Title: Mathematical deep learning for drug discovery 
Abstract: Designing efficient drugs for curing diseases is of essential importance for the 21^stcentury's life science. Computer-aided drug design and discovery has obtained a significant recognition recently. However, the geometric complexity of protein-drug complexes remains a grand challenge to conventional computational methods, including machine learning algorithms. We assume that the physics of interest of protein-drug complexes lies on low-dimensional manifolds or subspaces embedded in a high-dimensional data space. We devise topological abstraction, differential geometry reduction, graph simplification, and multiscale modeling to construct low-dimensional representations of biomolecules in massive and diverse datasets. These representations are integrated with various deep learning algorithms for the predictions of protein-ligand binding affinity, drug toxicity, drug solubility, drug partition coefficient and mutation induced protein stability change, and for the discrimination of active ligands from decoys. I will briefly discuss the working principle of various techniques and their performance in D3R Grand Challenges,a worldwide competition series in computer-aided drug design and discovery (http://users.math.msu.edu/users/wei/D3R_GC3.pdf).