Physics

Area metrics define generalized geometric backgrounds to describe spacetime. They are suggested at various places in classical field theory and arise within different approaches to quantum gravity. On these grounds, after introducing the notion of an area metric, I will consider covariant area-metric actions to second order in fluctuations and derivatives. I will then show how these give rise to effective length-metric actions with a distinct nonlocal Weyl-curvature squared term beyond general relativity. Finally, I will point out possible implications and routes for phenomenology.

Non-local operators, supported on submanifolds of spacetime, often encode fascinating physical insights about a theory and can serve as order parameters for phase transitions. In this talk, we will explore various aspects of 1/2​ BPS surface operators in N=4 super Yang-Mills. Specifically, I will show how supergravity computes exactly the planar limit of certain correlation functions of surface operators, even though they receive nontrivial quantum corrections. In particular, we will compute correlation functions with Chiral Primary Operators by localizing N = 4 super Yang-Mills on S^4 to a deformed version of 2d Yang-Mills on S^2. These correlation functions, which have a finite number of quantum corrections, can also be computed perturbatively in four dimensions. I will show the exact agreement between these approaches and the corresponding supergravity result. This talk is based on 2406.08541, work in collaboration with Changha Choi and Jaume Gomis.

Pairwise difference learning (PDL) has recently been introduced as a new meta-learning technique for regression by Wetzel et al. Instead of learning a mapping from instances to outcomes in the standard way, the key idea is to learn a function that takes two instances as input and predicts the difference between the respective outcomes. Given a function of this kind, predictions for a query instance are derived from every training example and then averaged. This presentation focus on the classification version of PDL, proposing a meta-learning technique for inducing a classifier by solving a suitably defined (binary) classification problem on a paired version of the original training data. This presentation will also discuss an enhancement to PDL through anchor weighting, which adjusts the influence of anchor points based on the reliability and precision of their predictions, thus improving the robustness and accuracy of the method.  We analyze the performance of the PDL classifier in a large-scale empirical study, finding that it outperforms state-of-the-art methods in terms of prediction performance. Finally, we provide an easy-to-use and publicly available implementation of PDL in a Python package.