Zobrazeno 1 - 10
of 109
pro vyhledávání: '"Salter, Nick"'
Autor:
Huxford, Peter, Salter, Nick
An equicritical stratum is the locus of univariate monic squarefree complex polynomials where the critical points have prescribed multiplicities. Tracking the positions of both roots and critical points, there is a natural ``monodromy map'' taking th
Externí odkaz:
http://arxiv.org/abs/2411.02222
Autor:
Salter, Nick
A linear system on a smooth complex algebraic surface gives rise to a family of smooth curves in the surface. Such a family has a topological monodromy representation valued in the mapping class group of a fiber. Extending arguments of Kuno, we show
Externí odkaz:
http://arxiv.org/abs/2410.05195
We compute the asymptotic number of cylinders, weighted by their area to any non-negative power, on any cyclic branched cover of any generic translation surface in any stratum. Our formulas depend only on topological invariants of the cover and numbe
Externí odkaz:
http://arxiv.org/abs/2409.06600
Autor:
Banerjee, Ishan, Salter, Nick
We compute the topological monodromy of every family of complete intersection curves. Like in the case of plane curves previously treated by the second-named author, we find the answer is given by the $r$-spin mapping class group associated to the ma
Externí odkaz:
http://arxiv.org/abs/2408.06479
Autor:
Salter, Nick
The space of monic squarefree polynomials has a stratification according to the multiplicities of the critical points, called the equicritical stratification. Tracking the positions of roots and critical points, there is a map from the fundamental gr
Externí odkaz:
http://arxiv.org/abs/2403.04496
Autor:
Chen, William Y., Salter, Nick
We show that the configuration space of four unordered points in $\mathbb{C}$ with barycenter 0 is isomorphic to the space of triples $(E,Q,\omega)$, where $E$ is an elliptic curve, $Q\in E^\circ$ a nonzero point, and $\omega$ a nonzero holomorphic d
Externí odkaz:
http://arxiv.org/abs/2402.11081
Autor:
Salter, Nick
This is an exposition of John H. Conway's tangle trick. We discuss what the trick is, how to perform it, why it works mathematically, and finally offer a conceptual explanation for why a trick like this should exist in the first place. The mathematic
Externí odkaz:
http://arxiv.org/abs/2309.11311
Autor:
Salter, Nick, Sane, Abdoul Karim
A unicellular collection on a surface is a collection of curves whose complement is a single disk. There is a natural surgery operation on unicellular collections, endowing the set of such with a graph structure where the edge relation is given by su
Externí odkaz:
http://arxiv.org/abs/2308.09165
Putman and Wieland conjectured that if $\tilde{\Sigma} \rightarrow \Sigma$ is a finite branched cover between closed oriented surfaces of sufficiently high genus, then the orbits of all nonzero elements of $H_1(\tilde{\Sigma};\mathbb{Q})$ under the a
Externí odkaz:
http://arxiv.org/abs/2305.13109
Autor:
Salter, Nick
The space of monic squarefree complex polynomials has a stratification according to the multiplicities of the critical points. We introduce a method to study these strata by way of the infinite-area translation surface associated to the logarithmic d
Externí odkaz:
http://arxiv.org/abs/2304.04627