# Mircea Petrache

## News:

**Link to internet discussion on "shortest superpermutations" (breakthrough time ago by an anonymous 4chan user)****Topics list**fixed for next semester for the seminar on**Metric Embeddings****(click for more info)****Teaching for 1st semester 2019: Measure Theory (Analisis I, MPG3100)**(click for more info) start**: March 6, 2019**- Next seminar on "
**First Passage Percolation & PDE's": -- to be fixed (March 2019)**. - With Daniel Pons (Universidad Andres Bello) we plan to start a
**Stochastic Geometry**working group (**start: end of March 2019**) - Going to
**ICIAM conference**, Valencia, Spain**, July 15-19, 2019,**-- giving talks in mini-symposia**"Discrepancy and Minimal Energy"**and**"Molecular simulation: quantum mechanical models"**

(last updated: Feb 04, 2019)

## If you want to do a PhD or Msc thesis with me, write me an email!

## Interests

### General fields:

I was formed in PDE, Geometric Measure Theory, Calculus of Variations, Geometric Analysis, Optimal Transport. I more recently became involved in topics from Metric/Discrete Geometry, Probability, Mathematical Physics, Point Configurations, Computer Science. Look at my papers for more.

### Topics that I'm interested in:

1) In geometry, physics or other fields, "optimization principles" (or more generally "the rules of the system") sometimes produce new structures "without human intervention", meaning that one doesn't include them as a hypothesis or part of the model that one is studying.

2) New structures can be created in the form of so-called * topological singularities (*also known as

*"charges", "vortices", "defects", etc.*, depending on what field one is coming from

*).*These new structures can for example form in

**nonlinear variational problems**, or as

**steady or limit states of dynamical systems**.

3) Further, the above singularities/defects often **interact between themselves**, and organize themselves, and **interact with the geometry/shape** of the ambient space they live in. **Exponential complexity** (exponential in terms of the number/density of singularities) is the landmark of systems of singularities, although the "complexity" often it is hard to rigorously define/bound in practice.

4) One way to understand/control complex systems including (but not limited to) the above, is to find clever ways to **encode group behavior **of a system.

The study of such "emergent properties" appears naturally in statistical physics, e.g. in **crystallization **and **phase transition** phenomena. In material science **rigidity** and **grain boundaries** can be studied by analytic techniques. In probability **large deviation principles** and **long-range correlations** play a similar role. In computer science, this relates to **metric dimension reduction** and **compressed sensing**.

## 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)

## Past events:

*BIRS workshop January 27th - February 1st, 2019 on***Optimal Transport Methods in Density Functional Theory.****Workshop that I co-organized**, on November 30th, 2018, London:**Symmetries, asymptotics and multi-scale approaches**- AIM workshop
**Discrete geometry and automorphic forms**, San Jose, California, September 24-28, 2018 - Workshop on
**Geometric Measure Theory in Verona**, June 11-15, 2018 - Workshop on
**Nonlocal interactions: Dislocations and beyond**, Bath, 11-14 June 2018 - ICERM trimester on
**Optimal and Random Point Configurations,**Brown University, Providence, February 26th - March 2nd, 2018 **Workshop that I co-organized**, on February 15-17, 2017, London:**New trends in Mathematical Physics at the interface of Analysis and Probability**