## Research

"Science is the poetry of reality."

*- Richard Dawkins*

Black hole analogues

In 1974 **Stephen Hawking** make a prediction that hints a connection between **quantum mechanics**, **general relativity** and **thermodynamics**. A prediction that was apparently doom to **never be tested** until a theoretical analogue proposed by **Bill Unruh** in 1980 connected Hawking's prediction with **moving media**. In recent years, **laboratory analogues** of the event horizon are getting closer to test one of the most elusive effects in Physics: **Hawking radiation**.

What if we could recreate some aspects of this **astrophysical** objects in the **quantum optics lab**?

Ultrashort pulse dynamics

The **nonlinear propagation of light** in media has been a topic of research since the 1980s through the **numerical simulation** of the **non-linear Schrödinger equation** (NLSE). On the other hand, thanks to the development of **photonic crystal fibers** (PCFs), **ultra-short pulses** have become a commonplace in optics labs, these pulses contain only few optical cycles and therefore its theoretical and numerical modeling is still a challenge due to **highly nonlinear effects** present in them, causing effects such as: **soliton pulse formation**, **optical four-wave mixing** and **supercontinuum generation**.

Factorization method

**Quantum mechanics** is one of the pillars of modern physics. Then, it comes as a surprise that only a handful of systems can be **exactly-solved** in quantum theory. All of those can be solved with an **algebraic method** known as **factorization method**. Nowadays, a generalization of this method is used to study quantum systems, algebras, differential equations, special functions and coherent states. This method is also known as **Darboux transformations**, **intertwining technique** or **supersymmetric quantum mechanics**.

Painlevé equations

The **special functions** play a fundamental role in mathematical physics; some of them are solutions to **linear differential equations**. In 1905, **Paul Painlevé** studied the nonlinear ordinary differential equations with specific mathematical properties. He obtained **six** of these equations, which can be considered as **nonlinear analogues** of the classical special functions. Lately, there has been an interest in these equations as they appear in several physical applications. **Painlevé equations** can be solved using algebraic techniques developed in **quantum theory**.