# School of Mathematics

## Open-Closed Gromov-Witten Invariants of Toric Calabi-Yau 3-Orbifolds

We study open-closed orbifold Gromov-Witten invariants of toric Calabi-Yau 3-orbifolds with respect to Lagrangian branes of Aganagic-Vafa type. We prove an open mirror theorem which expresses generating functions of orbifold disk invariants in terms of Abel-Jacobi maps of the mirror curves. This is a joint work with Bohan Fang and Hsian-Hua Tseng.

## The Simplicial Model of Univalence

## Type Systems

## Delegation for Bounded Space

## Information Complexity and Exact Communication Bounds

In this talk we will discuss information complexity -- a measure of the amount of information Alice and Bob need to exchange to solve a problem over distributed inputs. We will present an information-theoretically optimal protocol for computing the AND of two bits distributed between Alice and Bob. We prove that the information complexity of AND is ~1.4923 bits. We use the optimal protocol and its properties to obtain tight bounds for the Disjointness problem, showing that the randomized communication complexity of Disjointness on n bits is ~0.4827n ± o(n).

## Quantum Mechanics -- a Primer for Mathematicians

## Magnetic Vortices, Nielsen-Olesen-Nambu Strings and Theta Functions