Home page Nguyen Viet Dang

Full Professor,

Junior Member Institut Universitaire de France (2022-2027)

Institut de Recherche Mathématique Avancée (IRMA)

Université de Strasbourg

Analysis team

Courriel: nvdang@unistra.fr

Curriculum Vitae

For more informations, please look at my CV.

My Field of research

I started in research doing perturbative Quantum Field Theory. More accurately, in my phd thesis Renormalization of quantum field theory on curved space times: a causal approach ( lien arxiv), I studied the problem of perturbative renormalizability of scalar quantum field theories in curved spacetime, following the approach initiated by Brunetti–Fredenhagen and building on recent work of Borcherds and Yves Meyer.

For more information on my research around 2021, my memoir HDR Microlocal analysis from quantum fields to hyperbolic dynamics where I give a synthesis of part of my work since my thesis.

Using computational methods in quantum field theory based on the Berezin integral, in collaboration with G. Rivière, we studied the equidistribution of the conormal cycle at the zeros of random combinations of eigenfunctions.

Recently, in collaboration with G. Rivière, we combine methods from spectral theory and microlocal analysis in dynamical systems with certain methods stemming from my thesis to study Morse–Smale type flows. We are interested in the Pollicott–Ruelle resonances of these flows and in applications to topology, for instance to study Reidemeister torsion. We also applied our results to the spectral analysis of the Witten Laplacian and to the resolution of a conjecture of Fukaya on the Witten deformation of the exterior product. I started working on the Fried conjecture, first with Guillarmou, Rivière and Shen to find new situations in low dimensions where the conjecture holds, then in collaboration with Yann Chaubet we obtain results comparing dynamical zeta functions to Turaev torsions, which are refined versions of Reidemeister torsion.

With Gabriel Rivière, we proved the following result whose statement is extremely short. On a surface of strictly negative curvature, given two points x, y on the surface, the lengths of the geodesic arcs connecting the two points determine the genus of the surface. This is a corollary of a much more general result expressing the value at zero of the Poincaré series counting orthogeodesic arcs between two curves on the surface in terms of the linking number of the Legendrian knots lifting these two curves in the cotangent bundle.

With Michal Wrochna, we obtained the first generalization of Connes' spectral action formula to the case of asymptotically Minkowski and ultrastatic Lorentzian manifolds. We show that the diagonal restriction of the complex powers of the wave operator admits a meromorphic continuation and that the Einstein–Hilbert Lagrangian appears as a residue of this restriction. Moreover, we generalize the notion of Wodzicki residue to integer powers of the Feynman inverse of the wave operator.

With Ismael Bailleul and Antoine Mouzard, we began a collaboration aimed at applying Bony's paracontrolled methods to the analysis of the Anderson Hamiltonian on Riemannian surfaces. I continued this collaboration with Ismael Bailleul, Léonard Ferdinand and To Tat Dat, with the goal of marrying microlocal methods and paracontrol in order to construct field theories in a constructive manner. As consequence, we gave the first construction of the Phi43 Quantum Field Theory probability measure on 3-manifolds using singular SPDE methods together with harmonic analysis techniques on manifolds. But we still need to investigate nice properties of this measure in order to construct a full--fledged Phi43 QFT.

With Léo Bénard and Yann Chaubet, I have returned to exploring things in combinatorial topology. With Yannick Bonthonneau, Matthieu Léautaud and Gabriel Rivière, we are studying the geodesic flow on the torus in connection with trace formulas and convex geometry — I am trying to keep up.

Currently, together with Bonthonneau, Chhaibi, Rivière and To on the one hand and Nohra on the other hand, we gave the first construction of Yang-Mills measure on general surfaces at the level of random distributional connections. This uses a blend of dynamical systems, probability and also harmonic analysis. With Nohra, we were able to control the semiclassical limit of this Yang-Mills measure and we could recover a version of the Atiyah-Bott-Goldman measure on the moduli space of flat connections. These results answer questions by Thierry Lévy who is a pioneer in the study of gauge theories from a probabilistic viewpoint.

C. Brouder, N.V. Dang et F. Hélein , A smooth introduction to the wavefront set, Journal of Physics A: Mathematical and Theoretical, 2014, vol. 47, no 44, p. 443001. Version pdf

C. Brouder, N.V. Dang et F. Hélein , Boundedness and continuity of the fundamental operations on distributions having a specified wave front set , Studia Mathematica 232 (2016), 201-226 . Version pdf

N.V. Dang, The Euler characteristic of a surface from its Fourier analysis in one direction, Math. Research Letters, Volume 23, (2016) pp. 1263-1279. Version pdf lien arxiv

N.V. Dang, E. Herscovich Renormalization of Quantum Field Theory on Riemannian manifolds, Rev. Math. Phys. 31 (2019), no. 06, 1950017, 30 pp

N.V. Dang ,The extension of distributions on manifolds, a microlocal approach, Annales Henri Poincaré. Vol. 17. No. 4. Springer International Publishing, 2016 . Version pdf

N.V. Dang, Complex powers of analytic functions and meromorphic regularization in QFT ,

N.V. Dang et G. Rivière, Equidistribution of the conormal cycle of random nodal sets, Journal of Eur. Math. Soc. Volume 20, Issue 12, 2018, pp. 3017–3071 lien arxiv

N.V. Dang et G. Rivière, Spectral analysis of Morse-Smale gradient flows, Annales de l’ENS 2019 Tome 52 fascicule 6 p. 1403-1458 version longue pdf

N.V. Dang et G. Rivière, Spectral analysis of Morse-Smale flows I: construction of the anisotropic spaces, J. Inst. Math. Jussieu, Vol. 19 (2020), 1409-1465. version pdf

N.V. Dang et G. Rivière, Spectral analysis of Morse-smale flows II: resonances and resonant states, American J. Math., Vol. 142 (2020), 547-593 version pdf

N.V. Dang et G. Rivière Topology of Pollicott-Ruelle resonant states, Annali della Scuola normale di Pisa, DOI:10.2422/2036-2145.201804010. lien arxiv

C. Brouder, N.V. Dang, C. Laurent-Gengoux et K. Rejzner, Properties of field functionals and characterization of local functionals, Journal of Mathematical Physics, 2018, vol. 59, no 2, p. 023508 lien arxiv

N.V. Dang et G. Rivière Pollicott-Ruelle spectrum and Witten Laplacians, Journal of Eur. Math. Soc.

N.V. Dang et B. Zhang, Renormalization of Feynman amplitudes on manifolds by spectral zeta regularization and blow-ups, Journal of the European Mathematical Society, 2020, vol. 23, no 2, p. 503-556. preprint

N.V. Dang, C. Guillarmou, G. Rivière et S. Shen Fried conjecture in small dimensions, Inventiones Math. Vol. 220 (2020), 525-579,

N.V. Dang, Renormalization of determinant lines in Quantum Field Theory, 61p, Analysis and PDE, Vol 15 No 1 2022

N.V. Dang, Wick squares of the Gaussian Free Field and Riemannian rigidity, Probability and Mathematical physics, Vol. 3 (2022), No. 1, 1–34

Y. Chaubet et N.V. Dang, Dynamical torsion for contact Anosov flows, lien arxiv, accepté APDE

N.V. Dang et G. Rivière, Poincaré series and linking of Legendrian knots, lien arxiv , accepté Duke Maths Journal

N.V. Dang et M. Wrochna, Complex powers of the wave operator and the spectral action on Lorentzian scattering spaces, lien arxiv, J. Eur. Math. Soc. (2023), pp. 1–84

N.V. Dang et M. Wrochna, Dynamical residues of Lorentzian spectral zeta functions, lien arxiv, Journal de l’École polytechnique — Mathématiques, Tome 9 (2022), pp. 1245-1292.

N.V. Dang, Le principe d'incertitude fractal [d'après Bourgain, Dyatlov, Jin, Nonnenmacher, Zahl], Bourbaki Avril 2021 version pdf

I. Bailleul, N.V. Dang et A. Mouzard, Analysis of the Anderson operator, lien arxiv, accepté EJP😊️

N.V. Dang, M. Léautaud et Gabriel Rivière Length orthospectrum of convex bodies on flat tori, lien arxiv, Cambridge Journal of Mathematics, 2023, 11 (4), pp.917-1043

Léo Bénard, Yann Chaubet, Nguyen Viet Dang, Thomas Schick, Combinatorial zeta functions counting triangles, lien arxiv, soumis

I. Bailleul, N. V. Dang, L. Ferdinand, T.D. Tô, Phi43 measures on compact Riemannian 3-manifolds, lien arxiv, soumis

I. Bailleul, N. V. Dang, L. Ferdinand, T.D. Tô, Global harmonic analysis for Phi43 on closed Riemannian manifolds, lien arxiv, soumis

Ismael Bailleul, Nguyen Viet Dang, Léonard Ferdinand, Gaëtan Leclerc, Jiasheng Lin, Spectrally cut-off GFF, regularized Phi4 measure, and reflection positivity, lien arxiv, Annales Henri Poincaré

N.V. Dang, A. Vasy, M. Wrochna, Dirac operators and local invariants on perturbations of Minkowski space , lien arxiv

N.V.Dang, Jiasheng Lin, Frédéric Naud, Asymptotics of zeta determinants of Laplacians on large degree abelian covers, lien arxiv

Y. Guedes Bonthonneau, N.V. Dang, M. Léautaud et Gabriel Rivière, Poincaré series for analytic convex bodies,