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Spring Semester 2018

Date / Time Speaker Title Location
21 February 2018
15:45-16:45 		Arielle Leitner
Technion – Israel Institute of Technology
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Geometry Seminar

Title Generalized Cusps on Convex Projective Manifolds
Speaker, Affiliation Arielle Leitner, Technion – Israel Institute of Technology
Date, Time 21 February 2018, 15:45-16:45
Location HG G 43
Abstract Convex projective manifolds are a generalization of hyperbolic manifolds. They are more flexible, and some occur as deformations of hyperbolic manifolds. Generalized cusps occur naturally as ends of properly convex projective manifolds. We classify generalized cusps, discuss their geometry, and ways they can deform. Joint work with Sam Ballas and Daryl Cooper.
Generalized Cusps on Convex Projective Manifoldsread_more
HG G 43
28 February 2018
15:45-16:45 		Dr. Iuliya Beloshapka
ETH Zurich, Switzerland
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Geometry Seminar

Title Irreducible representations of finitely generated nilpotent groups: Parshin's conjecture
Speaker, Affiliation Dr. Iuliya Beloshapka, ETH Zurich, Switzerland
Date, Time 28 February 2018, 15:45-16:45
Location HG G 43
Abstract At ICM 2010 Parshin conjectured that irreducible complex representations of finitely generated nilpotent groups are monomial if and only if they have finite weight. This was previously known to be true for finite nilpotent groups and for unitary irreducible representations of connected nilpotent Lie groups (A.A. Kirillov and J. Dixmier). We prove Parshin's conjecture in full generality. We will also discuss how to approach moduli space problem for such representations since the question is related to higher-dimensional adeles, and it potentially has interesting geometry. For nilpotency classes 2 and 3 we obtained a full description.
Irreducible representations of finitely generated nilpotent groups: Parshin's conjectureread_more
HG G 43
7 March 2018
15:45-16:45 		Boris Hasselblatt
Tufts University
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Geometry Seminar

Title Contact Anosov flows on 3-manifolds
Speaker, Affiliation Boris Hasselblatt, Tufts University
Date, Time 7 March 2018, 15:45-16:45
Location HG G 43
Abstract Foulon surgery produces contact Anosov flows of the same topological type as those of Handel and Thurston and hence different from any algebraic system. On one hand, their larger orbit growth implies rapid orbit growth of any Reeb flow for the same contact structure, and on the other hand recent work by Bishop, Hughes, Vinhage and Yang promises a quantification of the gap between the Liouville and topological entropies.
Contact Anosov flows on 3-manifoldsread_more
HG G 43
14 March 2018
15:45-16:45 		Nicolas Monod
EPF Lausanne
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Geometry Seminar

Title Littlewood and large forests
Speaker, Affiliation Nicolas Monod, EPF Lausanne
Date, Time 14 March 2018, 15:45-16:45
Location HG G 43
Abstract I will review the Dixmier Problem, open since 1950, which asks for a condition ensuring that all representations of a given group are unitarisable. This can be related to analytic conditions and to geometric constructions such as random forests.
I will also present recent work with Gerasimova, Gruber and Thom, where the Dixmier Problem is related to the asymptotic properties of isoperimetric constants.
Littlewood and large forestsread_more
HG G 43
21 March 2018
15:45-16:45 		Ilya Khayutin
IAS, Princeton
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Geometry Seminar

Title Joint Equidistribution of Closed Geodesics and CM Points
Speaker, Affiliation Ilya Khayutin, IAS, Princeton
Date, Time 21 March 2018, 15:45-16:45
Location HG G 43
Abstract A packet of closed geodesics on a complex modular curve is a finite collection of closed geodesics obtained as an orbit of a Picard group of an order in a real quadratic field. A celebrated theorem of Duke states that packets of closed geodesics equidistribute in the limit when the absolute value of the discriminant goes to infinity. The same holds for Picard/Galois orbits of CM points. The equidistribution of Picard orbits of closed geodesics or CM points in products of modular curves was conjectured by Michel and Venkatesh and as part of the equidistribution strengthening of the André-Oort conjecture. After introducing these objectsI will discuss the proof of a recent theorem making progress towards the conjecture.Currently, this problem does not seem to be amenable to methods of automorphic forms even conditionally on GRH. Nevertheless, assuming a splitting condition at two primes, the joining rigidity theorem of Einsiedler and Lindenstrauss applies. As a result the obstacle to proving equidistribution is the potential concentration of mass on intermediate algebraic measures. I will present a method to discard this possibility using a geometric expansion of a relative trace and a sieve argument.
Joint Equidistribution of Closed Geodesics and CM Pointsread_more
HG G 43
28 March 2018
15:45-16:45 		Thomas Mettler
Goethe-Universität Frankfurt
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Geometry Seminar

Title Convex projective surfaces, holomorphic curves and hyperbolic metrics
Speaker, Affiliation Thomas Mettler, Goethe-Universität Frankfurt
Date, Time 28 March 2018, 15:45-16:45
Location HG G 43
Abstract I will explain a novel characterisation of hyperbolic Riemann surfaces among properly convex projective surfaces in terms of the existence of a certain holomorphic curve. Joint work with G. Paternain.
Convex projective surfaces, holomorphic curves and hyperbolic metricsread_more
HG G 43
11 April 2018
15:45-16:45 		Alexander Kolpakov
Université de Neuchâtel
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Geometry Seminar

Title Combinatorics of subgroup counting in free products of cyclic groups, and other stories
Speaker, Affiliation Alexander Kolpakov, Université de Neuchâtel
Date, Time 11 April 2018, 15:45-16:45
Location HG G 43
Abstract We shall derive a generating series for the number of free subgroups of finite index in certain free products of cyclic groups. We shall also give a generating series for the number of their conjugacy classes. This computation turns out the same as counting the number of orientable cellular complexes of dimension 2 and 3 (or even higher), as well as their isomorphism classes. Our solution rests on a classical theory by Jones and Singerman, later developed by Lienhardt and co-authors, and on the theory of species by Joyal, Flajolet and Sedgewick. There is also a number of curious facts related to the mentioned functions. The talk will focus on the interplay between algebra, geometry and combinatorics.This is joint work with Laura Ciobanu (Heriot-Watt University, UK).
Combinatorics of subgroup counting in free products of cyclic groups, and other storiesread_more
HG G 43
25 April 2018
15:45-16:45 		Elia Fioravanti
University of Oxford
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Geometry Seminar

Title Superrigidity of actions on finite rank median spaces
Speaker, Affiliation Elia Fioravanti, University of Oxford
Date, Time 25 April 2018, 15:45-16:45
Location HG G 43
Abstract Finite rank median spaces simultaneously generalise real trees and finite dimensional CAT(0) cube complexes. Requiring a group to act on a finite rank medianspace is in general much more restrictive than only asking for an action on a general median space. This is particularly evident for certain irreducible lattices in productsof rank-one simple Lie groups: they admit proper cocompact actions on infinite rank median spaces, but any action on a (connected) finite rank median space must fix a point. Our proof of the latter fact is based on a generalisation of a superrigidity result of Chatterji-Fernos-Iozzi. We will sketch the necessary techniques, focussing on differencesbetween cube complexes and general median spaces. We will also discuss applications of the fixed-point property to a large family of coarse median groups, which includesall hierarchically hyperbolic groups.
Superrigidity of actions on finite rank median spacesread_more
HG G 43
16 May 2018
15:45-16:45 		Todd Fisher
Brigham Young University
Details

Geometry Seminar

Title Entropy for C1 diffeomorphisms
Speaker, Affiliation Todd Fisher, Brigham Young University
Date, Time 16 May 2018, 15:45-16:45
Location HG G 43
Abstract We will begin with classical properties of entropy for dynamical systems, and review a construction due to Newhouse that shows on surfaces one creates horseshoes from hyperbolic periodic orbits with large period through local perturbations. Adapting these techniques to higher dimensions our main theorem shows that, when one works in the C1 topology, the entropy of such horseshoes can be made arbitrarily close to an upper bound derived from Ruelle's inequality, i.e., the sum of the positive Lyapunov exponents (or the same for the inverse diffeomorphism, whichever is smaller). This optimal entropy creation yields a number of consequences for C1-generic diffeomorphisms. For instance, in the conservative settings, we find formulas for the topological entropy, deduce that the topological entropy is continuous but not locally constant at the generic diffeomorphism, and we prove that these generic diffeomorphisms have no measure of maximum entropy.
Entropy for C1 diffeomorphismsread_more
HG G 43
30 May 2018
15:45-16:45 		Nicolaus Heuer
University of Oxford
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Geometry Seminar

Title RAAGs and Stable Commutator Length
Speaker, Affiliation Nicolaus Heuer, University of Oxford
Date, Time 30 May 2018, 15:45-16:45
Location HG G 43
Abstract Stable commutator length (scl) is a well established invariant of group elements g (write scl(g)) and has both geometric and algebraic meaning. Many classes of "non-positively curved" groups have a gap in stable commutator length: This is, for every non-trivial element g, scl(g) > C for some C > 0. This gap may be thought of as an algebraic injectivity radius and may be found in hyperbolic groups, Baumslag-solitair groups, free products, Mapping class groups, etc. However, the exact size of this gap usually unknown, which is due to a lack of a good source of “quasimorphisms”. In this talk I will construct a new source of quasimorphisms which yield optimal gaps and show that for Right-Angled Artin Groups and their subgroups the gap of stable commutator length is exactly 1/2. I will also show this gap for certain amalgamated free products.
RAAGs and Stable Commutator Lengthread_more
HG G 43
6 June 2018
15:45-16:45
Details

Geometry Seminar

Title RAAGs and Stable Commutator Length
Speaker, Affiliation
Date, Time 6 June 2018, 15:45-16:45
Location HG G 43
RAAGs and Stable Commutator Length
HG G 43

Organisers: Marc Burger, Manfred Einsiedler, 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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