Mircea Petrache Address:
Forschungsinstitut fuer Mathematik,
Raemistrasse 101, 8092, Zuerich, SwitzerlandOffice: G 36.1Email: mircea.petrache (you know what) protonmail.comPhone: +49 (0)1577 06 36 926 (This here is my work webpage. In case you prefer to see my old blog instead, you can find it here.)
(One-minute video summary about the beauty of science, by R. Feynmann)About
In 2013 I obtained my Ph.D at ETH Zürich, where I completed my thesis entitled " Research
Conferences and events
Publications and Preprints Large particle systems with long-range interactions - arxiv.org/abs/1707.07664
**Equality of the Jellium and Uniform Electron Gas next-order asymptotic terms for Riesz potentials**(with C. Cotar) - arxiv.org/abs/1706.06008
**Next-order asymptotic expansion for N-marginal optimal transport with Coulomb and Riesz costs**(with C. Cotar) - arxiv.org/abs/1609.03849
**Equidistribution of jellium energy for Coulomb and Riesz interactions**(with S. Rota-Nodari) - arxiv.org/abs/1507.00782
**Decorrelation as an avatar of convexity** - arxiv.org/abs/1409.7534
**Next-order asymptotics and renormalized energy for Riesz interactions**(with S. Serfaty) Journ. Inst. Math. Jussieu, Volume 16, Issue 3, June 2017, Pages. 501-569. DOI
(..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?) Crystals - arxiv.org/abs/1607.08716
**Dimension reduction techniques for theta functions on lattices**(with L. Bétermin) Journal of Mathematical Physics**58**, 071902 (2017). DOI: http://dx.doi.org/10.1063/1.4995401
Supercritical Yang-Mills theory and Nonlinear Sobolev spaces- 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, 405–427. DOI - 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- arxiv.org/abs/1707.03485
**Coefficient groups inducing nonbranched optimal transport**(with R. Züst) - arxiv.org/abs/1410.0062
**Matchings in metric spaces, the dual problem and calibrations modulo 2**(with R. Züst), New York Journal of Mathematics http://nyjm.albany.edu/j/2016/22-57.html. - arxiv.org/abs/1211.6677
**A continuous model of transportation revisited**(with L. Brasco) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov, Journ. Math. Sci., 196 (2014), no. 2, 119-137. DOI
Mean-field equations for higher-order laplacians- arxiv.org/abs/1001.5231
**Existence of solutions to a higher dimensional mean-field equation on manifolds**(with L. Martinazzi) - arxiv.org/abs/0904.3290
**Asymptotics and quantization for a mean-field equation of higher order**(with L. Martinazzi) Comm. Partial Differential equations 35 (2010), 1-22. , DOI
- 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
Some puzzling natural phenomena: Saturn "hexagonal" vortices, Ants vortex ( video 1, video 2, a paper) |