Research

Quantum Gravity

Noncommutative Quantum Gravity and String Theory

My research focuses on developing a noncommutative approach to quantum gravity, with particular emphasis on a Lorentzian spectral action. This work aims to better understand how geometric and spectral methods can be applied to quantum gravity. I have also worked out spectral and geometric developments of closed string nongeometric backgrounds but they did not lead to anywhere meaningful.

In addition, I have studied constraints on swampland conjectures using Solar System observations, and I am also working possible extensions of the Seiberg–Witten map. Together, these efforts form part of a broader program to understand the fundamental nature of geometry in fundamental physics.

Noncommutative Geometry

Lorentzian Noncommutative Geometry

As is seen from my work in quantum gravity, a crucial focus of my work is the development of Lorentzian formulations of noncommutative geometry. Primarily within these efforts, I am constructing a bosonic spectral action that preserves Lorentzian spacetime signature and this approach is designed to be as constrained and structurally grounded as possible, with the aim of establishing a spectral foundation suitable for quantum gravity. In parallel, I am working toward a general Lorentzian reconstruction theorem within noncommutative geometry. A key aspect of this research is the critique of elliptic replacement methods.