Thiago de Paiva

The idea of contributing to Science is very exciting for me

I am a PhD student in my fourth and final year at Monash University supervised by Prof. Jessica Purcell.

I am interested in Topology, Low-Dimensional Topology, Hyperbolic Geometry, Knot Theory, Braid Theory and applications of these areas in Science and other areas of Mathematics.

PAPERS

- Thiago de Paiva, Unexpected essential surfaces among exteriors of twisted torus knots, Algebr. Geom. Topol. 22 (2022), no. 8, 3965–3982. MR 4562562.
- Thiago de Paiva and Jessica S. Purcell, Satellites and Lorenz knots, Int. Math. Res. Not. IMRN (2023), no. 19, 16540–16573. MR 4651895
- Sangyop Lee and Thiago de Paiva, Torus knots obtained by negatively twisting torus knots, J. Knot Theory Ramifications 31 (2022), no. 1, Paper No. 2150080, 19. MR 4411809.
- Thiago de Paiva, Hyperbolic knots given by positive braids with at least two full twists, Proc. Amer. Math. Soc. 150 (2022), no. 12, 5449–5458. MR 4494619.
- Thiago de Paiva, Hyperbolic twisted torus links, Geom. Dedicata 217 (2023), no. 2, Paper No. 42, 16. MR 4551666.
- Thiago de Paiva, Torus Lorenz links obtained by full twists along torus links, Proc. Amer. Math. Soc. 151 (2023), no. 6, 2671–2677. MR 4576328.
- Thiago de Paiva, Satellite knots that cannot be represented by positive braids with full twists. arXiv preprint arXiv:2211.12816 (2022) (Submitted).
- Thiago de Paiva and Jessica S Purcell, Hyperbolic and satellite Lorenz links obtained by twisting. arXiv preprint arXiv:2301.01934 (2023) (Submitted).
- Burton, Benjamin A., Thiago de Paiva, Alexander He, and Connie On Yu Hui. Crushing Surfaces of Positive Genus. arXiv preprint arXiv:2403.11523 (2024). (Submitted).
- Thiago de Paiva, Geometry of Generalized Augmented Braids. arXiv preprint arXiv:2406.09736 (2024) (Submitted).
- Thiago de Paiva, Tetsuya Ito, Lorenz knots, Essential tori, and Half-twists (In preparation).
- Thiago de Paiva, Hyperbolic Lorenz links and full twists (In preparation).
- Thiago de Paiva, Braids and Flows (In preparation).
- Thiago de Paiva, Connie On Yu Hui and José Andrés Rodríguez Migueles, Upper volume bounds for hyperbolic links in the 3-sphere (In preparation).