In 1900, David Hilbert posed his list of 23 mathematical problems. While some of them have been resolved in subsequent years, a few of his challenging questions remain unanswered to this day. One of them is Hilbert's 16th problem, which asks questions about the number of limit cycles that a system of ordinary differential equations can have. Such equations appear in modelling real-world systems in biological, chemical or physical applications, where their solutions are functions of time.
13:00
Distinguishing SCFTs in Four and Six Dimensions
Abstract
When do two quantum field theories describe the same physics? I will discuss some approaches to this question in the context of superconformal field theories in four and six dimensions. First, I will discuss the construction of 6d (1,0) SCFTs from the perspective of the "atomic classification", focussing on an oft-overlooked subtlety whereby distinct SCFTs in fact share an effective description on the generic point of the tensor branch. We will see how to determine the difference in the Higgs branch operator spectrum from the atomic perspective, and how that agrees with a dual class S perspective. I will explain how other 4d N=2 SCFTs, which a priori look like distinct theories, can be shown to describe the same physics, as they arise as torus-compactifications of identical 6d theories.
13:00
Towards Hodge-theoretic characterizations of 2d rational SCFTs
Abstract
A 2d SCFT given as a non-linear sigma model of a Ricci-flat Kahler target
space is not a rational CFT in general; only special points in the moduli
space of the target-space metric, the 2d SCFTs are rational.
Gukov-Vafa's paper in 2002 hinted at a possibility that such special points
may be characterized by the property "complex multiplication" of the target space,
which has its origin in number theory. We revisit the idea, refine the Conjecture,
and prove it in the case the target space is T^4.
This presentation is based on arXiv:2205.10299 and 2212.13028 .