Graduate Lectures – XX/12

Wednesday, December 18, 2024, 13:15 - 16:30

Sebastian Baader

Prof. Sebastian Baader, Universität Bern

Dr. Danica Kosanovic, ETHZ, and Prof. Alain Valette, Université de Neuchâtel

The purpose of these traditional lectures is to present recent important developments in mathematics to a large audience of graduate students and young researchers. The lecturers are chosen as experts in their field, with demonstrated pedagogical talent.

The two math lectures are held by Danica Kosanovic (ETHZ) and Alain
Valette (Uni Neuchâtel). They will cover classical results and recent
developments in topology, geometry, and group theory; see the
summaries below.

There will be approximately 12 double lectures of 90
minutes on Wednesdays (13:15-14:45 & 15:00-16:30), at the University of Bern.

Here is a preliminary schedule; to be confirmed with the second
announcement.

Wednesday, 13h15-14-45: Dr. Danica Kosanovic

Title: The s-cobordism theorem and its 4d reincarnations

Summary: In the first part of the course we will discuss the proof of
the s-cobordism theorem, for cobordisms between smooth manifolds of
dimension at least 5 (in particular proving the Topological
Generalised Poincaré Conjecture and the Schönflies Conjecture), and
in the second part of the course we will see which arguments still
apply for s-cobordisms between 4-manifolds, and how to push them
further (touching on the work of Freedman and Quinn).

Wednesday, 15h00-16h30: Prof. Dr. Alain Valette

Title: L^2-Betti numbers for groups and equivalence relations

 Part 1: L^2-Betti numbers for spaces and groups

 1.1 Motivations, history, and successes of L^2-cohomology
 1.2 $\Gamma$-dimensions
 1.3 L^2-cohomology for manifolds and simplicial complexes
 1.4 Invariants of discrete groups

 Part 2: L^2-Bettti numbers for measurable equivalence relations

 2.1 Measurable equivalence relations
 2.2 Graphings and cost
 2.3 The von Neumann algebra of an equivalence relation
 2.4 Actions of equivalence relations
 2.5 L^2 Betti numbers (after Gaboriau)

University of Bern, building ExWi, room B78

Doctoral Students from CUSO Universities will get their travel expenses reimbursed (SBB ticket 2nd class, 1/2 tax)

Please register under: math.cuso.ch/activities/internal-program

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