8 papers
Log-concavity of flat arrangement polynomials
Yuan Gao, Tianyu Yuan
We prove log-concavity for the determinant-weighted external semi-activity polynomials of all real flat arrangements, strengthening their known trapezoidality. In fact, we establis…
A polynomial invariant of planar curves
Zhiyun Cheng, Yin Tian, Tianyu Yuan
We construct a polynomial invariant of planar curves via skein relations, which generalizes Arnold's numerical invariant .
Trapezoidality of flat arrangement polynomials
Yuan Gao, Tianyu Yuan
Fox's conjecture predicts that the absolute values of the coefficients of the Alexander polynomial of an alternating link form a trapezoidal sequence. Kálmán, Mészáros, and Postnik…
Obstructions to smoothing orbicurves and Orbifold Hecke algebras
Ko Honda, Roman Krutowski, Yin Tian +1
In this paper, we study obstructions to smoothing nodal orbicurves with orbighosts mapped into cyclic quotient singularities. As an application, we show, under some assumptions, th…
Algebra of free fermions: Classifying spaces, Hamiltonians, and computation
Tian Yuan, Yang Qi
Research on topological phases of matter is a core field in modern condensed matter physics. Free fermion systems, such as topological insulators and superconductors, have been stu…
Higher-dimensional Heegaard Floer homology and spectral networks
Ko Honda, Yin Tian, Tianyu Yuan
Given a closed surface and a real exact Lagrangian associated to a spectral curve, we construct a homomorphism $\operatorname{BSk}_κ(C)\to\operatorname{Mat}(N^κ…
Higher-dimensional Heegaard Floer homology and the polynomial representation of double affine Hecke algebras
Yuan Gao, Eilon Reisin-Tzur, Yin Tian +1
We show that the higher-dimensional Heegaard Floer homology between tuples of cotangent fibers and the conormal bundle of a homotopically nontrivial simple closed curve on re…
Morse theory of loop spaces and Hecke algebras
Ko Honda, Roman Krutowski, Yin Tian +1
Given a smooth closed -manifold and a -tuple of basepoints , we define a Morse-type -algebra , called the…