Mark R. Dennis

activity

20022023

most citedVortex knots in light

254 citations · 3k across the 56 of their papers we have counts for

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math.GT2016★ 5 cited

Constructing a polynomial whose nodal set is any prescribed knot or link

Benjamin Bode, Mark R. Dennis

We describe an algorithm that for every given braid $B$ explicitly constructs a function $f : C^{2} \to C$ such that $f$ is a polynomial in $u$ , $v$ and $\ove…

math.GT2016★ 17 cited

Constructing a polynomial whose nodal set is the three-twist knot $5_{2}$

Mark R Dennis, Benjamin Bode

We describe a procedure that creates an explicit complex-valued polynomial function of three-dimensional space, whose nodal lines are the three-twist knot $5_{2}$ . The construction g…

math.GT2016★ 47 cited

Knotted fields and explicit fibrations for lemniscate knots

Benjamin Bode, Mark R Dennis, David Foster +1

We give an explicit construction of complex maps whose nodal line have the form of lemniscate knots. We review the properties of lemniscate knots, defined as closures of braids whe…

Constructing a polynomial whose nodal set is any prescribed knot or link

Constructing a polynomial whose nodal set is the three-twist knot 52​

Knotted fields and explicit fibrations for lemniscate knots

Constructing a polynomial whose nodal set is the three-twist knot $5_{2}$