Title: Hidden symmetries in geometry, arithmetic, and physics

2016.04.29 |

Date | Tue 24 May |

Time | 10:00 — 11:00 |

Location | 1531-119 (Aud. D2) |

**Abstract**

Moduli problems often arise via a symmetry that is "visible" in the problem's description. However, there are many objects – and not just moduli – where "invisible" symmetries underlie important refined structures, which may be encoded in simpler, naturally attached spaces of higher dimension. These invisible symmetries are often non-reductive. Generalizing methods from the reductive case, we can then address a host of seemingly unrelated questions across geometry, arithmetic, and physics. These include: "What is the minimal degree curve passing through n given points in the plane?", "How many integer points are in a region bounded by a height function?", "When is a homology class represented by an algebraic subvariety?", and "How can one robustly characterize entangled states in quantum information theory?".

**NOTE: This talk is aimed at a general audience of mathematicians.**