This unique volume, resulting from a conference at the Chern Institute of Mathematics dedicated to the memory of Xiao-Song Lin, presents a broad connection between topology and physics as exemplified by the relationship between low-dimensional topology and quantum field theory. The volume includes works on picture (2+1) - TQFTs and their applications to quantum computing, categorification and Khovanov homology, Gromov - Witten type invariants, twisted Alexander polynomials, Faddeev knots, generalized Ricci flow, Calabi - Yau problems for CR manifolds, Milnor's conjecture on volume of simplexes, Heegaard genera of 3-manifolds, and the (A,B) - slice problem. It also includes five unpublished papers of Xiao-Song Lin and various speeches related to the memorial conference.

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