### 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:

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).