Non-positive curvature group actions and cohomology

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Programme theme

The concept of curvature describes a fundamental spatial attribute and it has found a place at the core of science since its inception.

This programme is about aspects of non-positive curvature as they occur in various research areas of contemporary mathematics, such as the geometry of manifolds, including those arising from Lie group theory; synthetic geometry (e.g. CAT(0) geometry) as used notably in modern group theory; coarse geometry, a fundamental tool of contemporary topology; non-commutative geometry; and algebra.

By combining and comparing the aspects that non-positive curvature displays in various contexts, the programme aims to acquire new insight and find meaningful new directions to explore. Among the tools used to uncover new aspects of non-positive curvature one numbers cohomology, originally a tool from algebra and topology and now a research field in itself, with countless applications throughout mathematics; perturbation stability -- investigating when small "errors" lead to completely new structures, or when, on the contrary, structures are robust when perturbed;fixed point and proper actions - a topic at the interface of analysis and algebra - with surprising ramifications in many other areas; and CAT(0) and coarse geometry, where CAT(0) cubical and large-scale techniques come into play to solve problems from topology and algebra. All these fields are on the cutting edge of current research, and have fruitful connections to other areas, e.g. theoretical computer science.

The focus of this programme is on breakthrough results and techniques stemming from this research. The general structure consists of activities held on a regular basis (e.g. weekly research seminars, series of lectures, etc.), enhanced by weeks of more intensive lecturing focusing on a topic, and workshops intended to cathalyse interchange and research progress in a specific field. These activities rely on the interaction between long term visitors, UK researchers, and the rapidly developing body of young experts working in the area.

Click here to download the programme's final scientific report

NPC programme: interview w/ organisers Alessandra Iozzi, Cornelia Drutu Badea, Goulnara Arzhantseva

Preprints

Title	Year	Programme
Constraint metric approximations and equations in groups Authors: Liviu Paunescu, Goulnara Arzhantseva Download PDF	2016	NPC
Rips construction without unique product Authors: Goulnara Arzhantseva, Markus Steenbock Download PDF	2016	NPC
Characterizatoins of morse quasi-geodesics via superlinear divergence and sublinear contraction Authors: Christopher Cashen, Dominik Gruber, David Hume, Goulnara Arzhantseva Download PDF	2016	NPC
Negative curvature in graphical small cancellation groups Authors: David Hume, Dominik Gruber, Christopher Cashen, Goulnara Arzhantseva Download PDF	2016	NPC
A rank one CAT(0) group is determined by its Morse boundary Authors: Devin Murray, Ruth Charney Download PDF	2016	NPC
On continued fraction expansions of quadratic irrationals in positive characteristic Authors: Frédéric Paulin, Uri Shapira Download PDF	2016	NPC
Unique continuation principles and their absence for Schrödinger eigenfunctions on combinatorial and quantum graphs and in continuum space Authors: Mr Matthias Täufer (Technische Universität Dortmund), Ivan Veselic, Norbert Peyerimhoff Download PDF	2016	NPC

Workshops

NPCW01

Seminars

Wednesday 18th January 2017
14:00 to 16:00	Pierre Pansu Université Paris Saclay 1. Lp-cohomology	Room 2

Thursday 19th January 2017
10:00 to 12:00	Andrzej Zuk Université Paris 7 - Denis-Diderot Random walks on random symmetric groups.	Room 2

Wednesday 25th January 2017
14:00 to 16:00	Pierre Pansu Université Paris Saclay 2. Lp-cohomology	Room 2

Thursday 26th January 2017
10:00 to 12:00	Ian Leary University of Southampton Generalizing Bestvina-Brady groups using branched covers	Room 2

Wednesday 1st February 2017
14:00 to 17:30	Pierre Pansu Université Paris Saclay 3. Lp-cohomology	Room 2

Thursday 2nd February 2017
10:00 to 12:00	Eric Swenson Brigham Young University On infinite torsion subgroups of CAT(0) groups	Room 2

Thursday 9th February 2017
10:00 to 12:00	Alessandro Sisto ETH Zürich Quasi-flats in hierarchically hyperbolic spaces	Room 2

Thursday 16th February 2017
10:00 to 12:00	Rémi Coulon Université de Rennes 1; CNRS (Centre national de la recherche scientifique) Monster groups acting on CAT(0) spaces	Room 2

Wednesday 22nd February 2017
14:00 to 16:00	Pierre Pansu Université Paris Saclay 4. Lp-cohomology	Room 2

Thursday 23rd February 2017
10:00 to 12:00	Anastasia Khukhro Université de Neuchâtel Geometry of finite quotients of groups.	Room 2

Wednesday 1st March 2017
14:00 to 16:00	Emmanuel Breuillard Universität Münster Approximate groups: an introduction	Room 2

Thursday 2nd March 2017
10:00 to 12:00	Romain Tessera Université Paris Saclay A Banachic generalization of Shalom's property H_FD.	Room 2

Tuesday 7th March 2017
10:00 to 12:00	Emmanuel Breuillard Universität Münster Approximate groups: basic definitions, structure theorem and geometric consequences	Room 2

Wednesday 8th March 2017
14:00 to 16:00	Pierre Pansu Université Paris Saclay 5. Lp-cohomology	Room 2

Thursday 9th March 2017
10:00 to 11:00	Ursula Hamenstadt University of Bonn Incompressible surfaces in closed locally symmetric manifolds	Room 2
11:00 to 12:00	Koji Fujiwara Kyoto University Computing Kazhdan constants by computer.	Room 2

Tuesday 14th March 2017
10:00 to 12:00	Emmanuel Breuillard Universität Münster Approximate groups: structure theorem for special classes of groups	Room 2

Wednesday 15th March 2017
14:00 to 16:00	Pierre Pansu Université Paris Saclay 6. Lp-cohomology	Room 2

Thursday 16th March 2017
10:00 to 11:00	Vladimir Markovic University of Warwick Caratheodory's metrics on Teichmuller spaces	Room 2
11:00 to 12:00	Narutaka Ozawa Kyoto University Finite-dimensional representations constructed from random walks	Room 2

Wednesday 5th April 2017
14:00 to 15:30	Pierre-Emmanuel Caprace Université Catholique de Louvain Exotic lattices and simple locally compact groups	Room 2

Thursday 6th April 2017
10:00 to 11:00	John Mackay University of Bristol The Poincaré profile of a graph or group	Room 2
11:00 to 12:00	Shahar Mozes Hebrew University of Jerusalem Topological finite generation of certain compact open subgroups of tree automorphisms.	Room 2

Friday 7th April 2017
16:00 to 17:00	Richard Schwartz Brown University Rothschild Lecture: Thomson's 5 point problem	Room 1

Tuesday 11th April 2017
10:00 to 12:00	Emmanuel Breuillard Universität Münster Approximate groups: Hrushovski's Lie model theorem	Room 2

Wednesday 12th April 2017
14:00 to 15:30	Pierre-Emmanuel Caprace Université Catholique de Louvain Exotic lattices and simple locally compact groups	Room 2

Thursday 13th April 2017
10:00 to 11:00	Indira Chatterji Université de Nice Median spaces and spaces with thin triangles.	Room 2
11:00 to 12:00	Karen Vogtmann University of Warwick RAAG subgroups of RAAGs	Room 2

Tuesday 18th April 2017
10:00 to 11:30	Pierre-Emmanuel Caprace Université Catholique de Louvain Exotic lattices and simple locally compact groups	Room 2

Wednesday 19th April 2017
10:00 to 11:00	Mikolaj Fraczyk Université Paris Saclay Benjamini-Schramm convergence of arithmetic orbifolds.	Room 2
14:00 to 16:00	Emmanuel Breuillard Universität Münster Hilbert's 5th problem and the Gleason-Yamabe theorem	Room 2

Thursday 20th April 2017
10:00 to 11:00	Andreas Aaserud Cardiff University Property (T) and approximate conjugacy of actions	Room 2
11:00 to 12:00	Brian Bowditch University of Warwick Bounding genera of singular surfaces	Room 2

Tuesday 25th April 2017
10:00 to 11:00	Frédéric Paulin Université Paris Saclay On diagonal group actions, trees and continued fractions in positive characteristic	Room 2
11:00 to 12:00	John Parker University of Durham Non-arithmetic lattices	Room 2

Wednesday 26th April 2017
14:00 to 16:00	Emmanuel Breuillard Universität Münster Approximate groups: nilprogressions and the structure theorem.	Room 2

Thursday 27th April 2017
09:30 to 11:30	Pierre-Emmanuel Caprace Université Catholique de Louvain Exotic lattices and simple locally compact groups	Room 2

Tuesday 2nd May 2017
10:00 to 11:00	Brita Nucinkis Royal Holloway, University of London Finiteness conditions for classifying spaces for the family of virtually cyclic subgroups.	Room 2
11:00 to 12:00	Adrien Le Boudec Université Catholique de Louvain Uniformly recurrent subgroups and lattice embeddings	Room 2

Wednesday 3rd May 2017
14:00 to 16:00	Richard Schwartz Brown University Pappus's Theorem and the Modular Group	Room 2

Thursday 4th May 2017
09:30 to 11:30	Pierre-Emmanuel Caprace Université Catholique de Louvain Exotic lattices and simple locally compact groups	Room 2

Friday 5th May 2017
15:45 to 17:15	Pierre-Emmanuel Caprace Université Catholique de Louvain Exotic lattices and simple locally compact groups	Room 2

Tuesday 16th May 2017
10:00 to 11:00	Michael Davis Ohio State University The action dimensions of some discrete groups	Room 2
11:00 to 12:00	Yves de Cornulier CNRS (Centre national de la recherche scientifique); Université Paris Saclay Commensurating actions of groups of birational transformations	Room 2
14:00 to 16:00	Viktor Schroeder ETH Zürich Moebius Geometry of Boundaries''	Discussion Room

Wednesday 17th May 2017
14:00 to 16:00	Richard Schwartz Brown University Iterated barycentric subdivision and steerable semigroups of SL_n(R)	Room 2

Friday 19th May 2017
15:45 to 17:15	Richard Schwartz Brown University Thurston's Shapes of Polyhedra	Room 2

Tuesday 23rd May 2017
10:00 to 11:00	Erik Guentner University of Hawaii Affine actions, cohomology and hyperbolicity	Room 2
11:00 to 12:00	Nicolas Matte Bon ETH Zürich Uniformly recurrent subgroups and rigidity of non-free minimal actions	Room 2
14:00 to 16:00	Viktor Schroeder ETH Zürich Moebius Geometry of Boundaries''	Discussion Room

Wednesday 24th May 2017
14:00 to 16:00	Richard Schwartz Brown University The pentagram map and discrete integrable systems	Room 2

Friday 26th May 2017
10:00 to 12:00	Richard Schwartz Brown University PETs, pseudogroup actions, and renormalisation	Room 2

Tuesday 30th May 2017
10:00 to 11:00	Alina Vdovina Newcastle University Buildings, surfaces and quaternions	Room 2
11:00 to 12:00	Ruth Charney Brandeis University Are geodesic metric spaces determined by their Morse boundaries?	Room 2
14:00 to 16:00	Viktor Schroeder ETH Zürich Moebius Geometry of Boundaries''	Room 1

Tuesday 13th June 2017
11:00 to 12:00	David Fisher Indiana University Strong property (T), subexponential growth of derivatives and invariant metrics	Room 2

Wednesday 14th June 2017
13:00 to 14:00	Vaughan Jones Vanderbilt University; University of California, Berkeley Knots and links from the Thompson groups	Room 1

Non-positive curvature group actions and cohomology

Organisers

Goulnara Arzhantseva University of Vienna
Cornelia Drutu Badea University of Oxford; Université des Sciences et Technologies de Lille
Alessandra Iozzi ETH Zürich
Nicolas Monod

Participants

Stergios Antonakoudis University of Cambridge
Mohammed Bardestani Westfalische Wilhelms-Universitat Munster
Jason Behrstock City University of New York
Arindam Biswas Université Paris Saclay
Brian Bowditch University of Warwick
Marc Burger ETH Zürich
Jack Button University of Cambridge
Danny Calegari University of Chicago
Pierre-Emmanuel Caprace Université Catholique de Louvain
Christopher Cashen Universität Wien
Ruth Charney Brandeis University
Indira Chatterji Université de Nice
Maurice Chiodo University of Cambridge
Rémi Coulon Université de Rennes 1; CNRS (Centre national de la recherche scientifique)
Francois Dahmani Université Joseph Fourier Grenoble
Michael Davis Ohio State University
Yves de Cornulier CNRS (Centre national de la recherche scientifique); Université Paris Saclay
Carlos Alberto De la Cruz Mengual ETH Zürich
Cornelia Drutu Badea University of Oxford; Université des Sciences et Technologies de Lille
Elia Fioravanti University of Oxford
David Fisher Indiana University
Koji Fujiwara Kyoto University
Bill Goldman University of Maryland, College Park
Ben Green University of Oxford
Dominik Gruber ETH Zürich
Erik Guentner University of Hawaii
Mark Hagen University of Cambridge
Ursula Hamenstaedt University of Bonn
Nicolaus Heuer University of Oxford
Alessandra Iozzi ETH Zürich
Lison Jacoboni Université Paris Saclay
Fanny Kassel CNRS (Centre national de la recherche scientifique)
Yannick Krifka ETH Zürich
Peter Kropholler University of Southampton
Adrien Le Boudec Université Catholique de Louvain
Ian Leary University of Southampton
Waltraud Lederle ETH Zürich
Alex Lubotzky Hebrew University of Jerusalem
John Mackay University of Bristol
Vladimir Markovic CALTECH (California Institute of Technology)
Timothée Marquis Université Catholique de Louvain
Alexandre Martin Universität Wien
Nicolas Matte Bon ETH Zürich
Masato Mimura Tohoku University; EPFL - Ecole Polytechnique Fédérale de Lausanne
Shahar Mozes Hebrew University of Jerusalem
Brita Nucinkis Royal Holloway, University of London
Tomasz Odrzygozdz Polish Academy of Sciences
Narutaka Ozawa Kyoto University
Gabriel Pallier Université Paris Saclay
Pierre Pansu Université Paris Saclay
John Parker University of Durham
Frédéric Paulin Université Paris Saclay
Norbert Peyerimhoff Durham University
Maria Beatrice Pozzetti University of Warwick
Pierre Py None / Other; Universidad Nacional Autonoma de Mexico (UNAM)
Nicolas Radu Université Catholique de Louvain
Viktor Schroeder ETH Zürich
Richard Schwartz Brown University
Cagri Sert Université Paris Saclay
Alessandro Sisto ETH Zürich
Markus Steenbock Universität Wien
Thierry Stulemeijer Université Catholique de Louvain
Eric Swenson Brigham Young University
Romain Tessera Université Paris Saclay
Stephan Tornier ETH Zürich; University of Newcastle, Australia
Alain Valette Université de Neuchâtel
Alina Vdovina Newcastle University
Federico Vigolo University of Oxford
Karen Vogtmann University of Warwick; Cornell University
Henry Wilton University of Cambridge
Andrzej Zuk Université Paris 7 - Denis-Diderot

Show All

Non-positive curvature group actions and cohomology

Programme theme

NPC programme: interview w/ organisers Alessandra Iozzi, Cornelia Drutu Badea, Goulnara Arzhantseva

Preprints

Constraint metric approximations and equations in groups

Rips construction without unique product

Characterizatoins of morse quasi-geodesics via superlinear divergence and sublinear contraction

Negative curvature in graphical small cancellation groups

A rank one CAT(0) group is determined by its Morse boundary

On continued fraction expansions of quadratic irrationals in positive characteristic

Unique continuation principles and their absence for Schrödinger eigenfunctions on combinatorial and quantum graphs and in continuum space

Workshops

Non-positive curvature in action

Young geometric group theory meeting VI

Asymptotic decomposition methods in geometry, dynamics and operator algebras

Approximation, deformation, quasification

Group actions and cohomology in non-positive curvature

Seminars

Organisers

Participants

Supported By

Non-positive curvature group actions and cohomology

Programme theme

NPC programme: interview w/ organisers Alessandra Iozzi, Cornelia Drutu Badea, Goulnara Arzhantseva

Preprints

Constraint metric approximations and equations in groups

Rips construction without unique product

Characterizatoins of morse quasi-geodesics via superlinear divergence and sublinear contraction

Negative curvature in graphical small cancellation groups

A rank one CAT(0) group is determined by its Morse boundary

On continued fraction expansions of quadratic irrationals in positive characteristic

Unique continuation principles and their absence for Schrödinger eigenfunctions on combinatorial and quantum graphs and in continuum space

Workshops

Non-positive curvature in action

Young geometric group theory meeting VI

Asymptotic decomposition methods in geometry, dynamics and operator algebras

Approximation, deformation, quasification

Group actions and cohomology in non-positive curvature

Seminars

Organisers

Participants

Supported By

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