Seminars in geometry/topology

September 25, 13:15 - 14:15, room 734, Sentralbygg 2

Ana Romero Ibáñez (Universidad de La Rioja): Kenzo, a Symbolic Computation system for Algebraic Topology: introduction and applications for the computation of persistent homology and generalized spectral sequences

Abstract: The Kenzo system, developed by Francis Sergeraert and some coworkers, is a Symbolic Computation system for Algebraic Topology. It works with complex algebraic structures: chain complexes, differential graded algebras, simplicial sets, simplicial groups, morphisms between these objects, etc. In particular, it implements the effective homology method and can be used to compute homology and homotopy groups of complicated spaces.

The talk will consist in an introductory description of the program with some examples of calculations. Moreover, we will explain some new modules that we have depeloped computing persistent homology and generalized spectral sequences.

Joint work with A. Guidolin, J. Rubio and F. Sergeraert.

October 16, 13:15 - 14:15, room 734, Sentralbygg 2

David Sprehn (Københavns Universitet): To be announced

Abstract: To be announced.

November 13, 13:15 - 14:15, room 734, Sentralbygg 2

Andreas Holmström (Stockholms Universitet): To be announced

Abstract: To be announced.

September 11, 13:15 - 14:15, room 734, Sentralbygg 2

Glen Wilson (University of Oslo): The eta-inverted sphere over the rationals

Abstract: For any field \(\mathbf{F}\) Morel and and Voevodsky associate to it a stable homotopy category \(SH(\mathbf{F})\) that encodes topologicalvinformation and information about algebraic varieties over \(\mathbf{F}\). Just as with the topological stable homotopy category, we would like to calculate the motivic stable homotopy groups of spheres \(\pi_{s,w}(1) = SH(\mathbf{F})(\Sigma^{s,w}1,1)\). To gain some relevant information about these groups, Guillou and Isaksen—with input from Andrews and Miller—calculated the eta-inverted stable homotopy groups of the \(2\)-complete sphere spectrum over the complex numbers and the real numbers. In this talk we will review the eta-inverted calculations of Guillou and Isaksen and present new results about the structure of the stable homotopy groups of the eta-inverted \(2\)-complete sphere spectrum over fields of cohomological dimension at most \(2\) (characteristic not \(2\)) and the field of rational numbers.