Key Objectives

Our Global BRL project (Aug. 2024 - Apr. 2027, 33 months) aims to develop and to disseminate various topics on the study of spaces of tensors including:

• Algebraic and Geometric complexities arose from (various notions of) tensor ranks and tensor decompositions
  - Geometry of higher secant varieties
  - Determinantal representations of polynomials
  - Algebra/Geometry of determinants and permanents

• Geometry and topology of matrix inversion map
  - Geometry of reciprocal varieties
  - Geometry of polar maps and Cremona transformations
  - Computing invariants of Gaussian graphical models

• Moduli and Quantization problems
  - Generalization of Schubert calculus
  - Quantum cohomology ring
  - Applications to Mathematical Physics