Anomalies in the Space of Couplings and Dynamical Applications

Clay Cordova
Member, School of Natural Sciences, IAS
April 26, 2019

Anomalies are invariants under renormalization group flow which lead to powerful constraints on the phases of quantum field theories.  I will explain how these ideas can be generalized to families of theories labelled by coupling constants like the theta angle in gauge theory.  Using these ideas we will be able to prove that certain systems, such as Yang-Mills theory in 4d, necessarily have a phase transition as these parameters are varied.  We will also show how to use the same ideas to constrain the dynamics of defects where coupling constants vary in spacetime.

Chow motives, L-functions, and powers of algebraic Hecke characters

Laure Flapan
Northeastern University/MSRI
April 22, 2019

The Langlands and Fontaine–Mazur conjectures in number theory describe when an automorphic representation f arises geometrically, meaning that there is a smooth projective variety X, or more generally a Chow motive M in the cohomology of X, such that there is an equality of L-functions L(M,s) = L(f,s). We explicitly describe how to produce such a variety X and Chow motive M in the case of powers of certain automorphic representations, called algebraic Hecke characters. This is joint work with J. Lang.

Anyonic-String/Brane Träumerei: Quantum 4d Yang-Mills Gauge Theories and Time-Reversal Symmetric 5d TQFT

Juven Wang
Member, School of Natural Sciences, IAS
April 19, 2019

My talk will aim to be a friendly introduction for condensed matter friends, mathematicians, and QFT theorists alike ---  I shall quickly review and warm up the use of higher symmetries and anomalies of gauge theories and condensed matter systems. Then I will present the results of recent work [arXiv:1904.00994].