Open for applications
Research project in
Algebraic Complexity Theory and Combinatorics
(Mathematics and Theoretical Computer Science)
(Including Summer internship position in Germany)
Number of positions: 2.
Deadline: 05 Feb 2024.
This project includes an internship phase in Germany this summer funded by the mentors.
Depending on the progress, a Ph.D. position might be offered.
Detailed information can be found below.
Application: Fill in the form here.
Studying the interplay between algebraic and combinatorial objects has proven extremely useful and productive, e.g., in algebraic complexity theory  and the theory of graph homomorphisms [3, 4]. Many important matrix polynomials, such as the determinant or the permanent, have combinatorial reinterpretations, e.g., as (weighted) enumerations of cycle covers in directed graphs. Conversely, polynomials derived from graph homomorphisms form a specific generating set of the invariant ring of Sn × Sn, which endows algebraic objects with new combinatorial meaning.
Going back and forth between these two points of view allows us to deduce new insights both about the algebraic objects (polynomials), as well as their combinatorial counterparts (graph homomorphisms). Even more, it is possible to gain insight about the computational complexity of combinatorial problems (such as counting cycle covers) through purely algebraic quantities. Most important in this context are various notions of rank that can be associated with tensors or polynomials  In this project, we will explore several related questions on objects arising in the combinatorial context of graph homomorphisms.