{'fraction_non_alphanumeric': 0.018315018315018316, 'fraction_numerical': 0.0, 'mean_word_length': 5.010989010989011, '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}}
Hilbert Metric Nonexpansive Maps

My research deals with the dynamics of nonexpansive maps and the analysis of positive operators on cones. The study of positive operators seeks to extend well known linear algebra results for nonnegative matrices, such as the Perron-Frobenius theorem, to nonlinear operators on general cones. In my thesis, I focus on applying Hilbert’s projective metric to problems in this area. I am also interested in the asymptotic behavior of iterated nonexpansive maps in Banach spaces, as well as in the Hilbert geometry.