Talks

The series of three short lectures provides an introduction to the subject of subgroup growth and related directions of research in asymptotic group theory. For instance, we will discuss polynomial subgroup growth and look at subgroup zeta functions of finitely generated nilpotent groups. We also cover methods from the theory of compact p-adic Lie groups, which have applications to subgroup growth and representation growth.

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.

In the framework of Non-Equilibrium Field Theory, I will construct the effective influence functional — generator of non-equilibrium correlation functions — for a mechanical system with degrees of freedom living on a group (e.g. rigid body) interacting with a thermal bath at high temperature. I will derive the constraints on the influence functional following from the group symmetry structure and the DKMS symmetry — generalization of the fluctuation-dissipation theorem. At the linear response level, group symmetry turns out to impose more constraints compared to DKMS. I will illustrate the general formalism with the diffusion in a Fermi gas and exhibit the large-N suppression of the non-linear response. Finally, I will introduce the Universal Bath — the generalization of the Caldeira-Leggett model. It is a dual field theory defined in one extra dimension that reproduces the classical non-equilibrium dynamics of the mechanical system. I will show that in the limit of Ohmic dissipation, when the temperature becomes the only relevant scale at play, the Universal Bath also reproduces the quantum corrections.