# Knots, Strings, Symplectic Geometry and Dualities

#### 01 September - 11 December 2020

Very fruitful interactions between geometry and physics has had large impact on mathematics over the last 35 years. Exceptionally symmetric theories in physics become topologically invariant and have found their mathematical counterparts. These physical theories are typically part of a larger framework that is often hard to capture mathematically but nevertheless very useful and effective for finding dualities between different theories.

For a brief description of how such dualities arise consider some intrinsically quantum theory. The classical limit of such a theory is not unique but any two of its classical limits are naturally related. This leads to dualities between distinct limits, and these can even interchange small fluctuations near one limit with large fluctuations near another.

A well-known example of a duality is mirror symmetry where certain twists in topological string theory gives rise to connections between symplectic (A-model topological string) and complex (B-model topological string) geometry. Another key example from the interface between geometry, topology, and physics that is central to this proposal is the connection between knot invariants and holomorphic curve counting that arise from a chain of dualities connecting Chern-Simons gauge theory to open strings and then through a geometric transition to closed string.

Interactions between geometry, topology and physics continue to pose and solve central mathematical problems and it is to this framework the proposed program belongs.

Participation in the program is by invitation only.