# Linear algebra made difficult

**Date**: Tuesday 14 February 2017, 15:15 – 16:15**Location**: Mathematics Level 8, MALL 1, School of Mathematics**Type**: Pure Mathematics seminars, Algebra seminars, Seminar series**Cost**: Free

#### Andrew Tonks, University of Leicester. Part of the algebra seminar series.

Classically, incidence (co)algebras are constructed from locally finite posets. Via the interpretation of a poset as a simplicial set (its nerve) Gálvez, Kock and myself introduced a substantial abstraction, constructing incidence (co)algebras from simplicial infinity-groupoids satisfying a straightforward pullback condition: these we call decomposition spaces (they are essentially Dyckerhoff and Kapranov's unital 2-Segal space). Under suitable finiteness conditions, the classical theory can be recovered by taking homotopy cardinality, but more importantly there are many new classes of examples not covered by the classical theory, such as Waldhausen\'s $S_\bullet$ construction, whose incidence algebras are Hall algebras.

*After each talk at 4:15pm there will be tea/coffee in the Common Room at level 9 in Maths building. The current seminar organiser is Eleonore Faber. *

**Andrew Tonks**, *University of Leicester*