Mircea Petrache

Research summer school Point Configurations: Deformations and Rigidity , London is Postponed to summer 2021

(last updated: Nov 30th, 2019)

Office: 142, edificio rolando Chaqui

Email: mpetrache [usual symbol] mat.puc.cl

Mathematics is there to interact with other sciences. I'm actively searching new ways to apply it in real-world problems. I will not work on a topic unless I actually believe that the gained knowledge can later be applied outside mathematics.

I was trained in PDEs, Calculus of Variations, Geometric Analysis and Geometric Measure Theory. Which I now use to study emergent behavior and structures, especially (but not only) for large point configurations.

A storyline including some of my interests

  • In geometry, physics, computer science, and other fields, "optimization principles" (or more generally "the rules of the system") sometimes produce new emergent structures.
  • New structure takes the form of topological singularities (such as as "charges", "vortices", "defects", etc. , depending on the field). Mathematically, these form e.g. in nonlinear variational problems, or as steady or limit states of dynamical systems.
  • The above belong to the topic of interacting point configurations, made of singularities/defects or otherwise. In general such configurations organize themselves in relation with the geometry/shape of the ambient space.
  • Exponential complexity, is the landmark property of the point configurations I work with, and is a key limiting factor in working with large systems of points.
  • A way to understand/control such high complexity, is to find new clever ways to quantify the group behavior in large systems, and find new problem-specific structures that furnish low-complexity approximations

Within statistical physics, I am interested in crystallization and phase transition phenomena. Material science has a long tradition of studying rigidity of materials and various macroscopic properties (both quantum and classical) as emergent behaviour of systems of defects. In probability theory, one builds ad-hoc large deviation principles and quantifies long-range correlations. In computer science, there are useful techniques known as metric dimension reduction, while other useful methods come from compressed sensing.

Look at my papers for the results I got so far.

And here for a selection of topics I'd like to work on, for example with student.

Pisa2019.pdf

Slides from a recent talk

A song making fun of maths

CV

Since January 2018 I am Assistant Professor at PUC Chile.

September 2017-December 2017: visited FIM in Zürich and Vanderbilt University.

2015-17: MIS Max Planck Institute in Leipzig and Max Planck Institute in Bonn. (Funding: European Post-Doc Institute. Mentors: B. Kirchheim, S. Müller)

2013-2015: Postdoc at Laboratoire Jacques-Louis Lions (Funding: Fondation de Sciences Mathèmatiques de Paris. Mentor: Sylvia Serfaty)

2013: Ph.D at ETH Zürich, (Thesis: "Weak bundle structures and a variational approach to Yang-Mills Lagrangians in supercritical dimensions". Advisor: Tristan Rivière).

2008: MSc Scuola Normale Superiore, (Thesis: "Differential Inclusions and the Euler equation". Advisor: Luigi Ambrosio)


cv.pdf

Past events: