In mathematics, the surface subgroup conjecture of Friedhelm Waldhausen states that the fundamental group of every closed, irreducible 3-manifold with infinite fundamental group has a surface subgroup. By "surface subgroup" we mean the fundamental group of a closed surface not the 2-sphere. This problem is listed as Problem 3.75 in Robion Kirby's problem list. Assuming the geometrization conjecture, the only open case was that of closed hyperbolic 3-manifolds. A proof of this case was announced in the summer of 2009 by Jeremy Kahn and Vladimir Markovic and outlined in a talk August 4, 2009 at the FRG (Focused Research Group) Conference hosted by the University of Utah. A preprint appeared in the arxiv.org server in October 2009. Their paper was published in the Annals of Mathematics in 2012. In June 2012, Kahn and Markovic were given the Clay Research Awards by the Clay Mathematics Institute at a ceremony in Oxford. (Wikipedia).
Martin Bridson - Subgroups of direct products of surface groups
After reviewing what is known about subgroups of direct products of surface groups and their significance in the story of which groups are Kähler, I shall describe a new construction that provides infinite families of finitely presented subgroups. These subgroups have varying higher-finite
From playlist Geometry in non-positive curvature and Kähler groups
Group Actions and Group Representations in Low Dimensional Topology
Speakers; Anda Tenie Iris Rosenblum-Sellers Destine Lee Jakwanul Safin Group leader: Nick Salter (Faculty). Graduate Student Assistant: Maithreya Sitaraman. The classification of surfaces theorem can give the misleading impression that the topology of surfaces is a finished project. W
From playlist 2020 Summer REU Presentations
Right-angled Coxeter groups and affine actions ( Lecture 01) by Francois Gueritaud
DISCUSSION MEETING SURFACE GROUP REPRESENTATIONS AND PROJECTIVE STRUCTURES ORGANIZERS: Krishnendu Gongopadhyay, Subhojoy Gupta, Francois Labourie, Mahan Mj and Pranab Sardar DATE: 10 December 2018 to 21 December 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore The study of spaces o
From playlist Surface group representations and Projective Structures (2018)
Right-angled Coxeter groups and affine actions (Lecture 03) by Francois Gueritaud
DISCUSSION MEETING SURFACE GROUP REPRESENTATIONS AND PROJECTIVE STRUCTURES ORGANIZERS: Krishnendu Gongopadhyay, Subhojoy Gupta, Francois Labourie, Mahan Mj and Pranab Sardar DATE: 10 December 2018 to 21 December 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore The study of spaces o
From playlist Surface group representations and Projective Structures (2018)
Right-angled Coxeter groups and affine actions (Lecture 02) by Francois Gueritaud
DISCUSSION MEETING SURFACE GROUP REPRESENTATIONS AND PROJECTIVE STRUCTURES ORGANIZERS: Krishnendu Gongopadhyay, Subhojoy Gupta, Francois Labourie, Mahan Mj and Pranab Sardar DATE: 10 December 2018 to 21 December 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore The study of spaces o
From playlist Surface group representations and Projective Structures (2018)
AlgTop24: The fundamental group
This lecture introduces the fundamental group of a surface. We begin by discussing when two paths on a surface are homotopic, then defining multiplication of paths, and then multiplication of equivalence classes or types of loops based at a fixed point of the surface. The fundamental grou
From playlist Algebraic Topology: a beginner's course - N J Wildberger
Weyl problem in the hyperbolic 3-space & the Koebe circle domain conjecture - Prof. Luo (Rutgers)
The classical Weyl problem (in the hyperbolic geometric setting) asks if every complete hyperbolic surface of genus zero can be isometrically embedded in to the hyperbolic 3-space as a convex surface and the Koebe circle domain conjecture states if every domain is conformal to a domain who
John Pardon: Totally disconnected groups (not) acting on three-manifolds
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Geometry
Lyapunov exponents of linear surface group representations (Lecture 01) by Bertrand Deroin
DISCUSSION MEETING SURFACE GROUP REPRESENTATIONS AND PROJECTIVE STRUCTURES ORGANIZERS: Krishnendu Gongopadhyay, Subhojoy Gupta, Francois Labourie, Mahan Mj and Pranab Sardar DATE: 10 December 2018 to 21 December 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore The study of spaces o
From playlist Surface group representations and Projective Structures (2018)
Arthur Bartels: The Farrell Jones conjecture for mapping class groups (part 1)
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "The Farrell-Jones conjecture" The main step in the proof of the Farrell-Jones conjecture for mapping class groups is the verification of a regularity condition, related to amenability, for the
From playlist HIM Lectures: Junior Trimester Program "Topology"
K-theory and actions on Euclidean retracts – Arthur Bartels – ICM2018
Topology Invited Lecture 6.8 K-theory and actions on Euclidean retracts Arthur Bartels Abstract: This note surveys axiomatic results for the Farrell–Jones Conjecture in terms of actions on Euclidean retracts and applications of these to GL_n(ℤ), relative hyperbolic groups and mapping cla
From playlist Topology
Francesc Fité, Sato-Tate groups of abelian varieties of dimension up to 3
VaNTAGe seminar on April 7, 2020 License: CC-BY-NC-SA Closed captions provided by Jun Bo Lau.
From playlist The Sato-Tate conjecture for abelian varieties
Ian Agol, Lecture 3: Applications of Kleinian Groups to 3-Manifold Topology
24th Workshop in Geometric Topology, Calvin College, June 30, 2007
From playlist Ian Agol: 24th Workshop in Geometric Topology
Growth of cohomology in towers of manifolds: a topological applica... - Mathilde Gerbelli-Gauthier
Members’ Colloquium Topic: Growth of cohomology in towers of manifolds: a topological application of the Langlands program Speaker: Mathilde Gerbelli-Gauthier Affiliation: Member, School of Mathematics Date: November 15, 2021 How does the dimension of the first cohomology grow in a tower
From playlist Mathematics
On the algebraic fundamental group of surfaces of general type by Margarida Lopes
Algebraic Surfaces and Related Topics PROGRAM URL : http://www.icts.res.in/program/AS2015 DESCRIPTION : This is a joint program of ICTS with TIFR, Mumbai and KIAS, Seoul. The theory of surfaces has been the cradle to many powerful ideas in Algebraic Geometry. The problems in this area
From playlist Algebraic Surfaces and Related Topics
Minerva Lectures 2012 - Ian Agol Talk 2: The virtual Haken conjecture & geometric group theory
Talk two of the second Minerva lecture series, by Prof. Ian Agol on October 23rd, 2012 at the Mathematics Department, Princeton University. More information available at: http://www.math.princeton.edu/events/seminars/minerva-lectures/minerva-lecture-ii-virtual-haken-conjecture-what-geomet
From playlist Minerva Lectures - Ian Agol
Invariant Measures for Horospherical Flows by Hee Oh
PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis
From playlist Ergodic Theory and Dynamical Systems 2022
The congruence subgroup property for SL(2,Z) - William Yun Chen
Arithmetic Groups Topic: The congruence subgroup property for SL(2,Z) Speaker: William Yun Chen Affiliation: Member, School of Mathematics Date: November 10, 2021 Somehow, despite the title, SL(2,Z) is the poster child for arithmetic groups not satisfying the congruence subgroup property
From playlist Mathematics
Lyapunov exponents of linear surface group representations (Lecture 03) by Bertrand Deroin
DISCUSSION MEETING SURFACE GROUP REPRESENTATIONS AND PROJECTIVE STRUCTURES ORGANIZERS: Krishnendu Gongopadhyay, Subhojoy Gupta, Francois Labourie, Mahan Mj and Pranab Sardar DATE: 10 December 2018 to 21 December 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore The study of spaces o
From playlist Surface group representations and Projective Structures (2018)