I am a third year mathematics PhD student at the University of Edinburgh, where I am advised by Nick Sheridan. I am funded by an ERC scholarship under the project Homological mirror symmetry, Hodge theory, and symplectic topology.
Before coming to Edinburgh I did a MASt degree (Part III) at the University of Cambridge, and a double degree in mathematics and physics at the University of Santiago de Compostela.
e-mail: amunizb [at] ed [dot] ac [dot] uk
My research focuses on Lagrangian cobordisms and their relation to the K-theory of the Fukaya category and the Chow groups of the mirror. More precisely, recently I've been thinking about:
Here are some things I have written:
Mathematics 2021, 9(16), 1993
The Hamilton-Jacobi formulation of classical (Hamiltonian) mechanics turns the problem of solving n PDEs of second order to 2n first order PDEs. In this paper, we extend this formalism to contact Hamiltonian systems (roughly speaking, contact dynamics deals with mechanical systems in which the energy is dissipated).
This paper studies the Lagrangian cobordism group of a closed symplectic 4-manifold. Whereas Sheridan-Smith show that when the canonical bundle is trivial Lagrangian cobordism groups are too large to be computed, I work with an example where the canonical bundle is 2-torsion but not trivial. This allows me to compute the subgroup generated by tropical Lagrangians. I also show this is an interesting subgroup: using Abouzaid's homological mirror symmetry result, I prove it maps isomorphically to the Grothendieck group of the Fukaya category.
This is a summary of the things I was thinking about for most of my first year. It includes a computation of the cobordism group of a two-torus without using homological mirror symmetry and discusses some essential differences for higher-dimensional tori. I also sketch how to define a Bloch-type filtration on the fibered Lagrangian cobordim group of tori. Using a Fourier transform as Beauville one can show that the filtration is finite.
Expository project on Morse theory for GLAMs. I contributed the second section on Lagrangian Floer homology, following Auroux's paper.
This is my Part III essay. It is a survey about intersection theory and the Chow rings. I focus on the Chow ring of the Grassmannian and develop its Schubert calculus. I use this to present the solution to two classical problems in intersection theory. A solution using Chern classes is also included.
This is my undergraduate physics dissertation, supervised by Prof. José Edelstein. I looked at (von Neumann) entropy as a measure of entanglement in a physical system. In the last sections, I discussed the Ryu-Takayanagi conjecture, which turns the computation of entanglement entropy from an algebraic problem to a geometric one.
| 2024 | |
| Lagrangian cobordisms and K-theory of bielliptic surfaces | Differential Geometry and Topology seminar, University of Cambridge |
| 2023 | |
| Lagrangian cobordisms and K-theory of bielliptic surfaces | EDGE seminar, Edinburgh |
| Tropical Chow groups | Tropical geometry reading group, Edinburgh |
| Family-Floer cohomology and mirror symmetry | Preprint seminar, Edinburgh |
| Grupo de cobordismos Lagrangianos | VI Congreso de Jóvenes Investigadores de la RSME, Zaragoza |
| 2022 | |
| Liouville sectors II | GPS reading group, Edinburgh |
| Introducción al grupo de cobordisms Lagrangianos | X Encuentro de Jóvenes Topólogos, León |
| Displaceability in the cylinder | GlaMS induction event, Edinburgh |
| Generalised Lagrangian correspondences | Hodge Club, Edinburgh |
| Introduction to Lagrangian cobordisms | Cob/CH reading group, Edinburgh |
| Lagrangian cobordisms and Chow groups | Hodge Club, Edinburgh |
| Displacebility in the cylinder | GlaMS example showcase, Edinburgh |
| 2021 | |
| Mirror symmetry: from physics to geometry | IYI Meeting 2021, A Coruña |
| Dous problemas clásicos de intersección no espazo proxectivo | Matemáticas: moito máis que números, Santiago de Compostela |