Notes
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.
| Description | Notes |
|---|---|
| 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.
| Description | Notes |
|---|---|
| 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.
| Description | Notes |
|---|---|
| Is overfitting… good? | here |
| PCA and supervised learning | here |
| Martingales 0 | here |
| Extreme value theory III | here |
| Empirical error | here |
| Extreme value theory II | here |
| Confidence intervals | here |
| The law of Anomalous numbers | here |
| Understanding bias and variance | here |
| Extreme value theory I | here |
| Large deviations | here |
| Central limit Theorem | here |
| Quantitative Borel-Cantelli lemma | here |
| Law of large numbers, part 1 | here |
| Borel-Cantelli lemma | 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.
| Date | Speaker | Description | Notes |
|---|---|---|---|
| 03/06 | Matt Nicol | Limit laws in Dynamical systems | here |
| 04/06 | Matt Nicol | Martingale approximation | here |
| 05/06 | Andrew Török | Quasi-compactness | here |
| 06/06 | Will Ott | Coupling | here |
Fractal Weyl laws. This reading group was held on the first term of year 2016-2017:
| Date | Speaker | Description | Notes |
|---|---|---|---|
| 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.