71 citations · 204 across the 14 of their papers we have counts for
15 papers
Cocycles for Kottwitz cohomology
Jack Sempliner, Richard Taylor
In his work on defining the pointed set B(G) for all local and global fields, Kottwitz introduced certain Galois gerbes and considered their 'algebraic' cohomology with values in a…
Potential automorphy over CM fields
Patrick B. Allen, Frank Calegari, Ana Caraiani +7
Let be a CM number field. We prove modularity lifting theorems for regular -dimensional Galois representations over without any self-duality condition. We deduce that al…
Finding Non-Zero Stable Fixed Points of the Weighted Kuramoto model is NP-hard
Richard Taylor
The Kuramoto model when considered over the full space of phase angles [) can have multiple stable fixed points which form basins of attraction in the solution space. In this…
On the Rigid Cohomology of Certain Shimura Varieties
Michael Harris, Kai-Wen Lan, Richard Taylor +1
We construct the compatible system of -adic representations associated to a regular algebraic cuspidal automorphic representation of over a CM (or totally real) field and…
Automorphy and irreducibility of some l-adic representations
Stefan Patrikis, Richard Taylor
In this paper we prove that a pure, regular, totally odd, polarizable weakly compatible system of -adic representations is potentially automorphic. The innovation is that we mak…
Synchronisation Properties of Trees in the Kuramoto Model
Anthony H. Dekker, Richard Taylor
We consider the Kuramoto model of coupled oscillators, specifically the case of tree networks, for which we prove a simple closed-form expression for the critical coupling. For sev…