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This is the second volume of a series of mainly expository articles on the arithmetic theory of automorphic forms. It forms a sequel to On the Stabilization of the Trace Formula published in 2011. The books are intended primarily for two groups of readers: those interested in the structure of automorphic forms on reductive groups over number fields, and specifically in qualitative information on multiplicities of automorphic representations; and those interested in the classification of I-adic representations of Galois groups of number fields. Langlands' conjectures elaborate on the notion that these two problems overlap considerably. These volumes present convincing evidence supporting this, clearly and succinctly enough that readers can pass with minimal effort between the two points of view. Over a decade's worth of progress toward the stabilization of the Arthur-Selberg trace formula, culminating in Ngo Bau Chau's proof of the Fundamental Lemma, makes this series timely.
Michael Harris started trading stocks, commodities, and currency futures 30 years ago. Michael is the author of the Price Action Lab Blog website. Michael also develops and sells trading strategies and software designed to empower traders and market professionals.
Michael was a pioneer in developing software for identifying price action anomalies 25 years ago. In the past 10 years, he has worked on the development of DLPAL LS, which is a software program that can identify short-term anomalies in market data for use with rule-based and machine-learning models. Michael has also developed several new technical indicators for the analysis of price action and identification of market regimes, such as the Momersion indicator.
Michael has worked in the past for several financial firms, where he developed a program for optimizing bond portfolios and strategies for trading commodities and equities. He has also worked as a long-short equity and ETF trader for a hedge fund.
In 1999, Michael published his first book, "Short-Term Trading with Price Patterns." He published his books "Stock Trading Techniques with Price Patterns" in 2000 and "Profitability and Systematic Trading" in 2008, respectively. In 2015, he published his most recent book, "Fooled by Technical Analysis: The Perils of Charting, Backtesting, and Data-Mining Bias." He has also published many articles as an invited author.
Michael holds two master's degrees, one in mechanical engineering with an emphasis in control systems and optimization and another in operations research with an emphasis in forecasting and financial engineering.
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