65 citations · 91 across the 20 of their papers we have counts for
21 papers
Searching for -holomorphic curves via machine: first steps
James Rowan, Yuan Yao
We assemble numerical algorithms to search for -holomorphic curves in symplectic manifolds. Each algorithm employs several different numerical techniques, each technique address…
Fixed Point Floer Cohomology of Dehn Twists I: Splitting Formulas
Maxim Jeffs, Yuan Yao, Ziwen Zhao
This paper is the first in a series following on our earlier work [arXiv:2205.14516, arXiv:2307.08180] studying the pair-of-pants product on fixed point Floer cohomology. In [arXiv…
Thouless pumps and universal geometry-induced drift velocity in multi-sliding quasi-periodic lattices
Zixun Xu, Yuan Yao
Quantized Thouless pumps in periodic systems, set by Chern numbers or Wannier-center winding, is by now fairly well established, whereas its quasi-periodic extensions still require…
An Invitation to Obstruction Bundle Gluing Through Morse Flow Lines
Ipsita Datta, Yuan Yao
We adapt "Obstruction Bundle Gluing (OBG)" techniques from Hutchings and Taubes (arxiv: 0701300, 0705.2074) to Morse theory. We consider Morse function-metric pairs with gradient f…
Linkage Axioms for Generic Tropical Oriented Matroids
Yuan Yao
We present a comprehensive overview of Ardila and Develin's (generic) tropical oriented matroids, as well as many related objects and their axiomatics. Moreover, we use a unifying…
The stellar decomposition of Gaussian quantum states
Arsalan Motamedi, Yuan Yao, Kasper Nielsen +4
We introduce the stellar decomposition, a novel method for characterizing non-Gaussian states produced by photon-counting measurements on Gaussian states. Given an -mode Gau…
Dualization of ingappabilities through Hilbert-space extensions
Yuan Yao
Typical dualities in arbitrary dimensions are understood through a Hilbert-space extension method. By these results, we rigorously dualize the quantum ingappabilities to discrete h…
Anchored symplectic embeddings
Michael Hutchings, Agniva Roy, Morgan Weiler +1
Given two four-dimensional symplectic manifolds, together with knots in their boundaries, we define an ``anchored symplectic embedding'' to be a symplectic embedding, together with…
Fine Mixed Subdivisions of a Dilated Triangle
Yuan Yao, Fedir Yudin
An upward equilateral triangle of side can be partitioned into unit upward equilateral triangles and unit rhombi with and angl…
Universal critical dynamics of quantum geometry
Shuohang Wu, Zhengxin Guo, Zijian Xiong +2
In this study, we prove that the quantum critical point in the ground state of quantum many-body systems, can also govern the universal dynamical behavior when the systems are driv…
On Symplectic Packing Problems in Higher Dimensions
Kyler Siegel, Yuan Yao
Let denote the closed -dimensional symplectic ball of area , and let be a closed symplectic surface of genus and area . We prove that there is a…
Fixed point Floer cohomology and closed-string mirror symmetry for nodal curves
Maxim Jeffs, Yuan Yao, Ziwen Zhao
We show that for singular hypersurfaces, a version of their genus-zero Gromov-Witten theory may be described in terms of a direct limit of fixed point Floer cohomology groups, a co…
Legendrian embedded contact homology
Julian Chaidez, Oliver Edtmair, Luya Wang +2
We give a construction of embedded contact homology (ECH) for a contact -manifold with convex sutured boundary and a pair of Legendrians and contained in $\parti…
Computing Embedded Contact Homology in Morse-Bott Settings
Yuan Yao
Given a contact three manifold with a nondegenerate contact form , and an almost complex structure compatible with , its embedded contact homology is defin…
Spectral conditions for spherical two-distance sets
Iliyas Noman, Yuan Yao
A set of points in -dimensional Euclidean space is called a 2-distance set if the set of pairwise distances between the points has cardinality two. The 2-dist…
From Cascades to -holomorphic Curves and Back
Yuan Yao
This paper develops the analysis needed to set up a Morse-Bott version of embedded contact homology (ECH) of a contact three-manifold in certain cases. In particular we establish a…
Product and Coproduct on Fixed Point Floer Homology of Positive Dehn Twists
Yuan Yao, Ziwen Zhao
We compute the product and coproduct structures on the fixed point Floer homology of iterations on the single Dehn twist, subject to some mild topological restrictions. We show tha…
Spherical two-distance sets and eigenvalues of signed graphs
Zilin Jiang, Jonathan Tidor, Yuan Yao +2
We study the problem of determining the maximum size of a spherical two-distance set with two fixed angles (one acute and one obtuse) in high dimensions. Let denote th…
Equiangular lines with a fixed angle
Zilin Jiang, Jonathan Tidor, Yuan Yao +2
Solving a longstanding problem on equiangular lines, we determine, for each given fixed angle and in all sufficiently large dimensions, the maximum number of lines pairwise separat…
Embeddings and immersions of tropical curves
Dustin Cartwright, Andrew Dudzik, Madhusudan Manjunath +1
We construct immersions of trivalent abstract tropical curves in the Euclidean plane and embeddings of all abstract tropical curves in higher dimensional Euclidean space. Since not…
(Quasi-)Poisson enveloping algebras
Yan-Hong Yang, Yuan Yao, Yu Ye
We introduce the quasi-Poisson enveloping algebra and Poisson enveloping algebra for a non-commutative Poisson algebra. We prove that for a non-commutative Poisson algebra, the cat…