معرفی
Daniel Alvarez-Gavela is an Assistant Professor of Mathematics at Brandeis University, holding the Berger-Leighton junior chair. His research explores symplectic and contact topology with emphasis on flexible aspects, connections to parametrized Morse theory, algebraic K-theory, and singularity theory.
Alvarez-Gavela's work bridges symplectic geometry with algebraic topology, focusing on nearby Lagrangian invariants, arborealization techniques, and Legendrian invariants via generating families. Current projects investigate K-theoretic approaches to symplectic topology and develop h-principle techniques for geometric structures.
Recent publications advance understanding of arboreal singularities, Lagrangian caustics, and invariants derived from twisted cohomology. Articles appear in journals including Journal of Symplectic Geometry, Inventiones mathematicae, and Journal de l'École polytechnique.
Teaching responsibilities include Differential Geometry (Math225b) and Algebra II (Math201b). Previously at MIT, he taught Topics in Algebraic Topology, Algebraic Topology I, and Introduction to Topology, developing lecture notes and interactive pedagogical approaches.
Alvarez-Gavela organizes workshops on symplectic topology and K-theory collaborations, most recently at Woods Hole Marine Biological Laboratory. He co-founded the Madrid Summer School on the h-principle and contributes to mathematics outreach programs including Navajo Math Circles and prison education initiatives.
