaoyun Bai, Daniel Pomerleano
Let be a product of unitary groups and let be a compact symplectic manifold with Hamiltonian -action. We prove an equivariant formality result for any complex-orient…
Franks' dichotomy for toric manifolds, Hofer-Zehnder conjecture, and gauged linear sigma model
Shaoyun Bai, Guangbo Xu
We prove that for any compact toric symplectic manifold, if a Hamiltonian diffeomorphism admits more fixed points, counted homologically, than the total Betti number, then it has i…
Arnold conjecture over integers
Shaoyun Bai, Guangbo Xu
For any closed symplectic manifold, we show that the number of 1-periodic orbits of a nondegenerate Hamiltonian thereon is bounded from below by a version of total Betti number ove…
A new transversality condition on orbifolds and integer-valued Gromov-Witten type invariants
Shaoyun Bai, Guangbo Xu
Following a proposal of Fukaya-Ono and the exploration by B. Parker, we introduce a new transversality condition, the FOP transversality condition, for sections of orbifold vector…
On the Rouquier dimension of wrapped Fukaya categories and a conjecture of Orlov
Shaoyun Bai, Laurent Côté
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…
Bifurcations of embedded curves and towards an extension of Taubes' Gromov invariant to Calabi-Yau 3-folds
Shaoyun Bai, Mohan Swaminathan
We define an integer-valued virtual count of embedded pseudo-holomorphic curves of two times a primitive homology class and arbitrary genus in symplectic Calabi--Yau -folds, whi…
A symplectic formula of generalized Casson invariants
Shaoyun Bai
Suppose Y is an integer homology 3-sphere, Taubes proved that the number of irreducible critical orbits of the perturbed Chern-Simons functional on Y, counted with signs, is equal…
Equivariant Cerf theory and perturbative Casson invariants
Shaoyun Bai, Boyu Zhang
We develop an equivariant Cerf theory for Morse functions on finite-dimensional manifolds with group actions, and adapt the technique to the infinite-dimensional setting to study t…