Oberseminar Geometrie, Topologie und Analysis

Oberseminar Geometrie, Topologie und Analysis

H. Geiges, A. Lytchak, G. Marinescu, S. Sabatini

Sommersemester 2017

Freitag, 10:30-11:30, Seminarraum 2 (Raum 204)

21.4.17 BHKM Seminar in Köln

19.5.17 Joan Licata (ANU Canberra)
Talk for graduate students and postdocs in the framework of the Graduate School, 10:00-11:30

2.6.17 BHKM Seminar in Heidelberg

16.6.17 Gerard Freixas i Montplet (Paris)
On a geometric interpretation for the Cappell-Miller torsion

Abstract: Cappell and Miller introduced a complex-valued version of the Ray-Singer analytic torsion, for holomorphic vector bundles endowed with flat connections. An open question is whether this invariant satisfies analogous properties as the Ray-Singer torsion, as in work of Bismut-Gillet-Soulé. In this talk I will recall the definition of this torsion invariant and explain its geometric content in the rank 1 case and over Riemann surfaces.

23.6.17 BHKM Seminar in Bochum

7.7.17 Joint Seminar on Complex Algebraic Geometry and Complex Analysis in Köln

14.7.17 Roger Züst (Bern)
Calibrations and calibrations modulo 2

Abstract: To show that a given oriented submanifold has minimal volume among all submanifolds with a fixed boundary or homology class is hard, in general. The tool most often used for testing such minimality are calibrations. These are closed differential forms with pointwise unit norm. The 1-dimensional problem asks for the length minimal filling of a given, say finite, set of sources and drains. The Kantorovich duality of optimal mass transport guarantees the existence of calibrations in this situation. Similar to the oriented minimal filling problem one may be interested in the unoriented one, where coefficients modulo 2 are considered. In dimension one this asks for a minimal matching among an even number of points. In a joint work with Mircea Petrache we obtained a version of calibrations for this case.

28.7.17 Raphael Zentner (Regensburg)
Irreducible SL(2,C)-representations of homology 3-spheres

Abstract: We prove that the splicing of any two non-trivial knots in the 3-sphere admits an irreducible SU(2)-representation of its fundamental group. Using a result of Boileau, Rubinstein and Wang, it follows that the fundamental group of any integer homology 3-sphere different from the 3-sphere admits irreducible representations of its fundamental group in SL(2,C). Our result uses instanton gauge theory and in particular holonomy perturbations of the flatness equation in an essential way.

H. Geiges, 5.4.02


21.4.17	BHKM Seminar in Köln
19.5.17	Joan Licata (ANU Canberra) Talk for graduate students and postdocs in the framework of the Graduate School, 10:00-11:30
2.6.17	BHKM Seminar in Heidelberg
16.6.17	Gerard Freixas i Montplet (Paris) On a geometric interpretation for the Cappell-Miller torsion Abstract: Cappell and Miller introduced a complex-valued version of the Ray-Singer analytic torsion, for holomorphic vector bundles endowed with flat connections. An open question is whether this invariant satisfies analogous properties as the Ray-Singer torsion, as in work of Bismut-Gillet-Soulé. In this talk I will recall the definition of this torsion invariant and explain its geometric content in the rank 1 case and over Riemann surfaces.
23.6.17	BHKM Seminar in Bochum
7.7.17	Joint Seminar on Complex Algebraic Geometry and Complex Analysis in Köln
14.7.17	Roger Züst (Bern) Calibrations and calibrations modulo 2 Abstract: To show that a given oriented submanifold has minimal volume among all submanifolds with a fixed boundary or homology class is hard, in general. The tool most often used for testing such minimality are calibrations. These are closed differential forms with pointwise unit norm. The 1-dimensional problem asks for the length minimal filling of a given, say finite, set of sources and drains. The Kantorovich duality of optimal mass transport guarantees the existence of calibrations in this situation. Similar to the oriented minimal filling problem one may be interested in the unoriented one, where coefficients modulo 2 are considered. In dimension one this asks for a minimal matching among an even number of points. In a joint work with Mircea Petrache we obtained a version of calibrations for this case.
28.7.17	Raphael Zentner (Regensburg) Irreducible SL(2,C)-representations of homology 3-spheres Abstract: We prove that the splicing of any two non-trivial knots in the 3-sphere admits an irreducible SU(2)-representation of its fundamental group. Using a result of Boileau, Rubinstein and Wang, it follows that the fundamental group of any integer homology 3-sphere different from the 3-sphere admits irreducible representations of its fundamental group in SL(2,C). Our result uses instanton gauge theory and in particular holonomy perturbations of the flatness equation in an essential way.