About Me

Hi there! I am a postdoctoral researcher in the Cluster of Excellence at Mathematics Münster. Before this, I did my PhD in Eindhoven, where I was fortunate to have Jaron Sanders as my promotor.

My research focuses on random matrix theory and its applications to other areas. For instance, my PhD thesis Latent structures in Markovian processes and associated random matrices pursued fundamental insight on algorithms that extract information from stochastic processes, including spectral methods that rely on matrices constructed from observed data. Lately, I have also become fascinated by the intersection of random matrix theory with algebraic combinatorics such as the question: “Is a random graph typically characterized by spectral information?” Below, I explain these topics in more detail.

Aside from random matrices and stochastic processes, I have also worked in algebraic geometry; specifically on D-modules and Bernstein-Sato polynomials.  Additionally, just for fun, I dabble in computer proof formalization using Lean4 and enjoy creating math-inspired art.

Spectral characterization of random networks

A great deal about a network can be learned from the eigenvalues of associated matrices. For example, communities, the chromatic number, and mixing rates of random walks can be studied using eigenvalues. This is the beautiful subject of spectral graph theory. One may wonder how far one can take this perspective. Is a graph characterized completely by spectral information?

This fundamental question has attracted attention since the 1950s, when it was first posed by Günthard and Primas in a paper on quantum chemistry. While it is known that nonisomorphic graphs with the same adjacency spectrum exist, it remains unclear if such examples are typical or exceptional. If we sample a random graph on \(n\) nodes, will it almost surely be characterized uniquely by its spectrum as \(n\to \infty\)? Despite the topic having a long and rich history, our understanding of such “typical case” scenarios is still limited. My work aims to clarify this; see e.g., arXiv:2401.12655.

Latent structures in stochastic processes

Sequential data—where the order of observations matters—occurs in many scientific areas, making it crucial to understand the information encoded in its structure. This is challenging because the processes that one encounters are often very complex. This makes it desirable to uncover simpler latent structures that capture the key features. I work on rigorous mathematical theory to understand algorithms that can uncover such structures. For instance:

Spectral algorithms use matrices constructed from data to uncover structure. For example, spectral clustering methods group together similar states of a Markov chain to mitigate the curse of dimensionality that arises from large state spaces. Since the matrices are typically built from random observed data, analyzing spectral algorithms fundamentally reduces to studying random matrices. A key challenge here is that the matrix here arises from dependent Markovian data while classical random matrix theory heavily relies on independence assumptions. Developing proofs for a dependent setting can be quite delicate! [arXiv:2307.11632, arXiv:2210.01679, arXiv:2204.13534]

Barriers can hinder the movements of a stochastic process, and this has important implications across various scientific fields. In ecology, for example, it is key to understand how roads restrict animal movement. In cell biology, for another, single-molecule tracking has uncovered that plasma membranes are divided by barriers that hinder lateral diffusion. I have studied the effect of barriers on a variant of Brownian motion, and uncovered different fundamental phases where the associated statistical problem has qualitatively different behavior. [arXiv:2412.14740]

Applications to real-world data

I am also interested in empirical investigations that probe to what extent theory matches the real-world systems that it models, perhaps with a degree of interest that is exceptional for a researcher whose main focus lies on fundamental mathematical research. It is particularly fascinating when things do not match, as this can suggest lines for future research! My coauthors and I have analyzed data from various real-world processes such as text, animal movements, taxi data, the stock market, and DNA. [arxiv:2204.13534, arXiv:2210.01679, arXiv:2412.14740].

Contact info

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