Jan

28

2022

Jan

31

2022

Finite gap theory of operators and solutions to completely integrable systems were introduced by Novikov, Dubrovin, Matveev, Its, McKean and VanMoerbeke in the 1970s in the context of the periodic solutions to the KdV equation and the spectral theory of one dimensional periodic Schordinger operators. This theory led to explicit formulas for solutions to problems in these areas in terms of theta functions. This theory was also applied in the context of solutions to the Toda lattice and the spectral theory of Jacobi operators by Krechiver.

Jan

31

2022

Given the classical Apollonian gasket, what are all the circles that intersect it in countably many points, and how are they distributed? Equivalently, what are all the elementary geodesic planes in the Apollonian orbifold, and how do they behave topologically?

Jan

31

2022

Feb

01

2022

Persistent homology is one of the main tools of topological data analysis and has had many successes in applications. Multi-persistence is a natural extension of the idea of persistence but has not yet enjoyed the same success. The main obstacle is the increased complexity of the underlying algebraic structure. In this talk, I will introduce the idea of multi-persistence and show why it is a natural object to consider. I will give an overview of the challenges introduced by the multi-persistence that need to be solved before one can successfully apply it in TDA.