Publications:

All my papers are listed on ORCID and all recent ones are available on arXiv. Here are the links to my Google Scholar and my MathSciNet profiles.

Current Research Interests:

My research interests lie in the area of Combinatorial, Computational and Applied Algebraic Geometry. In particular, I am interested in developing mathematical tools to study problems in statistics and probability theory, theoretical computer science, mathematical optimization, and quantum physics. On the theoretical side, I work on toric varieties, combinatorial divisor theory, determinantal varieties, tensors and their decompositions, algebraic statistics (conditional probabilities, graphical models, causality), matroids, and system reliability theory.

• Numerical algebraic geometry: solving polynomial systems

• Tensors: algebra, geometry and applications in quantum physics

• Solving structured polynomial systems

• Combinatorial rigidity theory and geometric tensegrity

• Toric degenerations of varieties using tools from representation theory, tropical geometry and cluster algebra

• Algebraic and combinatorial divisor theory for graphs and matroids

• Algebraic statistics with a focus on graphical models and maximal likelihood degree of varieties

• Sandpile models (avalanche dynamics)

• Hyperplane arrangements and Orlik-Terao ideals

• Gröbner bases and its applications

• Deformation, minimal free resolutions, and cellular resolution of ideals

• Determinantal ideals and their applications in conditional independence statements

• System reliability theory and percolation theory

• Combinatorial persistent homology and computational topology

PI for the Research Grants and Fellowships (since 2018):

My research has been supported by the following grants:

• KU Leuven iBOF Research Grant (2023-2026), co-PI

joint grant with Professors Bart De Moor, Lieven De Lathauwer, Johan Suykens, and Frank Verstraete

• FWO Odysseus Group I Project Grant (2021-2026), PI

• FWO Research Project Grant (2021-2025), PI

• Ghent University BOF Research Grant (2020-2024), PI

• EPSRC Early Career Fellowship (2018-2020), PI

• London Mathematical Society Scheme 7 Grants (2018-2019), PI

• London Mathematical Society Scheme 1 Grants (2018-2019), PI

Promoter for the Research Fellowships (since 2021):

I have been the promoter for the following grants to support my team's research at KU Leuven:

• FWO PhD Fellowship awarded to Sebastian Seemann (2023-2025)

• FWO travel grant for Francesca Zaffalon for a long-term visit to MPI Leipzig (2024)

• FWO PhD Fellowship awarded to Francesca Zaffalon (2022-2024)

• SofinaBoël Fellowship for Harshit J Motwani to visit HKUST (2022)

• FWO Junior Postdoctoral Fellowship awarded to Daniele Taufer (2022-2025)

• FWO Junior Postdoctoral Fellowship awarded to Tim Seynnaeve (2022-2025)

• FWO Junior Postdoctoral Fellowship awarded to Yairon Cid-Ruiz (2021-2024)

• BOF Postdoctoral Fellowship (UGent) awarded to Job Rock (2021-2024)

• BOF Fellowship (UGent) to hire Harshit Motwani as a PhD student (2021-2023)

Travel Grants and Fellowships (since 2022):

• AIM SQuaREs Grant, USA (2023-2025)

• Oberwolfach Research Fellow, MFO, Germany (2022).