Here I will list the reading groups or seminars in which I will be participating/organising. I will also occasionally upload some notes taken at each of the seminars. My notes can (and will usually) be a bit sloppy, and I declare myself responsible for any mistakes in them.

Quantum theory for mathematicians: here I will post (handwritten) notes from our reading group (co-organized with Gastón Burull). The discussions are lead by myself and the notes taken by Gastón.

In preparation… 

Notes on dynamical systems and ergodic theory: here I will post some notes on topics related to my research that I have written.

The ergodic theoremhere
Statistical laws in Dynamical Systemshere

Notes on probability theory and statistics: here I will post notes on a variety of topics related to probability theory which are of my interest in one way or another. They have an expository character while keeping the formality.

Is overfitting… good?here
PCA and supervised learninghere
Martingales 0here
Extreme value theory IIIhere
Empirical errorhere
Extreme value theory IIhere
Confidence intervalshere
The law of Anomalous numbershere
Understanding bias and variancehere
Extreme value theory Ihere
Large deviationshere
Central limit Theoremhere
Quantitative Borel-Cantelli lemmahere
Law of large numbers, part 1here
Borel-Cantelli lemmahere
Weak law of large numbershere

Problems in data science: here I will post a number of problems and solutions, related to the discipline of data science. This includes statistics, probability, algorithms, among others.

Statistical properties in hyperbolic dynamics: course from the Houston Summer School on Dynamical Systems 2019 by the Department of Mathematics of the University of Houston. For more information, see here.

03/06Matt NicolLimit laws in Dynamical systemshere
04/06Matt NicolMartingale approximationhere
05/06Andrew TörökQuasi-compactnesshere
06/06Will OttCouplinghere

Fractal Weyl laws. This reading group was held on the first term of year 2016-2017:

17/10Jimmy TsengSymbolic spaces, Hausdorff dimension, Thermodynamic formalismhere
24/10Sebastian MullerNon-fractal Weyl lawshere
31/10Felipe PérezThermodynamic formalismhere
07/11Felipe PérezIterated functions systems, transfer operatorhere
14/11Thomas JordanJulia sets, determinant formulashere
21/11Felipe PérezZeta functions, zeroes countinghere
28/11Sebastian MullerNon-fractal Weyl lawsLost

M.I. Gordin, On the central limit for stationary processes: this is a very rough translation of the paper by Gordin, where he introduced the martingale approximation method to derive statistical results in dynamical systems. Russian original/English translation.

Bowen’s formula and transfer operators: here. In these notes I present a sketch of the proof of the Bowen’s formula for the Hausdorff dimension of the repeller of an IFS, as well as introducing notions of thermodynamic formalism.