Quantum field theories provide precise descriptions of the fundamental particles that make up the universe. To transform our understanding of field theories, we need new mathematical ideas to uncover hidden patterns within them. Dr. Karen Yeats, Canada Research Chair in Combinatorics of Quantum Field Theory, is using combinatorial tools to build these new mathematical ideas and gain a deeper understanding of quantum field theory and the fundamental building blocks of our universe.
She and her research team aim to shed light on the combinatorics of transseries and resurgence in order to understand how the non-perturbative can be obtained from the perturbative. They are also developing a general theory of chord diagram expansions to build a new framework for perturbative expansions in quantum field theory. To more fully understand the connections between geometry and quantum field theory, they are also proving the completion conjecture for the c_2 invariant of Feynman graphs. Ultimately, their findings will answer deep questions in physics and build new fundamental knowledge in pure mathematics.