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Mathematics in action: from pandemic to drug discovery

Mathematics in action: from pandemic to drug discovery

Mathematics underpins fundamental theories in physics such as quantum mechanics, general relativity, and quantum field theory. Nonetheless, its success in modern biology, namely cellular biology, molecular biology, chemical biology, genomics, and genetics, has been quite limited. Artificial intelligence (AI) has fundamentally changed the landscape of science, engineering, and technology in the past decade and holds a great future for discovering the rules of life. However, AI-based biological discovery encounters challenges arising from the intricate complexity, high dimensionality, nonlinearity, and multiscale biological systems. We tackle these challenges by a mathematical AI paradigm. We have introduced persistent cohomology, persistent spectral graphs, persistent path Laplacians, persistent sheaf Laplacians, and evolutionary de Rham-Hodge theory to significantly enhance AI's ability to tackle biological challenges. Using our mathematical AI approaches, my team has been the top winner in D3R Grand Challenges, a worldwide annual competition series in computer-aided drug design and discovery for years. By further integrating mathematical AI with millions of genomes isolated from patients, we discovered the mechanisms of SARS-CoV-2 evolution and accurately forecast emerging dominant SARS-CoV-2 variants months in advance.

The recording with full transcript is available at https://umass-amherst.zoom.us/rec/share/mX-Yvtyj0lv7vNSFtwTe6BueXNWpVAgx...

## Department of Mathematics and Statistics