# Paolo Grazieschi

SAMBa PhD Student at the University of Bath
Hello! I am a **SAMBa PhD student** at the University of Bath studying probability, SPDEs and interacting particle systems. My supervisor is Prof. Hendrik Weber. My PhD project concentrates on the study of the **convergence of the three-dimensional Ising-Kac model to $\phi^4_3$**: the Ising-Kac model, particularly, is a variant of the Ising model where particles have a long-range type interaction with a radius of interaction descreasing to $0$ in a non-trivial way; the $\phi^4_3$ equation, on the other hand, is formally described as $(\partial_t - \Delta) \phi = - \phi^3 + \xi$, with $\xi$ being space-time white noise, and its solution requires non-classical approaches.

**MARCH 1, 1992**BIRTH

**ITALIAN**NATIONALITY

**ITALIAN (NATIVE), ENGLISH (FLUENT), GERMAN (BEGINNER)**LANGUAGE

**DOWNLOAD MY CV: ENGLISH; ITALIAN.**

## My Specialities

### Probability and Stochastic Analysis

My research is on Stochastic Partial Differential Equations (SPDEs) and convergence of interacting particle systems. On top of that, I have successfully completed graduate level courses on brownian motion, Itô calculus, mathematical statistics, mathematical finance and discrete probability.

### The $\phi^4_3$ theory and the Ising-Kac model

A part of my PhD project is the understanding of the $\phi^4_3$ equation, the criticalities involved because of the low regularity of white noise and ultimetely how to make sense of that equation. This part leads to the Theory of Regularity Structures. The other part of my PhD project is proving convergence of the Ising-Kac particle system to the solution of that equation, which is also meaningful to understand the modeling properties of $\phi^4$ itself.

### Stochastic particle Systems models of neuronal networks

At the end of my Master's Degree, under the supervision of Prof. Marco Romito (Università di Pisa), I concentrated on the study of biological stochastic models describing the human brain: particularly, the so called *'Integrate and Fire model'* is at the heart of the mean-field theory developed by Delarue, Inglis, Rubenthaler and Tanré (here and here). After my graduation from Pisa, I then spent one month and a half at a Summer School in Marseille to develop variations of that model and to simulate them numerically.

## Education

### SAMBa PhD student

#### University of Bath

United Kingdom, Bath

### MASDOC PhD student

#### University of Warwick

United Kingdom, Coventry

### Master's Degree in Mathematics with honours

#### University of Pisa

Italy, Pisa

### Bachelor's Degree in Mathematics with honours

#### University of Perugia

Italy, Perugia

### Erasmus Exchange Program

#### Technische Universität Berlin

Germany, Berlin

### High School Diploma

#### Liceo Scientifico "Italo Calvino"

Italy, Città della Pieve

## Skills

### CODING SKILLS

### OTHER COMPUTER RELATED SKILLS

## Research Experiences, Talks and Publications

**"Numerical methods for stochastic models: control, uncertainty quantification, mean-field"**: development and simulation of biological models for the behaviour of the human brain. Preprint available online.

**“Scaling limits, Rough paths, Quantum field theory”**(SRQ) at the Isaac Newton Institute in Cambridge.

In this this article possible modifications of a model for the human brain developed by Delarue, Inglis, Rubenthaler and Tanré are explored and their behaviour is simulated numerically.

## Contact

**Address**

4 West 2.15

Dept of Mathematical Sciences

University of Bath

Bath, BA2 7AY, United Kingdom

p [dot] grazieschi [at] bath.ac.uk