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

• Matroids and their associated algebraic varieties

• 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