Below are some project files on which I spent a significant amount of time, which are structured enough to share. They are not original works by me, but are more like lecture notes or reviews I wrote for myself based on my studies. The projects are ordered chronologically, where the most recent one appears first.
If you detect any errors or would like to give feedback, feel free to contact me at oguz.burak@metu.edu.tr.
This is the report of my term project on the bootstrap of non-invertible symmetries as part of my undergraduate project course. I studied two-dimensional Conformal Field Theories, the Rational Conformal Field Theory, Verlinde's seminal paper, and a diagrammatic computation that reproduces the result. Up to this point, the report is essentially the same as my DRP project on RCFT & Verlinde Lines, which can be accessed below. After this point, I discuss the 2d critical Ising Model, generalized global symmetries, the conformal bootstrap program, non-invertible symmetry lines in 2d, and the Symmetry Topological Field Theory (SymTFT) construction. Having gathered the necessary tools to study the bootstrap of non-invertible symmetries, I give a review of the recent paper by Lin and Shao, arXiv:2302.13900, on the modular bootstrap approach to categorical symmetries.
You can access the project files from my GitHub repository:
In the graduate-level bootstrap course I took in the fall of the 2024-2025 academic year, the grading was based on a small project on a topic of students' choosing. I chose a research problem I was tackling at the time, which has to do with the holographic description of superconductors. Based on an interesting correspondence between the Josephson junction and the compact QED in 3d constructed by Hosotani, I was trying to understand the corresponding gravity dual. I did not make much progress on this problem.
See the PDF file from my GitHub.
These are notes I took from Anton Kapustin's recent works concerning the phases of matter, Kitaev's conjecture on invertible systems and their phases, and how to construct topological invariants of gapped phases on quantum lattice systems using constructions like Higher Berry curvatures and other (mathematically involved) tools. You can find the lecture series of Kapustin from the YouTube link here.
You can access my notes on the subject from my GitHub.
This is a detailed review of the standard constructions of 2d Conformal Field Theory (CFT). I mostly follow the textbook by Ketov on CFT and sometimes the yellow book (Francesco et. al.). After going through 2d CFT, I discuss rational CFT (RCFT), and try to explain Verlinde's seminal paper on fusion rules of RCFT on the torus, and how modular invariance diagonalizes the fusion algebra. Following the recent literature concerning non-invertible defects of 2d CFT, I give a diagrammatic computation of this, which mostly imitates the diagrams of arXiv:2208.05495.
I wrote this as part of the Directed Reading Program (DRP) for undergraduate students, where the undergrads are paired with graduate students and they work on some topic (it is mainly aimed for mathematics students) for 2-3 months and then they give a presentation on what they studied. The recording of my presentation can be found here and also in the Talks & Presentations section of this webpage.
You can access the project files from my GitHub repository:
This is an incomplete review of Seiberg-Witten theory. The part concerning the juicy stuff about Seiberg-Witten theory is not present in the paper because at the time, I did not understand it very well. It contains a short review of topological solitons in field theory, explicit calculations about 't Hooft-Polyakov monopole in the Georgi-Glashow model -Yang-Mills-Higgs theory in d=4 with SU(2) gauge group Higgsed down to U(1)-, and spinors in 4 dimensions. The supersymmetry part is not particularly good, and I must confess I did not carry out some of the computations at the end of the SUSY side because of the deadline. This was a particle physics course term project, but I view it as an incomplete project of mine that I will come back to in the future.
You can access the project files from my GitHub repository: