Hello! I’m an assistant professor at the Brandeis mathematics department, where I am grateful to hold the Berger-Leighton junior chair. I am also grateful for the support of the National Science Foundation under grant DMS-2203455.
My research is in symplectic and contact topology. I am particularly interested in the flexible side of the field as well as in the connections with parametrized Morse theory, algebraic K-theory and singularity theory.
Publications & preprints
- Legendrian and Lagrangian higher torsion
Joint with K. Igusa and M. Sullivan,
arXiv:2603.28007 - Normal invariant of nearby Lagrangians via twisted derivative
Joint with M. Abouzaid, S. Courte and T. Kragh
arXiv:2505.12515, submitted - On arborealization, Maslov data, and lack thereof
Joint with T. Large and A. Ward
arxiv:2503.09783, submitted - Framed bordism of nearby Lagrangian homotopy spheres via generating functions
to appear in the proceedings of the 2026 International Georgia Topology Conference - Positive arborealization of polarized Weinstein manifolds
Joint with Y. Eliashberg and D. Nadler
arXiv:2011.08962, under revision (splitting up into three different papers) - Arboreal models and their stability
Joint with Y. Eliashberg and D. Nadler
Journal of Symplectic Geometry, 21(2) (2023), pp. 331-381 - Caustics of Lagrangian homotopy spheres with stably trivial Gauss map
Joint with D. Darrow
Journal of Symplectic Geometry 20(5) (2023) 995-1036 - Geomorphology of Lagrangian ridges
Joint with Y. Eliashberg and D. Nadler
Journal of Topology 15(2) (2022) 844-877 - A Legendrian Turaev torsion via generating families
Joint with K. Igusa
Journal de l’École polytechnique — Mathématiques 8 (2021), 57-119 - Embeddings of free groups into asymptotic cones of Hamiltonian diffeomorphisms
Joint with V. Kaminker, A. Kislev, K. Kliakhandler, A. Pavlichenko, L. Rigolli, D. Rosen, O. Shabtai, B. Stevenson, and J. Zhang
Journal of Topology and Analysis 11(02) (2019) 267-298. - The simplification of singularities of Lagrangian and Legendrian fronts
Inventiones mathematicae 214(2) (2018) 641-737 - Refinements of the holonomic approximation lemma
Algebraic & Geometric Topology 18(4) (2018) 2265–2303
Expository
- Flexibility of singularities and beyond
Celebratio Mathematica, volume in honor of Yakov Eliashberg (2025) - Lo mínimo que debe uno saber sobre superficies mínimas
La Gaceta de la RSME 17(1) 2014 49-69 - Sutured Manifolds and the Thurston Norm
(Part III essay) - Gaussian Curvature in codimension > 1
(just a computation)
Contact
dgavela@brandeis.edu
Department of Mathematics
Goldsmith 304
MS 050
Brandeis University
415 South Street
Waltham, MA 02453
USA
Daniel Alvarez-Gavela 