I am a PhD student working in the department of Mathematics and Computer science at TU/Eindhoven under the supervision of Jaron Sanders.
My research concerns random matrix theory and its applications to dependent processes such as Markov chains. I am also fascinated by the intersection of random matrix theory with problems from algebraic combinatorics such as the question: “Is a random graph typically determined up to isomorphism by its spectrum?”
A concrete application of my research is the study of spectral clustering techniques. Real-world Markov chains often have huge state spaces which makes it difficult to extract insight. Clustering addresses this challenge by grouping together similar states, thereby reducing the size of the state space. In spectral clustering techniques, the algorithm relies on the eigenvectors of a matrix which is constructed based on the data. Random matrix theory can be used to understand when such an algorithm works. My coauthors and I have used our results to gain insight about real-world processes such as text, animal movements, the stock market, and DNA. At the theoretical level, a key challenge is that the matrix arises from a dependent process while classical random matrix theory heavily relies on independence assumptions. Developing proofs for a dependent setting can be quite delicate!
I have also worked in algebraic geometry, specifically on D-modules and Bernstein-Sato polynomials. Additionally, I dabble with computer proof formalization in Lean4 and enjoy creating math-inspired art.
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