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.
I studied mathematics at the Universidad Autónoma de Madrid, Boston University and Cambridge University, obtained my PhD at Stanford University under the supervision of Yasha Eliashberg, and have previously held positions at the Institute for Advanced Study, Princeton University and MIT. Here is my CV.
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.
Teaching
Math 31a – Advanced Linear Algebra, materials on moodle.
Previous teaching
Fall 2025 – Math225a – Geometry of manifolds, materials on moodle.
Spring 2025 — Math225a – Differential Geometry & Math201b – Algebra II, materials on moodle.
Spring 2024 — Topics in Algebraic Topology, aka 18.917, course webpage and lecture notes here.
Spring 2023 — Multivariable Calculus, aka 18.02, course webpage on canvas.
Fall 2022 — Algebraic Topology I, aka 18.905, course webpage and lecture notes here.
Spring 2022 — Introduction to Topology, aka 18.901, course webpage and lecture notes here.
Symplectic topology meets K-theory at Woods Hole
Last summer I organized a workshop on the interactions between symplectic topology and algebraic K-theory at the Woods Hole Marine Biological laboratory. More information at the website here.
Madrid summer school on the h-principle
Two summers ago, together with Álvaro del Pino Gómez and Mélanie Theillière I organized a graduate summer school at the ICMAT on the h-principle. Find the website here and the recordings here.
Mathematics instruction in correctional facilities
During my time at MIT, together with Marisa Gaetz, I have coordinated a team of volunteers to teach math an various correctional facilities in the Boston area. You can read about our work here.
Navajo Math circles
For the past couple of years I have worked with Dave Auckley, Henry Fowler and the rest of the Navajo Nation Math Circles team, helping with their teacher training sessions and summer camp.
Publications & preprints
- 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 2025 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)
Videos
- The holonomic approximation lemma II
Madrid summer school on the h-principle, 2024 - The holonomic approximation lemma I
Madrid summer school on the h-principle, 2024 - Normal invariant of nearby Lagrangians via twisted generating functions
Floer homotopical methods in low dimensional and symplectic topology, SLMath, 2022 - K-theoretic aspects of the nearby Lagrangian conjecture
Giroux 60 – convexity in contact and symplectic topology, Institut Henri Poincaré, 2022 - The flexibility of caustics and its applications
Workshop on the h-principle and beyond, IAS, 2021 - A Legendrian Turaev torsion via generating families
AMS Spring Central Virtual Sectional Meeting, 2021 - Caustics of Lagrangian homotopy spheres with stably trivial Gauss map
IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar, 2021 - The nearby Lagrangian conjecture from the K-theoretic viewpoint
Western Hemisphere Virtual Symplectic Seminar, 2020 - Vicent Caselles Prize video
RSME/BBVA, 2019 - Caustics of fronts and the arborealization conjecture
Short talk, IAS, 2018 - The simplification of singularities of Lagrangian and Legendrian fronts
Princeton/IAS symplectic geometry seminar, 2017
Contact
dgavela@brandeis.edu
Department of Mathematics
Goldsmith 304
MS 050
Brandeis University
415 South Street
Waltham, MA 02453
USA
Daniel Alvarez-Gavela 