The purpose of this article is to provide a key ingredient of [W2] by es-tablishing that certain
minimal Hecke algebras considered there are complete intersections. As is recorded in [W2], …

This book aims first to prove the local Langlands conjecture for GLn over a p-adic field and,
second, to identify the action of the decomposition group at a prime of bad reduction on the l-…

As the world's largest distributed store of fresh water, ground water plays a central part in
sustaining ecosystems and enabling human adaptation to climate variability and change. The …

We extend the methods of Wiles and of Taylor and Wiles from GL2 to higher rank unitary
groups and establish the automorphy of suitable conjugate self-dual, regular (de Rham with …

A basic consideration in the evaluation of professional medical literature is being able to
understand the statistical analysis presented. One of the more frequently reported statistical …

We have analyzed the rings, ring systems, and frameworks in drugs listed in the FDA Orange
Book to understand the frequency, timelines, molecular property space, and the application …

We prove new potential modularity theorems for n-dimensional essentially self-dual l-adic
representations of the absolute Galois group of a totally real eld. Most notably, in the ordinary …

Background: Chat Generative Pre-trained Transformer (ChatGPT) is a 175-billion-parameter
natural language processing model that can generate conversation-style responses to user …

The Chemscore function was implemented as a scoring function for the protein–ligand
docking program GOLD, and its performance compared to the original Goldscore function and …

Software architectures shift the focus of developers from lines-of-code to coarser-grained
architectural elements and their overall interconnection structure. Architecture description …