Research

My research lies in algebraic geometry and multilinear algebra, with a focus on tensor methods and rank notions, and their interactions with complexity theory, network models, and applications.

A recurring theme of my work is the use of algebraic and geometric tools to understand how structural properties of tensors reflect computational, combinatorial, and network phenomena.

Tensor methods and rank notions

A central part of my research concerns tensor rank and border rank, both from a structural and an asymptotic point of view. I am interested in how different rank notions capture intrinsic complexity properties of multilinear maps, with particular attention to matrix multiplication tensors and related problems in algebraic complexity theory.

In this direction, I have worked on border-rank decompositions and on algebraic approaches to approximate algorithms, combining theoretical tools with computational experiments.

Algebraic models of networks and tensor products

Another main research line focuses on algebraic descriptions of networks through tensorial constructions. I study how directed acyclic graphs and more general network structures can be encoded by tensors, and how network behavior can be described via tensor products and invariants.

In particular, I have investigated the Bhattacharya–Mesner product as a natural multilinear operation for modeling signal propagation in networks. This approach leads to a global tensor associated with the network, whose algebraic properties reflect structural features of the underlying graph. I am especially interested in inverse problems and identifiability questions arising from this framework.

Interactions with complexity theory, machine learning, and applications

I am interested in connections between algebraic methods and modern applications, including machine learning and computational biology. My work includes the use of algebraic and geometric tools to analyze neural-network–type models, model explainability techniques, and biological data representations.

These interactions motivate new algebraic questions, particularly concerning tensor invariants, identifiability, and complexity measures, and provide a testing ground for theoretical developments.

Future directions

My future research aims to further explore the role of tensorial and geometric methods in complexity theory and network analysis, with an emphasis on rank and subrank phenomena, asymptotic behavior, and algebraic characterizations of computational models.