Singularity categories and singular Hochschild cohomology
Montag, 5.7.21, 16:15-17:15, Anderssen (BBB)
The singularity category was introduced by Buchweitz and then rediscovered by Orlov motivated by the homological mirror symmetry conjecture. Following Buchweitz, in analogy with Hochschild cohomology, one defines the singular Hochschild cohomology of an algebra as the Yoneda algebra of the diagonal bimodule in the singularity category of bimodules. \n\nThe first half of the talk is an introduction to singularity categories and Hochschild cohomology. The second half will show that singular Hochschild cohomology is endowed with the same rich algebraic structure as classical Hochschild cohomology, namely a Gerstenhaber bracket in cohomology and a B-infinity structure at the cochain complex level. We will also talk about its relationship with the deformation theory of singularities.
Relativistische Modelle des Universums um einen zentralen Stern
Montag, 12.7.21, 16:15-17:15, bbb Raum Anderssen
Wir betrachten in diesem Vortrag eine zentrale Masse, die wir als statisch und kugelsymmetrisch annehmen. Ziel wird es sein, die diese Masse umgebende Raumzeit differentialgeometrisch zu beschreiben. Wir werden hierzu zwei Modelle entwickeln und untersuchen: Die intuitivere Schwarzschild-Raumzeit, sowie die Kruskal-Raumzeit. Dabei werden wir ein besonderes Augenmerk auf die auftretenden Singularitäten legen, wobei wir zwischen Koordinatensingularitäten und physikalischen Singularitäten unterscheiden.
Determinants, group cocycles and multiplicative Chern character
Montag, 19.7.21, 16:15-17:15, Anderssen (BBB)
The well known central extension of loop groups is an example of a group two-cocycle naturally constructed from action of the restricted linear group on a certain non-linear category of idempotents in a polarised Hilbert space. We will explain the concepts involved in this construction, its generalisation to a construction of higher cocycles and give some examples of non-trivial three-cocycles for the double loop group, both formal and smooth. On the other hand, these group cocycles lead to functionals on algebraic K-theory, the so called regulators. We will sketch this relation and, in particular, the relation to the Tate tame symbol in algebraic geometry and multiplicative Chern of Connes and Karoubi associated to universal finitely summable Fredholm modules.