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].

Loops in hydrodynamic turbulence

Katepalli Sreenivasan
New York University; Member, School of Mathematics
April 17, 2019
An important question in hydrodynamic turbulence concerns the scaling proprties in the inertial range. Many years of experimental and computational work suggests---some would say, convincingly shows---that anomalous scaling prevails. If so, this rules out the standard paradigm proposed by Kolmogorov. The situation is not so obvious if one considers circulation around loops as the scaling objects instead of the traditional velocity increments.

On the possibility of an instance-based complexity theory.

Boaz Barak
Harvard University
April 15, 2019
Worst-case analysis of algorithms has been the central method of theoretical computer science for the last 60 years, leading to great discoveries in algorithm design and a beautiful theory of computational hardness. However, worst-case analysis can be sometimes too rigid, and lead to an discrepancy between the "real world" complexity of a problem and its theoretical analysis, as well as fail to shed light on theoretically fascinating questions arising in connections with statistical physics, machine learning, and other areas.

Etale and crystalline companions

Kiran Kedlaya
University of California, San Diego; Visiting Professor, School of Mathematics
April 15, 2019

Deligne's "Weil II" paper includes a far-reaching conjecture to the
effect that for a smooth variety on a finite field of characteristic p,
for any prime l distinct from p, l-adic representations of the etale
fundamental group do not occur in isolation: they always exist in
compatible families that vary across l, including a somewhat more
mysterious counterpart for l=p (the "petit camarade cristallin"). We
explain in more detail what this all means, indicate some key