Mircea Petrache    

Facultad de Matemáticas
Avda. Vicuña Mackenna 4860
Macul, Santiago,

Office: 142
Phone: 23544038

Email: mircea.petrache (you know what) protonmail.com
Phones: +49 (0)1577 06 36 926, +56 93 49 58 140
(This here is my work webpage. For my old blog, you can look here.)

(last updated: August 21, 2018)


I am interested in Calculus of Variations, PDEs, Geometric Measure Theory, with special emphasis on interactions/applications to Probability, Optimization and Physics.

Point-like (or more complicated) topological singularities arising in Nonlinear Sobolev Spaces and Gauge Theory can be interpreted as particles or vortices, and I study the asymptotic behavior of minimizing configurations as the number of vortices increases. The sharp asymptotics appearing in these studies are relevant in Approximation theory, in Statistical Physics and
in Random Matrix theory.

At the moment I am especially interested in uniformization/crystallization phenomena, where for large numbers of points one can prove/quantify that the configurations come close to forming lattice-like structures. New notions of curvature seem to arise in the study of these asymptotics.

Related to the previous point is also the study of asymptotics of a large number of quantum particles, which is relevant to the computations of shapes of large molecules via Density Functional Theory. Here a multimarginal Optimal Transportation problem with an exotic cost appears, and I'm interested in the asymptotics as the number of marginals grows to infinity.

The appearance of collective behaviour allows to make rigorous the link between micro- to macroscopic properties in fluids, solids and gases. Here the goal is to rigorously deduce the macroscopic properties in physically realistic situations, such as for a moving droplet of liquid.

Past events

About me:
Since January 2018 I am Assistant Professor at PUC Chile.
September 2017-December 2017: I have been visiting the FIM in Zürich and Vanderbilt University.
2015-17: I was at the MIS Max Planck Institute in Leipzig and Max Planck Institute in Bonn, under a scholarship of the European Post-Doc Institute (mentors: B. Kirchheim, S. Müller)
2013-2015: I had a postdoctoral position at Laboratoire Jacques-Louis Lions in collaboration with Sylvia Serfaty and under a scholarship of the Fondation de Sciences Mathèmatiques de Paris. 
2013: I obtained my Ph.D at ETH Zürich, where I completed my thesis entitled   "Weak bundle structures and a variational approach to Yang-Mills Lagrangians in supercritical dimensions" (advisor: Tristan Rivière).
2008: I graduated at Scuola Normale Superiore, with a thesis entitled "Differential Inclusions and the Euler equation" (advisor: Luigi Ambrosio)

[for more informations see my CV]


Large particle systems with long-range interactions

(..see this YouTube video for a fun simulation from "Cody's lab" channel, that anybody can reproduce at home: Why do those magnets produce that pattern?)

Fluid dynamics
Supercritical Yang-Mills theory and Nonlinear Sobolev spaces
  • The Space of Weak Connections in High Dimensions (with T. Rivière) in preparation
  • arxiv.org/abs/1306.2010 The resolution of the Yang-Mills Plateau problem in super-critical dimension (with T. Rivière) Advances in Mathematics, Volume 316, 20 August 2017, Pages 469-540, DOI
  • arxiv.org/abs/1508.07813 Controlled singular extension of critical trace Sobolev maps from spheres to compact manifolds (with J. Van Schaftingen) Int. Math. Res. Not., 2017 (12), Pages 3647-3683, DOI
  • arxiv.org/abs/1306.6763 A singular radial connection over B^5 minimizing the Yang-Mills energy Calc. Var. and PDE, 54 (2015) no.1, 631-642. DOI 
  • arxiv.org/abs/1302.5659 Global gauges and global extensions in optimal spaces (with T. Rivière)  Analysis and PDE, 7 (2014), No. 8, 1851–1899.  DOI
  • arxiv.org/abs/1204.0209 Interior partial regularity for minimal L^p-vectorfields with integer fluxes Ann. S.N.S. Pisa Cl. Sci., Vol. XIV (2015), issue 4, 1119-1156. DOI
  • arxiv.org/abs/1204.0175 Notes on a slice distance for sigular L^p-bundles Journ. Funct. Anal., 267 (2014), no. 2,   405–427DOI
  • arxiv.org/abs/1007.0681 An integrability result for L^p-vectorfields in the plane Adv. Calc. Var., 6 (2013), no. 3, 299–319. DOI
  • arxiv.org/abs/1007.0668 Weak closure of singular abelian L^p-bundles in 3-dimensions (with T. Rivière)  Geom. Funct. Anal. 21 (2011), 1419-1442. DOI
Optimal transport and currents

Mean-field equations for higher-order laplacians


  • PhD thesis: Weak bundle structures and a variational approach to Yang-Mills Lagrangians in supercritical dimensions  Download
  • Master's degree thesis: Differential inclusions and the Euler equation Download

Links about some puzzling phenomena: