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