{'fraction_non_alphanumeric': 0.04, 'fraction_numerical': 0.014545454545454545, 'mean_word_length': 5.073529411764706, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
An introduction to Berkovich analytic spaces and non-archimedean potential theory on curves

This is an expository set of lecture notes meant to accompany the author’s lectures at the 2007 Arizona Winter School on p-adic geometry. It is partially adapted from the author’s monograph with R. Rumely [BR08], and also draws on ideas from V. Berkovich’s monograph [Ber90], A. Thuillier’s thesis [Thu05], and Rumely’s book [Rum89]. We have purposely chosen to emphasize examples, pictures, discussion, and the intuition behind various constructions rather than emphasizing formal proofs and rigorous arguments. (Indeed, there are very few proofs given in these notes!) Once the reader has acquired a basic familiarity with the ideas in the present survey, it should be easier to understand the material in the sources cited above.