Marcel Vonk (Instituto Superior Técnico, Lisbon)
When a coupling constant in a physical theory is small, one can get a grip on the theory by using perturbative techniques. However, such an approach has two well-known problems. Often, perturbative expansions have a vanishing radius of convergence, making them only well-defined as asymptotic series. Moreover, many physical effects (solitons, instantons, branes) depend on the coupling constant in a way which does not allow for a perturbative expansion.
These two problems are actually closely related. For example, if one obtains an asymptotic series expansion for a certain quantity, the growth of the perturbative coefficients generally contains information about the size of the first nonperturbative contribution. I will review this relation, and show how one can use the mathematical theory of resurgence to immensely generalize it. In particular, I will discuss a class of matrix models and simple string theories where one can obtain a very detailed understanding of all possible instanton and D-brane corrections, starting from perturbative information alone.
Arnold Sommerfeld Center