Math & Stats Colloquium: Re-normalied Link Invariants

In the last few years, C. Blanchet, F. Costantino, M. De Renzi, B.Patureau, N. Reshetikhin, V. Turaev and myself (in variouscollaborations) have developed a theory of renormalized quantuminvariants of links and 3-manifolds which lead to TopologicalQuantum Field Theories.This talk will start out by giving a quickoverview of this work.A principal feature of this work is its interplaybetween quantum algebra and low-dimensional topology.In thesecond part of the talk I will discuss the idea of renormalizedquantum invariants of links without discussing the technical algebraic tools and instead replace them with usual vector spaces.This talk should be accessible to students who know the basic properties of vector spaces.The only concepts which might not be covered in a basic linear algebra coarse are dual vector spaces and tensor products of finite dimensional vector spaces.If you are not familiar with these concepts it would be helpful to take a quick look athttps://mathworld.wolfram.com/DualVectorSpace.html andhttps://mathworld.wolfram.com/VectorSpaceTensorProduct.html.