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.
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 theorem||here|
|Statistical laws in Dynamical Systems||here|
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 learning||here|
|Extreme value theory III||here|
|Extreme value theory II||here|
|The law of Anomalous numbers||here|
|Understanding bias and variance||here|
|Extreme value theory I||here|
|Central limit Theorem||here|
|Quantitative Borel-Cantelli lemma||here|
|Law of large numbers, part 1||here|
|Weak law of large numbers||here|
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.
- Problem 5: Unbiased and consistent esimators
- Problem 4: producing normal vectors
- Problem 3: rearrange of lists
- Problem 2: expectation of minimum of uniform rv
- Problem 1: random unfair coin
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.
|03/06||Matt Nicol||Limit laws in Dynamical systems||here|
|04/06||Matt Nicol||Martingale approximation||here|
Fractal Weyl laws. This reading group was held on the first term of year 2016-2017:
|17/10||Jimmy Tseng||Symbolic spaces, Hausdorff dimension, Thermodynamic formalism||here|
|24/10||Sebastian Muller||Non-fractal Weyl laws||here|
|31/10||Felipe Pérez||Thermodynamic formalism||here|
|07/11||Felipe Pérez||Iterated functions systems, transfer operator||here|
|14/11||Thomas Jordan||Julia sets, determinant formulas||here|
|21/11||Felipe Pérez||Zeta functions, zeroes counting||here|
|28/11||Sebastian Muller||Non-fractal Weyl laws||Lost|
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.