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Autumn Semester 2019

Date / Time Speaker Title Location
25 September 2019
15:45-16:45 		Allison Miller
Rice University, Houston
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Geometry Seminar

Title Satellite operations and knot genera
Speaker, Affiliation Allison Miller, Rice University, Houston
Date, Time 25 September 2019, 15:45-16:45
Location 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 October 2019
15:45-16:45 		Dr. Matthias Nagel
ETH Zurich, Switzerland
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Geometry Seminar

Title Slice disks in stabilized 4-balls
Speaker, Affiliation Dr. Matthias Nagel, ETH Zurich, Switzerland
Date, Time 2 October 2019, 15:45-16:45
Location 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 October 2019
15:45-16:45 		Matthieu Dussaule
Université de Nantes
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Geometry Seminar

Title The Guivarc'h inequality in relatively hyperbolic groups
Speaker, Affiliation Matthieu Dussaule, Université de Nantes
Date, Time 9 October 2019, 15:45-16:45
Location 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 October 2019
15:45-16:45 		Doron Puder
Tel Aviv University
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Geometry Seminar

Title Matrix Group Integrals, Surfaces, and Mapping Class Groups
Speaker, Affiliation Doron Puder, Tel Aviv University
Date, Time 16 October 2019, 15:45-16:45
Location 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
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Geometry Seminar

Title Volumes of random 3-manifolds
Speaker, Affiliation Gabriele Viaggi, Universität Bonn
Date, Time 13 November 2019, 15:45-16:45
Location 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
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Geometry Seminar

Title Approaching quasi-isometry classification of Lie groups using isometries
Speaker, Affiliation Ville Kivioja, University of Jyväskylä
Date, Time 20 November 2019, 15:45-16:45
Location 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 December 2019
15:45-16:45 		Alexander Lytchak
Universität Köln
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Geometry Seminar

Title Topological stability in upper curvature bounds
Speaker, Affiliation Alexander Lytchak, Universität Köln
Date, Time 11 December 2019, 15:45-16:45
Location 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 December 2019
15:45-16:45 		Stephan Stadler
LMU München
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Geometry Seminar

Title Intermediate Quasiflats
Speaker, Affiliation Stephan Stadler, LMU München
Date, Time 18 December 2019, 15:45-16:45
Location 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

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

Archive: AS 24 SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 AS 20 SS 20 AS 19 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11 SS 11 AS 10 SS 10 AS 09 SS 09

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