Departement Mathematik

Geometry seminar

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Herbstsemester 2019

Datum / Zeit Referent:in Titel Ort
25. September 2019
15:45-16:45 		Allison Miller
Rice University, Houston
Details

Geometry Seminar

Titel Satellite operations and knot genera
Referent:in, Affiliation Allison Miller, Rice University, Houston
Datum, Zeit 25. September 2019, 15:45-16:45
Ort HG G 43
Abstract The classical 3-genus of knots behaves predictably under the satellite operation: a formula of Schubert states that a winding number w pattern P has g3(P(K))=g3(P)+|w|g3(K), for an appropriately defined g3(P) bounded below by g3(P(U)). In this talk, I’ll discuss the extent to which analogous formulae, particularly the intuition that the genus of P(K) should be roughly |w| times the genus of K, hold in the context of the slice genus. In the smooth setting the winding number continues to play a pivotal role, but in new joint work with Peter Feller and Juanita Pinz{‘o}n-Caicedo we give surprising evidence that in the topological category the winding number of a pattern is almost irrelevant in its effect on the 4-genus!
Satellite operations and knot generaread_more
HG G 43
2. Oktober 2019
15:45-16:45 		Dr. Matthias Nagel
ETH Zurich, Switzerland
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Geometry Seminar

Titel Slice disks in stabilized 4-balls
Referent:in, Affiliation Dr. Matthias Nagel, ETH Zurich, Switzerland
Datum, Zeit 2. Oktober 2019, 15:45-16:45
Ort HG G 43
Abstract We consider knots K that bound (nullhomotopic) slice disks in a stabilized 4-ball, that is in D^4 # nS^2×S^2. We explain how to construct examples of such disks, and discuss bounds on the minimal number n of stabilizations needed. Then we compare this minimal number to the 4-genus of K.
Slice disks in stabilized 4-ballsread_more
HG G 43
9. Oktober 2019
15:45-16:45 		Matthieu Dussaule
Université de Nantes
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Geometry Seminar

Titel The Guivarc'h inequality in relatively hyperbolic groups
Referent:in, Affiliation Matthieu Dussaule, Université de Nantes
Datum, Zeit 9. Oktober 2019, 15:45-16:45
Ort HG G 43
Abstract Consider a random walk on a finitely generated group. The Guivarc'h inequality states that $h
The Guivarc'h inequality in relatively hyperbolic groupsread_more
HG G 43
16. Oktober 2019
15:45-16:45 		Doron Puder
Tel Aviv University
Details

Geometry Seminar

Titel Matrix Group Integrals, Surfaces, and Mapping Class Groups
Referent:in, Affiliation Doron Puder, Tel Aviv University
Datum, Zeit 16. Oktober 2019, 15:45-16:45
Ort HG G 43
Abstract Since the 1970's, Physicists and Mathematicians who study random matrices in the standard models of GUE or GOE, are aware of intriguing connections between integrals of such random matrices and enumeration of graphs on surfaces. We establish a new aspect of this theory: for random matrices sampled from classical matrix groups such as U(n) or O(n). The group structure of these matrices allows us to go further and find surprising algebraic quantities hidden in the values of these integrals. Based on joint work with Michael Magee (Durham).
Matrix Group Integrals, Surfaces, and Mapping Class Groupsread_more
HG G 43
13. November 2019
15:45-16:45 		Gabriele Viaggi
Universität Bonn
Details

Geometry Seminar

Titel Volumes of random 3-manifolds
Referent:in, Affiliation Gabriele Viaggi, Universität Bonn
Datum, Zeit 13. November 2019, 15:45-16:45
Ort HG G 43
Abstract We discuss a law of large numbers for the volumes of random 3-manifolds. Such objects, introduced by Dunfield and Thurston, come from the observation that certain families of 3-manifolds, such as Heegaard splittings of a fixed genus, are naturally parametrized by the elements of the mapping class group of a closed orientable surface. We can sample a random Heegaard splitting simply by picking at random the gluing map that defines it. In order to do this systematically, we make a random walk on the mapping class group of the Heegaard surface. We will see that the (simplicial) volumes of the associated 3-manifolds grow linearly in the step of the walk (with an exact asymptotic).
Volumes of random 3-manifoldsread_more
HG G 43
20. November 2019
15:45-16:45 		Ville Kivioja
University of Jyväskylä
Details

Geometry Seminar

Titel Approaching quasi-isometry classification of Lie groups using isometries
Referent:in, Affiliation Ville Kivioja, University of Jyväskylä
Datum, Zeit 20. November 2019, 15:45-16:45
Ort HG G 43
Abstract The talk is motivated by searching strategies to attack the conjecture stating that if two simply connected nilpotent Lie groups are quasi-isometric, they must be isomorphic. This conjecture has a related cousin for Heintze groups, and these conjectures also give rise to questions of the following type: Given two Lie groups, when does it actually happen that one can find left-invariant distances on them such that they become isometric as metric spaces. I will give some answers to these questions, concentrating on groups of polynomial growth on the onehand, and on Heintze groups on the other. Finally I will remark how Lie groups with left-invariant distances appear naturally in metric geometry as model spaces for homogeneous metric spaces, and sometimes as their visual boundaries.
Approaching quasi-isometry classification of Lie groups using isometriesread_more
HG G 43
11. Dezember 2019
15:45-16:45 		Alexander Lytchak
Universität Köln
Details

Geometry Seminar

Titel Topological stability in upper curvature bounds
Referent:in, Affiliation Alexander Lytchak, Universität Köln
Datum, Zeit 11. Dezember 2019, 15:45-16:45
Ort HG G 43
Abstract In the talk I would like to discuss an analog of Pereleman's stability theorem in upper curvature bounds and related results about the topological regularity of spaces with upper curvature bounds and extendable geodesics. The talk is based on joint works with Koichi Nagano.
Topological stability in upper curvature boundsread_more
HG G 43
18. Dezember 2019
15:45-16:45 		Stephan Stadler
LMU München
Details

Geometry Seminar

Titel Intermediate Quasiflats
Referent:in, Affiliation Stephan Stadler, LMU München
Datum, Zeit 18. Dezember 2019, 15:45-16:45
Ort HG G 43
Abstract In the early 80s, Gromov initiated a far reaching program to study groups as geometric objects. He asks to identify an infinite group up to a natural geometric equivalence. In my talk I will concentrate on Gromov's program in the realm of nonpositive curvature and highlight the role of quasiflats, i.e. spaces/groups which are equivalent to  Euclidean spaces. I will present new structural results on quasiflats, explain their relevance to the classification program and provide applications. Part of the talk is based on joint work with Jingyin Huang and Bruce Kleiner.
Intermediate Quasiflatsread_more
HG G 43

Organisatoren:innen: Marc Burger, Manfred Einsiedler, Peter Feller, Alessandra Iozzi, Urs Lang, Viktor Schröder, Alessandro Sisto

Archiv: FS 24 HS 23 FS 23 HS 22 FS 22 HS 21 HS 20 FS 20 HS 19 FS 19 HS 18 FS 18 HS 17 FS 17 HS 16 FS 16 HS 15 FS 15 HS 14 FS 14 HS 13 FS 13 HS 12 FS 12 HS 11 FS 11 HS 10 FS 10 HS 09 FS 09

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