Speaker : 1.Emma Yu Jin (Institute of Discrete Mathematics and Geometry, TU Wien) 2.Mihyun Kang (Graz University of Technology)
Title : 1.Strips, thickened strips and skew Schur determinants 2.Graphs on Surfaces and Beyond
Time : 2017-11-01 (Wed) 10:00 - 12:00
Place : Seminar Room 617, Institute of Mathematics (NTU Campus)
Abstract: 1.One of the most fundamental results on the symmetric functions is the determinantal expression of the Schur function $s_{\lambda/\mu}(X)$ for any skew shape, which, after applying the exponential specialization, gives us the number of standard Young tableaux of any skew shape.
In this talk first we will meet a natural generalization of Hamel and Goulden's theorem on the outside decompositions of the skew shape $\lambda/\mu$, which simplifies the enumeration of $m$-strip tableaux. Baryshnikov and Romik first introduced and counted m-strip tableaux via extending the Elkies's transfer operator approach. Second, we will see how Willigenburg applied Hamal and Goulden's theorem to characterize the equivalences between skew Schur functions. Finally we end up with some open problems and conjectures.
This talk will require no prior knowledge of any of the above terms.

2.We discuss asymptotic enumeration and properties of graphs on surfaces and the so-called block-stable graphs. Proof methods include singularity analysis, saddle-point method, and combinatorial Laplace's method, based on the constructive decomposition along connectivity or the core-kernel approach.