prof. Piotr Sułkowski, UW

Physical mathematics, string theory, and knots-quivers correspondence

String theory, apart from motivations and applications related to phenomenology, has been an important source of inspiration for mathematicians. It has led to a number of deep mathematical predictions, and even gave rise to a broad research direction, which has been referred to as a "physical mathematics" in recent years. As one such prediction, in this seminar I will present the so-called "knots-quivers correspondence" (where a "knot" means a closed loop in three dimensions, and a "quiver" is a graph that consists of nodes connected by arrows). From a physics perspective, this correspondence is the statement that two descriptions of a certain system in string theory are equivalent. From mathematical viewpoint, this correspondence is the statement that certain quantities in two seemingly unrelated mathematical fields are intimately related; in consequence it enables to prove some important conjectures in knot theory, it reveals new interesting properties of hypergeometric functions, etc.