Dr. Majdouline Borji

Mathematics Department

Date: Monday, October 13th, 2025

Time: 11:00 a.m.

Location: Bldg. 6/Room 125

Abstract:

In this talk I will give a general overview of the rigorous proof of perturbative renormalization based on the Polchinski flow equations. First, I will explain the general method for the simple case of the massive scalar field theory with a quartic self-interaction in the full space R4. Then, I will explain the difficulties one encounters for theories that break translation invariance, in particular by the presence of a surface and explain how the renormalization of these models is motivated by the critical behavior of some models with boundaries from condensed matter physics. Then I will explain how the renormalizability of the scalar field model on a half-space can be established in the Polchinski framework. I will present my main results in this direction which are based on uniform bounds with respect to the UV cutoff of the correlators in position space.

Biography:

Dr. Borji completed her PhD in 2023 with Prof. Dr. Christoph Kopper on the renormalization of Euclidean boundary field models in the theoretical physics center (CPHT) in Ecole Polytechnique (Palaiseau, France). In 2024, she joined as a post-doc researcher the research groups of Prof. Dr. Felix Otto at the Max-Planck institute for mathematics in the sciences and Prof. Dr. Stefan Hollands at the Institute of theoretical physics (ITP) in Leipzig (Germany) where she worked on renormalizability in curved spacetimes with and without boundaries, and more recently on singular stochastic PDEs in domains with boundaries. Currently, she joined the mathematics department in KFUPM as an assistant professor.

 All faculty, researchers and students are invited to attend.