Projects
I am interested in all sorts of problems, especially those which connect techniques from combinatorics and algebraic geometry to questions about non-negativity in the sciences. Do not hesitate to reach out if such a problem occurs in your research and you would like to chat.Present
The Algebraic Boundary Of The SONC Cone
If one fixes a sparse support set, the set of all polynomials supported on this set which have a decomposition as a sum of non-negative circuit polynomials is a convex cone called the SONC cone. The Zariski closure of its boundary is a union of discriminental hypersurfaces, in this project we study the geometry and the combinatorics of this arrangement.
Combinatorial Lyapunov Analysis
The notion of stability of dynamical systems is prevalent across many applications. One well studied method to verify stability of a system is to construct a Lyapunov function (a function which behaves like an energy function for the system). In this project we study when such a function exists which is also polynomial. We give methods for describing all possible supports of such polynomials and we give certain obstructions for their existence.
Past
Euler Stratification For Segre Varieties
In this project we study Euler stratifications of the space of hyperplane sections of Segre varieties in the torus. These topological invariants correspond to maximum likelihood degrees of toric models in algebraic statistics. We give a complete stratification in small cases and give combinatorial information about the general case.
