# Simon

Guisset

informal introduction

research

teaching

informal introduction

research

teaching

## some words about me …

I am currently a fourth year PhD student in Mathematics at Queen Mary University of London (QMUL), under the supervision of Dr. Arick Shao, where I am part of the group *Geometry, Analysis and Gravitation*.

I am also a Teaching Assistant at QMUL and King’s College of London in Mathematics since 2022.

My main interests lie at the intersection of physics questions in the context of **General Relativity** (GR) and **Partial Differential Equations** (PDE). I am particularly fascinated by the mathematical foundations of Theoretical Physics. More specifically, I am studying the uniqueness properties at infinity of a class of spacetimes known as *Asymptotically Anti-de Sitter* in the hope of giving a rigourous formulation to the now famous *AdS/CFT correspondence*.

I also hold a strong interest in the computation of conserved quantities at infinity, namely **Asymptotic Charges**, in the so-called covariant phase space formalism.

view my curriculum vitae

view my publications

## the informal introduction blah-blah-blah

This section will be devoted to the non-mathematicians among us. It could potentially be called ‘what does this guy do for a living’?

Working as a mathematician certainly brings a lot of questions to those whose last mathematical memories stopped at their final exams in high school, when they could finally say ‘never again’.

I’m a mathematician working in gravity, which means I use math to understand how the universe bends and warps. My job is to develop mathematical tools that help us understand gravity, black holes, and the overall structure of the universe. I spend my days working with complex equations and abstract concepts. It’s like exploring a whole new world, but instead of a map, I have a pencil and paper. And who knows, maybe someday my work will lead to a breakthrough that changes the way we see the universe (nope). Or maybe I’ll just end up proving that cats are the true rulers of the cosmos. Either way, it’s a wild ride!

As a future mathematician, my job is to **prove theorems** – *but what exactly is a theorem*? In my case, these theorems apply to **General Relativity** (GR), a theory of gravitation. To study it, there are many methods, including numerical and analytical ones. In the analytical approach, GR can be seen as a theory involving complex equations of functions that fall into the beautiful category of **Non-linear Partial Differential Equations** (NLPDE). So, what do I do? I analyze NLPDEs.

Now, you may wonder, what’s the point of proving theorems? How does that relate to physics? It’s a deep question that could fill books. Essentially, I’m trying to write mathematical statements. Of course, I can’t just expect people to take my word for it – I need to prove those statements. While the notion of truth in math isn’t the same as in physics or natural sciences, the two are certainly not unrelated. Mathematics has proven incredibly effective at describing the world, and any quantitative theory has to make sense mathematically. In my case, that means studying the math behind gravitation.

Certainly, those questions warrant more detailed explanations, which you may find on this website in the future. So, stay tuned and keep connected!

## about my research

My interests lie at the intersection of Nonlinear PDEs and General Relativity. Currently, I am studying asymptotic properties of asymptotically Anti-de Sitter solutions, with the AdS/CFT correspondence as a main motivation. Here are, in inverse chronological order, my different publications.

Publications

- Simon Guisset, Arick Shao,
*On counterexamples to unique continuation for critically singular wave equations*, Journal of Differ. Eq. 395 (2024), arXiv - Mahdi Godazgar, Simon Guisset,
*Dual charges for AdS spacetimes and the first law of black hole mechanics*, Phys.Rev.D 106 (2022) 2, 024022, arXiv

A list of the seminars and conferences in which I have been invited to give a talk, in inverse chronological order:

Seminars and conferences

- Junior Analysis Seminar, Imperial College, London, March 2024
- Séminaire de Relativité, LJLL, Sorbonne Université, February 2024
- Geometry, Gravitation and Analysis Seminar, Queen Mary University of London, December 2023

## about the teaching

Before the start of my PhD, I had the opportunity to teach at a A-level at *École Notre-Dame des Champs* in Mathematics in Physics. At the same time, I worked as a GTA for the **Université de Namur** for the Mathematics Department in *Analysis, Linear Algebra* and *Graph Theory*.

I am now currently teaching as a GTA at **King’s College of London (KCL)** from 2022 in *Calculus (Year 4)* and *Supersymmetry (Year 7)*. Simultaneously, I am also teaching *Vectors and Matrices (Year 4)* at the **Queen Mary University of London (QMUL)**.

Find in the next box my teaching experience summed up.

**2022-2023**

- GTA at
**King’s College of London (KCL)**in*Calculus I*(4CCM111A)*, Calculus II*(4CCM112A)*, Supersymmetry and Conformal Field Theory*(7CCMMS40). - GTA at
**Queen Mary University of London (QMUL)**in*Vectors and Matrices (MTH4115 / MTH4215), Partial Differential Equations (MTH6151).*

**2019-2020**

- GTA at
**Université de Namur**in*Real Analysis I & II*(SMATB102. SMATB103),*Analysis I & II*(INFOB124/INFOB127),*Mathematics*(SMATB111),*Graph Theory*(SMATB254). - A-level Teacher in Mathematics (4h) and Physics (3h) at CESL Notre-Dame des Champs.