8 papers
Quantum braid Floer homology
Cristina Ana-Maria Anghel, András Juhász
Given a braid whose closure is a knot, we associate to it a doubly pointed Heegaard diagram with additional marked points that we call a quantum Heegaard diagram. This is obtained…
Polynomiality of the Striling coefficients of and Fano schemes
László M. Fehér, András P. Juhász
We prove that the -dependence of , the Chern class of the -representation of degree homogeneous polynomials in complex v…
Data for Mathematical Copilots: Better Ways of Presenting Proofs for Machine Learning
Simon Frieder, Jonas Bayer, Sam Looi +13
The datasets and benchmarks commonly used to train and evaluate the mathematical capabilities of AI-based mathematical copilots (primarily large language models) exhibit several sh…
On Fox's trapezoidal conjecture
Soheil Azarpendar, András Juhász, Tamás Kálmán
We investigate Fox's trapezoidal conjecture for alternating links. We show that it holds for diagrammatic Murasugi sums of special alternating links, where all sums involved have l…
Leading terms of generalized Plücker formulas
András P. Juhász
Generalized Plücker numbers are defined to count certain types of tangent lines of generic degree complex projective hypersurfaces. They can be computed by identifying them as…
Plücker formulas using equivariant cohomology of coincident root strata
László M. Fehér, András P. Juhász
We give a new method to calculate the universal cohomology classes of coincident root loci. We show a polynomial behavior of them and apply this result to prove that generalized Pl…
Examples of topologically unknotted tori
András Juhász, Mark Powell
We show that certain smooth tori with group in have exteriors with standard equivariant intersection forms, and so are topologically unknotted. These include the…
New invariants for virtual knots via spanning surfaces
András Juhász, Louis H. Kauffman, Eiji Ogasa
We define three different types of spanning surfaces for knots in thickened surfaces. We use these to introduce new Seifert matrices, Alexander-type polynomials, genera, and a sign…