- 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!
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.
Since January 2018 I am Assistant Professor at PUC Chile.
- 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