Thursday, September 26, 2019
Time  Items 

All day 

3pm 
09/26/2019  3:00pm Eigenvectors of nonHermitian matrices are typically nonorthogonal, and their distance to a unitary basis can be quantified through the matrix of overlaps. These variables quantify the stability of the spectrum. They first appeared in the physics literature; well known work by Chalker and Mehlig calculated the expectation of these overlaps for complex Ginibre matrices. For the same model, we extend their results by deriving the distribution of the overlaps and their correlations. Some results are based on an explicit solvable Precursive equation, for which conceptual understanding is lacking. (Joint work with Guillaume Dubach). Location:
DL 316

4pm 
09/26/2019  4:15pm Abstract: What is the most powerful topological quantum field theory (TQFT)? And, which 4manifold invariants can detect the Gluck twist? Guided by questions like these, we will look for new invariants of 3manifolds and smooth 4manifolds. Traditionally, a construction of many such invariants and TQFTs involves a choice of certain algebraic structure, so that one can talk about “invariants for SU(2)” or a “TQFT defined by a given Frobenius algebra.” Surprisingly, recent developments lead to an opposite phenomenon, where algebraic structures are labeled by 3manifolds and 4manifolds, so that one can speak of VOAvalued invariants of 4manifolds or MTCvalued invariants of 3manifolds. Explaining these intriguing connections between topology and algebra will be the main goal of these lectures. Location:
LOM 215
