Abstract Lectures at the 1998 Les Houches Summer School: Topological Aspects of Low
Dimensional Systems. These lectures contain an introduction to various aspects of Chern …

The literature on the spectral analysis of second order elliptic differential operators contains
a great deal of information on the spectral functions for explicitly known spectra. The same is …

One of the aims of this book is to explain in a basic manner the seemingly difficult issues of
mathematical structure using some specific examples as a guide. In each of the cases …

We review the parity anomaly and a duality web in 2+ 1 dimensions. An odd dimensional
non‐interacting Dirac fermion theory is not parity invariant at quantum level. We demonstrate …

A bstract In this paper we consider gravitational parity anomaly in three and four dimensions.
We start with a re-computation of this anomaly on a 3D manifold without boundaries and …

We present our numerical study of three-dimensional QED with two, four, six and eight
flavors of massless two-component fermions using a parity-preserving lattice regularization …

A bstract We present state-of-the-art extractions of the strong coupling based on N 3 LO+
NNLL accurate predictions for the two-jet rate in the Durham clustering algorithm at e+ e …

A bstract A generalization of the 4d Chern-Simons theory action introduced by Costello and
Yamazaki is presented. We apply general arguments from symplectic geometry concerning …

In an analogy to the odd-dimensional case we define the parity anomaly as the part of the
one-loop effective action for fermions associated with spectral asymmetry of the Dirac …

The unconventional (half-integer) quantum Hall effect for a single species of Dirac fermions
is analyzed. We discuss possible experimental measurements of the half-integer Hall …