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

Publications and Preprints

• Complex optical vortex knots, Proceedings of the Royal Society A 481 (2025), 20240605. (arXiv version)

• Dislocations and fibrations: The topological structure of knotted smectic defects. (with P. Severino and R. Kamien) New Journal of Physics 27 (2025), 064402. (arXiv version)

• Totally tangential $\mathbb{C}$-links and electromagnetic knots (2024), (arXiv version)

• Ultraknots and limit knots. Journal of the Mathematical Society of Japan (in press), (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)  Kodai Mathematical Journal (in press) (arXiv version)

• The topology of stable electromagnetic structures and Legendrian fields on the 3-sphere. (with D. Peralta-Salas) International Mathematics Research Notices 2025, 11 (2025), rnaf155. (arXiv version)

• Closures of T-homogeneous braids are real algebraic. Algebraic and Geometric Topology 25 (2025), 1075--1115. (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)

• All links are semiholomorphic. European Journal of Mathematics 9 (2023), article no. 85. (arXiv version)

• Braided open book decompositions in $S^3$. Revista Matemática Iberoamericana 39 (2023), no. 6, 2187-2232. (arXiv version) 

• Twisting and satellite operations on P-fibered braids. Communications in Analysis and Geometry 31, 8 (2023), 2013--2038. (arXiv version)

• Stable knots and links in electromagnetic fields. Communications in Mathematical Physics 387 (2021), 1757–1770. (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)