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Mircea Petrache

Profesor Asociado

Pontificia Catolica Universidad de Chile

Santiago, Chile

Deep Learning Theory: Neural Networks Equivariance and Symmetries, Compositional Generalization, Flow Matching Mathematics: Optimal Transport, Metric Geometry, Geometric Measure Theory, Large Point Configurations, Crystallization, Coulomb gases

Mathematics, EIDGENOSSISCHE TECHNISCHE HOCHSCHULE. Suiza, 2013
Mathematics, SCUOLA NORMALE SUPERIORE. Italia, 2008
Mathematics, UNIVERSITA DEGLI STUDI DI PISA. Italia, 2008
Mathematics, UNIVERSITA DEGLI STUDI DI PISA. Italia, 2006

PhD/teaching assistant Full Time

EIDGENOSSISCHE TECHNISCHE HOCHSCHULE

Mathematics

Zurich, Suiza

2008 - 2013
Postdoc of the Fondation Sciences Mathematiques de Paris Full Time

UNIVERSITE PIERRE ET MARIE CURIE-PARIS VI

Laboratoire Jacques-Louis Lions

Paris, Francia

2013 - 2015
European Post-doc Institute fellow Full Time

Max-Planck Institut fur Mathematik in den Naturwissenschaften

Leipzig, Alemania

2015 - 2016
European Post-doc Institute fellow Full Time

Max-Planck Institut fur Mathematik

Bonn, Chile

2016 - 2017
Visiting Researcher Full Time

Forschungsinstitut fur Mathematik, ETH Zurich

Zurich, Suiza

2017 - 2017
Postdoc 3 months Full Time

VANDERBILT UNIVERSITY

Nashville, Estados Unidos

2017 - 2017
Honorary Reader Other

UNIVERSITY COLLEGE LONDON

Londres, Reino Unido

2019 - A la fecha
Profesor Asistente Full Time

PONTIFICIA UNIVERSIDAD CATOLICA DE CHILE

Santiago, Chile

2017 - A la fecha

Profesor Asistente Full Time

Pontificia Universidad Catolica de Chile

Santiago, Chile

2017 - 2025
International Coordinator project MATH190004 PDEGeInt Part Time

Math-AmSud

Chile

2019 - A la fecha
Coordinator in Chile, project on "Cooperación en investigación en matemáticas en el campo del análisis matemático y ecuaciones diferenciales parciales no lineales" Part Time

Federation Wallonie-Bruxelles

Chile

2019 - A la fecha
Profesor Asociado Full Time

Pontificia Universidad Catolica de Chile

Santiago, Chile

2025 - A la fecha

Does not apply.

In 2016-2018 I obtained, jointly with Codina Cotar (UCL London), a Royal Society Pillinger International Exchange Award, for outreach and vulgarization on the project “The next-order term in the Hohenberg-Kohn functional”

I gave the following dissemination talks in Chile:

10/01/2019 “Que significa distribuir puntos uniformemente?”, SUMA 2019 popularization seminar for high-school
students, Santiago, Chile

02/10/2018 “Que significa distribuir puntos uniformemente?”, Futuro Novato popularization seminar for High
School students, Santiago, Chile

Fondecyt Iniciacion

FONDECYT

Chile, 2017

3 year individual grant for conducting independent research, including funding for trips, inviting visitors, and other research-related costs


Corrigendum to “Asymptotics for the Unconstrained Polarization (Chebyshev) Problem” Hardin, D; Saff, E Article SCOPUS POTENTIAL ANALYSIS (2022)
Unconstrained Polarization (Chebyshev) Problems: Basic Properties and Riesz Kernel Asymptotics Hardin D.P.; Petrache M.; Saff E.B. Article SCOPUS Potential Analysis (2022)
CLASSIFICATION OF UNIFORMLY DISTRIBUTED MEASURES OF DIMENSION 1 IN GENERAL CODIMENSION Article SCOPUS ASIAN JOURNAL OF MATHEMATICS (2021)
Crystallization to the Square Lattice for a Two-Body Potential BÃƒÂ©termin L.; De Luca L.; Petrache M. Article SCOPUS Archive for Rational Mechanics and Analysis (2021)
Crystallization for Coulomb and Riesz interactions as a consequence of the Cohn-Kumar conjecture Article SCOPUS Proceedings of the American Mathematical Society (2020)
Cyclically monotone non-optimal N-marginal transport plans and Smirnov-type decompositions for N-flows Petrache M. Article SCOPUS ESAIM - Control, Optimisation and Calculus of Variations (2020)
Optimal and non-optimal lattices for non-completely monotone interaction potentials BÃ©termin L. Article ISI SCOPUS ANALYSIS AND MATHEMATICAL PHYSICS (2019)
Equidistribution of Jellium Energy for Coulomb and Riesz Interactions Nodari, Simona Rota Article ISI CONSTRUCTIVE APPROXIMATION (2018)
The Navier-slip thin-film equation for 3D fluid films: Existence and uniqueness Gnann, MV Article ISI SCOPUS JOURNAL OF DIFFERENTIAL EQUATIONS (2018)
Dimension reduction techniques for the minimization of theta functions on lattices Betermin, Laurent Article ISI JOURNAL OF MATHEMATICAL PHYSICS (2017)
NEXT ORDER ASYMPTOTICS AND RENORMALIZED ENERGY FOR RIESZ INTERACTIONS Serfaty, Sylvia Article ISI JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU (2017)
The resolution of the Yang-Mills Plateau problem in super-critical dimensions Article ISI ADVANCES IN MATHEMATICS (2017)
Matchings in metric spaces, the dual problem and calibrations modulo 2 Zust, Roger Article New York Journal of Mathematics (2016)
A singular radial connection over B-5 minimizing the Yang-Mills energy Article ISI CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS (2015)
A continuous model of transportation revisited Brasco, Lorenzo Article Journal of Mathematical Sciences (2014)
GLOBAL GAUGES AND GLOBAL EXTENSIONS IN OPTIMAL SPACES Article ISI ANALYSIS & PDE (2014)
Notes on a slice distance for singular L-p-bundles Article ISI JOURNAL OF FUNCTIONAL ANALYSIS (2014)
An integrability result for L-p-vector fields in the plane Article ISI ADVANCES IN CALCULUS OF VARIATIONS (2013)
WEAK CLOSURE OF SINGULAR ABELIAN L-p-BUNDLES IN 3 DIMENSIONS Riviere, Tristan Article ISI GEOMETRIC AND FUNCTIONAL ANALYSIS (2011)
Asymptotics and Quantization for a Mean-Field Equation of Higher Order Martinazzi, Luca; Petrache, Mircea Article ISI COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS (2010)
Existence of solutions to a higher dimensional mean-field equation on manifolds Article ISI MANUSCRIPTA MATHEMATICA (2010)


Rigidity, stability and uniformity for large point configurations Proyecto (2021)
Cooperation de recherche en mathematiques dans le domaine de l'analyse mathematique et des equations aux derivees partielles non lineaires Premoselli, Bruno Proyecto (2019)
PDEGeInt - Nonlinear PDE's and Geometry of Interfaces Proyecto (2019)
Sharp Asymptotics for Large Particle Systems and Topological Singularities Proyecto (2017)
The next-order term in the Hohenberg-Kohn functional” Cotar, Codina Proyecto (2016)
The next-order term in the Hohenberg-Kohn functional Proyecto “Research in Paris” grant, on the topic “The next-order term in the Hohenberg-Kohn functional”, Institut Henri Poincaré. (0)
Uniformly distrubuted measures in higher codimension Laurain, Paul Proyecto Research in Paris grant for a research stay at IHP Paris (0)

Mircea Petrache

Profesor Asociado

Mathematics

Pontificia Catolica Universidad de Chile

Santiago, Chile

Mircea Petrache

Líneas de Investigación

Educación

Mathematics, EIDGENOSSISCHE TECHNISCHE HOCHSCHULE. Suiza, 2013

Mathematics, SCUOLA NORMALE SUPERIORE. Italia, 2008

Mathematics, UNIVERSITA DEGLI STUDI DI PISA. Italia, 2008

Mathematics, UNIVERSITA DEGLI STUDI DI PISA. Italia, 2006

Experiencia Académica

PhD/teaching assistant Full Time

Postdoc of the Fondation Sciences Mathematiques de Paris Full Time

European Post-doc Institute fellow Full Time

European Post-doc Institute fellow Full Time

Visiting Researcher Full Time

Postdoc 3 months Full Time

Honorary Reader Other

Profesor Asistente Full Time

Experiencia Profesional

Profesor Asistente Full Time

International Coordinator project MATH190004 PDEGeInt Part Time

Coordinator in Chile, project on "Cooperación en investigación en matemáticas en el campo del análisis matemático y ecuaciones diferenciales parciales no lineales" Part Time

Profesor Asociado Full Time

Formación de Capital Humano

Difusión y Transferencia

Premios y Distinciones

Fondecyt Iniciacion

Article (21)

Proyecto (7)