Research
Research
My research interests lie in low-dimensional topology. I mostly study braids and knots and their relationship to Physics and other areas of Mathematics.
CV
You can look at my CV here: CV
Publications and Preprints
Ultraknots and limit knots (2024), (arXiv version)
Saddle point braids of braided fibrations and pseudo-fibrations. (with M. Hirasawa) Research in the Mathematical Sciences 11 (2024), article no. 33. (arXiv version)
Links of singularities of inner non-degenerate mixed functions, Part II (2023) (arXiv version)
Inner and partial non-degeneracy of mixed functions. (with E. L. Sanchez Quiceno) (2023) (arXiv version)
The topology of stable electromagnetic structures and Legendrian fields on the 3-sphere. (with D. Peralta-Salas) (2023) (arXiv version)
Closures of T-homogeneous braids are real algebraic. Algebraic and Geometric Topology (in press) (arXiv version)
All links are semiholomorphic. European Journal of Mathematics 9 (2023), article no. 85. (arXiv version)
Links of singularities of inner non-degenerate mixed functions. (with R. N. Araújo dos Santos and E. L. Sanchez Quiceno) Bulletin of the Brazilian Mathematical Society 55 (2024), article no. 34. (arXiv version)
Braided open book decompositions in $S^3$. Revista Matemática Iberoamericana 39 (2023), no. 6, 2187-2232. (arXiv version)
Stable knots and links in electromagnetic fields. Communications in Mathematical Physics 387 (2021), 1757–1770. (arXiv version)
Twisting and satellite operations on P-fibered braids. Communications in Analysis and Geometry (in press) (arXiv version)
Knotted surfaces as vanishing sets of polynomials. (with S. Kamada) Journal of the Mathematical Society of Japan 73 (2021), 1289-1322. (arXiv version)
Quasipositive links and electromagnetism. Topology and its Applications: 301 (2021), 107495. (arXiv version)
Real algebraic links in $S^3$ and braid group actions on the set of $n$-adic integers. Journal of Knot Theory and its Ramifications 29, No. 6 (2020), 2050039. (arXiv version)
Real algebraic links in $S^3$ and simple branched covers. Intelligence of Low-Dimensional Topology 2019 conference proceedings, Kyoto, RIMS Kokyuroku No. 2129 (2019), 13-28.
Braids, polynomials and real algebraic links. The 66th Topology Symposium, Akita City, conference proceedings (2019), 23-32.
Constructing links of isolated singularities of polynomials $\mathbb{R}^4\to\mathbb{R}^2$. Journal of Knot Theory and its Ramifications 28, No. 1 (2019), 1950009. (arXiv version)
Constructing a polynomial whose nodal set is any prescribed knot or link. (with M. R. Dennis) Journal of Knot Theory and its Ramifications 28, No. 1 (2019), 1850082. (arXiv version)
Crossing numbers of composite knots and spatial graphs. Topology and its Applications 243 (2018), 33-51. (arXiv version)
Constructing a polynomial whose nodal set is the three-twist knot $5_2$. (with M. R. Dennis) Journal of Physics A 50 (2017) 265204. (arXiv version)
Knotted fields and explicit fibrations for lemniscate knots. (with M. R. Dennis, D. Foster and R. P. King) Proceedings of the Royal Society A 473 (2017) 20160829. (arXiv version)
Thesis
Knotted fields and real algebraic links, University of Bristol (2018)