hey there.

My name is Ákos Nagy, I am a mathematician, and I was born and raised in Szekszárd, Hungary.

I received my Ph.D. from Michigan State University in May, 2016. My advisor was Tom Parker.

I am a William W. Elliott Assistant Research Professor of Mathematics at Duke University, where my postdoc mentors are Mark Stern and Robert Bryant.

I am an organizer of the Geometry & Topology Seminar at Duke with Michael Abel.

Before coming to North Carolina, I was a postdoc at the University of Waterloo and the Fields Institute, where my mentors were Benoit Charbonneau and Spiro Karigiannis, respectively.

curriculum vitæ

Click here to open my curriculum vitæ,

or

click here to download it.

research interests

past and current projects, and future plans

I am mainly interested in geometric analysis and its applications to gauge theory and mathematical physics. More concretely, I usually deal with elliptic PDE's coming from physics and/or gauge theories.

Currently I am interested in/working on the following projects:

The L²-geometry of moduli spaces in gauged non-linear sigma models (also referred to as Hamiltonian Gromov–Witten theory).
This is a joint work with Nuno Romão.
Construction of SU(N) monopoles with arbitrary symmetry breaking via the Nahm transform.
This is a joint work with Benoit Charbonneau.
Construction of SU(N) instantons on asymptotically locally flat (ALF) black hole metrics via solving Kazdan–Warner type equations.
This is a joint work with Gonçalo Oliveira and a continuation of a previous project.

Preprints of these projects are coming "soon".

I am also learning about Higgs bundles, gauge theory on G₂ and Spin(7) manifolds, and supersymmetry.

You can find out more about my research on arXiv, on Google Scholar, or on ORCID.

invited talks

future

Geometry and Physics of Gauge Theories at Infinity (conference), Saskatoon, Saskatchewan, August 3-6, 2018
SIAM Annual Meeting 2018, Quantum Dynamics Minisymposium (conference), Portland, Oregon, July 9-13, 2018

past

Duke University, Geometry & Topology Seminar, February 26, 2018
Rényi Institute, Hungarian Academy of Sciences, Algebraic Geometry and Differential Topology Seminar, December 15, 2017
CMS Winter Meeting (conference), University of Waterloo, December 8-11, 2017
Perimeter Institute, Mathematical Physics Seminar — video, December 4, 2017
University of Waterloo, Geometry and Topology Seminar, December 1, 2017
Michigan State University, Institute for Mathematical and Theoretical Physics, Mathematical Physics and Gauge Theory Seminar, October 3, 2017
Postdoctoral Seminar of the Thematic Program on Geometric Analysis, Fields Institute, August 17, 2017
Mathematical Congress of the Americas (conference), Montréal, Quebec, July 24-28, 2017
The Sen Conjecture and Beyond (conference), University College London, June 19-23, 2017
Mathematics of topological phases of matter (thematic program) — video, Simons Center for Geometry and Physics, May 23, 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
Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, Theoretical Physics Seminar, March 12, 2010

papers

published

Ákos Nagy: Irreducible Ginzburg–Landau fields in dimension 2, The Journal of Geometric Analysis (2017)
[ arXiv | doi | abstract ]

Irreducible Ginzburg–Landau fields in dimension 2

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.
Ákos Nagy: The Berry connection of the Ginzburg–Landau vortices, Communications in Mathematical Physics, 350(1), 105-128 (2017)
[ arXiv | doi | abstract ]

The Berry connection of the Ginzburg–Landau vortices

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.
Gábor Etesi and Ákos Nagy: S-duality in Abelian gauge theory revisited, Journal of Geometry and Physics 61, 693-707 (2011)
[ arXiv | doi | abstract ]

S-duality in Abelian gauge theory revisited

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.

preprints

Ákos Nagy and Gonçalo Oliveira: From vortices to instantons on the Euclidean Schwarzschild manifold, submitted (2017)
[ arXiv | abstract ]

From vortices to instantons on the Euclidean Schwarzschild manifold

Abstract. The first irreducible solution of the SU(2) self-duality equations on the Euclidean Schwarzschild (ES) manifold was found by Charap and Duff in 1977, only 2 years later than the famous BPST instantons on ℝ⁴ were discovered. While soon after, in 1978, the ADHM construction gave a complete description of the moduli spaces of instantons on ℝ⁴, the case of the ES manifold has resisted many efforts for the past 40 years.
By exploring a correspondence between the planar Abelian vortices and spherically symmetric instantons on ES manifold, we obtain: a complete description of a connected component of the moduli space of unit energy SU(2) instantons; new examples of instantons with non-integer energy and non-trivial holonomy at infinity; a complete classification of finite energy, spherically symmetric, SU(2) instantons.
As opposed to the previously known solutions, the generic instanton coming from our construction is not invariant under the full isometry group, in particular not static. Hence disproving a conjecture of Tekin.

teaching

In the Spring semester of 2018 I am teaching

Linear Algebra and Applications
(math 221.01 & math 221.02)

at Duke University.

contact

You can find current contact info here.