Mircea Petrache
Facultad de Matemáticas Avda. Vicuña Mackenna 4860 Macul, Santiago,
6904441, Chile
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.)
About
Since January 2018 I am Assistant Professor at PUC Chile.
In 2013 I obtained my Ph.D at ETH Zürich, where I completed my thesis entitled
"Weak bundle structures and a variational approach to YangMills Lagrangians in supercritical dimensions" (advisor: Tristan Rivière). In 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]
Research
I am interested in Calculus of Variations, PDEs, Geometric Measure Theory, with special emphasis on interactions/applications to Probability, Optimization and Physics.
Pointlike (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 latticelike 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.
 Here is a workshop that I coorganized, on 15th17th February 2017, London:
Publications and Preprints
Large particle systems with longrange 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?)
Supercritical YangMills theory and Nonlinear Sobolev spaces arxiv.org/abs/1306.2010 The resolution of the YangMills Plateau problem in supercritical dimension (with T. Rivière) Advances in Mathematics, Volume 316, 20 August 2017, Pages 469540, 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 36473683, DOI
 arxiv.org/abs/1306.6763 A singular radial connection over B^5 minimizing the YangMills energy Calc. Var. and PDE, 54 (2015) no.1, 631642. 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^pvectorfields with integer fluxes Ann. S.N.S. Pisa Cl. Sci., Vol. XIV (2015), issue 4, 11191156. DOI
 arxiv.org/abs/1204.0175 Notes on a slice distance for sigular L^pbundles Journ. Funct. Anal., 267 (2014), no. 2, 405–427. DOI
 arxiv.org/abs/1007.0681 An integrability result for L^pvectorfields in the plane Adv. Calc. Var., 6 (2013), no. 3, 299–319. DOI
 arxiv.org/abs/1007.0668 Weak closure of singular abelian L^pbundles in 3dimensions (with T. Rivière) Geom. Funct. Anal. 21 (2011), 14191442. DOI
Optimal transport and currents
Meanfield equations for higherorder laplacians
Theses  PhD thesis: Weak bundle structures and a variational approach to YangMills Lagrangians in supercritical dimensions Download
 Master's degree thesis: Differential inclusions and the Euler equation Download
Links about some puzzling phenomena:

