past and current projects, and future plans
I am mainly interested in gauge theory and its applications to mathematical physics.
Currently I am working on two projects: The first originates from my Ph.D. research, and concerns the geometric-analytic properties of Majorana spinors on Kähler manifolds. The second project is about the construction and the moduli space of BPS monopoles with arbitrary symmetry breaking for the classical (compact) Lie groups. This is a joint work with Benoit Charbonneau
. Preprints of both projects are coming soon!
Nowadays I am also learning about Higgs bundles, G2
instantons, and supersymmetry.
You can find out more about my research on arXiv
and on ResearchGate
The Sen Conjecture and Beyond (conference), University College London, June 19-23, 2017
Mathematical Congress of the Americas (conference), Montréal, July 24-28, 2017
CMS Winter Meeting (conference), University of Waterloo, December 8-11, 2017
Caltech, Noncommutative Geometry Seminar, March 8, 2017
UQAM, CIRGET Geometry and Topology Seminar, February 24, 2017
University of Waterloo, Geometry and Topology Seminar, September 23, 2016
McMaster University, Geometry and Topology Seminar, September 16, 2016
AMS Fall Sectional Meeting (conference), Rutgers University, November 14-15, 2015
Budapest University of Technology, Geometry Seminar, December 16, 2014
Algebra, Geometry, and Mathematical Physics VI (conference), Tjärnö, October 25-30, 2010
|2. Ákos Nagy:
The Berry connection of the Ginzburg–Landau vortices, Communications in Mathematical Physics, 350(1), 105-128 (2017)
Abstract: We analyze 2-dimensional Ginzburg–Landau vortices at critical coupling, and establish asymptotic formulas for the tangent vectors of the vortex moduli space using theorems of Taubes and Bradlow. We then compute the corresponding Berry curvature and holonomy in the large volume limit.
|1. Gábor Etesi and Ákos Nagy:
S-duality in Abelian gauge theory revisited, Journal of Geometry and Physics 61, 693-707 (2011)
Abstract: Definition of the partition function of U(1) gauge theory is extended to a class of four-manifolds containing all compact spaces and certain asymptotically locally flat (ALF) ones including the multi-Taub–NUT spaces. The partition function is calculated via zeta-function regularization with special attention to its modular properties. In the compact case, compared with the purely topological result of Witten, we find a non-trivial curvature correction to the modular weights of the partition function. But S-duality can be restored by adding gravitational counter terms to the Lagrangian in the usual way. In the ALF case however we encounter non-trivial difficulties stemming from original non-compact ALF phenomena. Fortunately our careful definition of the partition function makes it possible to circumnavigate them and conclude that the partition function has the same modular properties as in the compact case.
Irreducible Ginzburg–Landau fields in dimension 2, (2016)
Abstract: Ginzburg–Landau fields are the solutions of the Ginzburg–Landau equations which depend on two positive parameters, α and β. We give conditions on α and β for the existence of irreducible solutions of these equations. Our results hold for arbitrary compact, oriented, Riemannian 2-manifolds (for example, bounded domains in ℝ2, spheres, tori, etc.) with de Gennes–Neumann boundary conditions. We also prove that, for each such manifold and all positive α and β, Ginzburg–Landau fields exist for only a finite set of energy values and the Ginzburg–Landau free energy is a Palais–Smale function on the space of gauge equivalence classes.
|Benoit Charbonneau and Ákos Nagy:
||Monopoles with non-maximal symmetry breaking,
|Manousos Maridakis and Ákos Nagy:
||The Łojasiewicz–Simon inequality in gauge theories on non-compact manifolds,
||Majorana spinors on Kähler manifolds.