May 20, 2021

### Vortices: Bogomol'ny equations and Taubes Theorem

In this post we will cover the classic calculation of Bogomolny and obtain the energy bound. This bound is saturated in a very especial way leading to the linear Bogomolnyi equation, of great importance in the study of solitons. These equations hide a remarkable complex structure of solitons. Results on the dynamics of multivortex solutions are gouped in Taubes Theorem.

May 15, 2021

### Solitons: Vortices in the Ginzburg-Landau Theory - the gauged theory case

In this post we will cover the vortex solutions in the gauged Ginzburg-Landau theory.

May 01, 2021

### The aulos: An Ancient Greek wind instrument

In this post we talk about an ancient greek wind instrument called aulos and introduce one of the best history pages on the web.

April 29, 2021

### Solitons: Vortices in the Ginzburg-Landau Theory - the global theory case

In this post we will cover the vortex solutions in the Ginzburg-Landau theory. We will focus on the global theory only.

April 02, 2021

### Solitons: Generalizations of the kink

We give a brief discussion about domain wall junctures. This arise as a consecuence of the potencial of having more than two degenerate minima. We also treat the Bogomolny equations for this problem.

March 16, 2021

### Solitons: Sine-Gordon kink

In this post we talk about the Sine-Gordon kink solution. We discuss the Bogomolnyi bound for this case and its non linear realization.

March 13, 2021

### An introduction to Ancient Greek: The Greek Alphabet and Pronunciation Part 2

This is part two of the previous post on the greek alphabet and pronunciation.

March 11, 2021

### Solitons: The kink

In this post we talk about the most basic soliton, the kink. We review some of its properties and the conserved topological charge.

March 09, 2021

### An introduction to Ancient Greek: The Greek Alphabet and Pronunciation Part 1

Finally I pick the courage to start this journey of learning Ancient Greek. In this post we will learn the Greek alphabet and pronunciation.

February 26, 2021

### The Reeh-Schlieder Theorem and vacuum entanglement

In this post I present my final assignment for the elective course Seminar on Quantum Mechanics and Information Theory.

February 12, 2021

### Homotopy Theory and Classification of Topological Solitons

In this post I present my work on homotopy theory and its role in the classification of topological solitons in dimensions $d=1,2,3$. This work was the final assignment for approving the course on Mathematical Methods in Mathematical Physics at my university.

February 05, 2021

### The field equations for a Gauge Theory

This second post will be about the field equations for a gauge theory. This is a direct generalization of Maxwell's equations.

February 02, 2021

### The principle of symmetric criticality

In this post we will treat the Principle of Symmetric Criticality. We will see that this principle is not universally valid. We will also illustrate some examples of application of the principle.

December 20, 2020

### The geometry of Gauge Fields

This will be the first in a series of post about concepts in geometry of gauge fields and properties of Yang-Mills equations based on the book of Sir Michael Atiyah, Geometry of Yang-Mills Fields.

November 23, 2020

### Integration of p-forms over p-chains

Finally, we give introduce the concept of integration of p-forms over p-chains.

November 19, 2020

### Introduction to r-simplexes and r-chains

We give an introduction to r-simplexes and r-chains in order to introduce the notion of integration over r-chains.

July 19, 2020

### The ALPHA experiment at CERN

We review how to find the solution for the electromagnetic four-potential in the Lorentz gauge.

June 29, 2020

### Covariant solution of Maxwell Equations

We review how to find the solution for the electromagnetic four-potential in the Lorentz gauge.

June 17, 2020

### Closed Subsets and Bases for a Topology

In this second post about topology we introduce the concept of closed subsets and bases for a topology.

May 19, 2020

### Early Monarchy and The Unification

This is a short text about the firsts pharaos of Egypt and how the unification happened.

May 15, 2020

### Topological Spaces

This is the first in a series of post about certain topics of Topology.In this post we treat one of the biulding blocks of Mathematics, that it, Topological Spaces as well as introducing open subsets.

April 10, 2020

### Packaging Python Projects

In this blogpost I explain how to create and upload a package to Python Package Index.

April 08, 2020

### Clifford Algebra and SO(2n) representations

In this post I review Spinor representations of SO(2n). Also, we treat Clifford algebra generators and its connection with orthogonal groups.

April 07, 2020

### How to Install Git on Windows

En este post voy a detallar como instalar Git en Windows .