This article is based on my research project1 in mathematical physics. I outline the central ideas in broader terms. The project examines the possibility that gravity may be an emergent phenomenon rather than a fundamental interaction. It begins with black hole thermodynamics and entropy bounds, including Bousso’s bound, and discusses the holographic principle and its realization in the AdS/CFT correspondence. Finally, it presents selected approaches to emergent gravity, most notably Jacobson’s thermodynamic derivation of Einstein’s equations and Verlinde’s entropic gravity.

This article is based on my seminar report1 on topological insulators, prepared at Leiden University. The work gives a pedagogical overview of the topological description of band insulators, with a primary focus on the Kane–Mele model of graphene and the emergence of the ℤ₂ topological phase. Along the way, I introduce the necessary mathematical tools like vector bundles and their topological invariants and illustrate them on the Haldane and Kane–Mele models.

This article is based on a computational physics project1 carried out at Leiden University. In the project, the two-dimensional XY model was simulated on a square lattice using the Metropolis Monte Carlo algorithm with periodic boundary conditions. The goal was to explore the thermodynamic behaviour of the model and to reproduce the Kosterlitz–Thouless phase transition. Here I give a short conceptual overview of the work. The simulation code used in the project is available on GitHub.

This article is based on a computational physics project1 carried out at Leiden University. In the project, the motion of a relatively small number of Argon atoms was simulated using simple Newtonian dynamics with the Lennard–Jones potential, integrated using the Verlet algorithm with periodic boundary conditions. The aim was to see how this microscopic model reproduces the three phases of matter and to study their basic properties. Here I give a short conceptual exposition of the work. The simulation code used in the project is available on GitHub.

This article is based on my Bachelor’s thesis1 in mathematical physics. I outline the main ideas and motivations of the work in broader terms. In the thesis, I investigate how deformations of the standard uncertainty relations can be interpreted, at the classical level, as deformations of the Poisson algebra of observables. I then explore how this modified structure affects Hamiltonian dynamics, with applications to geodesic motion in Schwarzschild and Kerr spacetimes and to black hole thermodynamics.