Friday's Topology Seminar 2019-2020 |
Speaker: Rune Haugseng (University of Trondheim)
Title: The universal property of bispans Place: Room Seminar C3b (C3b/158) Date: Friday January 10th, 12:00 Abstract: TBA
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Speaker: Luis Javier Hernández Paricio (Universidad de La Rioja) We have developed and implemented in Julia language a collection of algorithms for the iteration of a rational function that avoids the problem of overflows caused by denominators close to zero and the problem of indetermination which appears when simultaneously the numerator and denominator are equal to zero. This is solved by working with homogeneous coordinates and the iteration of a homogeneous pair of bivariate polynomials. This homogeneous pair induces in a canonical way a self-map of the pointed Hopf fibration. Moreover, if the homogenous pair is irreducible, we also have a self-map of the standard Hopf fibration. We study the points of indeterminacy evaluating a canonical map associated with a homogeneous pair on the orbit of a point of the Riemann sphere. These algorithms can be applied to any numerical method that builds a rational map to find the roots of an univariate polynomial equation. In particular with these procedures we analyze the existence of multiple roots for the Newton method and the relaxed Newton method.
This project is being developed together with J.I. Extremiana, J. M. Guti\'errez and M. T. Rivas (University of La Rioja). Speaker: Guillem Sala (UPC) The goal of this talk is to follow the work of Lars Hesselholt and extend this result to the realm of homotopy theory, providing a cohomological interpretation of the Hasse-Weil zeta function using the cohomology associated to a certain spectrum, namely the Topological Periodic Cyclic Homology spectrum. Speaker: Michelle Strumila (University of Melbourne) Abstract: Infinity categories are a way of taking categories up to homotopy. This talk is about how this can be extended to infinity operads, along with generalisations to the non-directional and higher genus cases. Speaker: Eva Belmont (Northwestern University) Abstract: The Adams spectral sequence is one of the main tools for computing stable homotopy groups of spheres. In this talk, I will give an introduction to the Adams spectral sequence in motivic homotopy theory over C and over R, and describe some connections with classical and C_2-equivariant homotopy theory. I will describe joint work with Dan Isaksen to compute the motivic Adams spectral sequence over R and obtain applications to the Mahowald invariant. Speaker: Assaf Libman (Aberdeen University) |