Past Junior Topology and Group Theory Seminar

8 May 2013
16:00
Abstract
<p><span style="font-size: x-small;"><span style="font-size: 10pt;">The integers (while wonderful in many others respects) do not make for fascinating Geometric Group Theory. They are, however, essentially the only infinite finitely generated group which is both hyperbolic and amenable. In the class of locally compact topological groups, the intersection of these two notions is richer, and the major aim of this talk will be to give the structure of a classification of such groups due to Caprace-de Cornulier-Monod-Tessera, beginning with Milnor's proof that any connected Lie group admitting a left-invariant negatively curved Riemannian metric is necessarily soluble.</span></span></p>
  • Junior Topology and Group Theory Seminar
1 May 2013
16:00
Robert Kropholler
Abstract


To continue the day's questions of how complex groups can be I will be looking about some decision problems. I will prove that certain properties of finitely presented groups are undecidable. These properties are called Markov properties and include many nice properties one may want a group to have. I will also hopefully go into an algorithm of Whitehead on deciding if a set of n words generates F_n.

  • Junior Topology and Group Theory Seminar
6 March 2013
16:00
Henry Bradford
Abstract
<p>I will outline Bergeron-Wise’s proof that the Virtual Haken Conjecture follows from Wise’s Conjecture on virtual specialness of non-positively curved cube complexes. If time permits, I will sketch some highlights from the proof of Wise’s Conjecture due to Agol and based on the Weak Separation Theorem of Agol-Groves-Manning. </p>
  • Junior Topology and Group Theory Seminar
20 February 2013
16:00
Alejandra Garrido Angulo
Abstract
<p>Self-similarity is a fundamental idea in many areas of mathematics. In this talk I will explain how it has entered group theory and the links between self-similar groups and other areas of research. There will also be pretty pictures. </p>
  • Junior Topology and Group Theory Seminar
13 February 2013
16:00
Martin Palmer
Abstract
<p><span>First of all, I will give an overview of what the phenomenon of homological stability is and why it's useful, with plenty of examples. I will then introduce configuration spaces -- of various different kinds -- and give an overview of what is known about their homological stability properties. A "configuration" here can be more than just a finite collection of points in a background space: in particular, the points may be equipped with a certain non-local structure (an "orientation"), or one can consider unlinked embedded copies of a fixed manifold instead of just points. If by some miracle time permits, I may also say something about homological stability with local coefficients, in general and in particular for configuration spaces. <br /></span></p>
  • Junior Topology and Group Theory Seminar
6 February 2013
16:00
Montserrat Casals-Ruiz
Abstract
<p><span style="font-size: x-small;"><span style="font-size: 10pt;">The theory of equations over groups goes back to the very beginning of group theory and is linked to many deep problems in mathematics, such as the Diophantine problem over rationals. In this talk, we shall survey some of the key results on equations over groups, give an outline of the Makanin-Razborov process (an algorithm for solving equations over free groups) and its connections to other results in group theory and low-dimensional topology. <br /></span></span></p>
  • Junior Topology and Group Theory Seminar
30 January 2013
16:00
David Hume; Robert Kropholler; Martin Palmer and Alessandro Sisto
Abstract
<p><span style="font-size: x-small;"><span style="font-size: 10pt;">We will discuss (very) recent work by Hensel; Przytycki and Webb, who describe unicorn paths in the arc graph and show that they form 1-slim triangles and are invariant under taking subpaths. We deduce that all arc graphs are 7-hyperbolic. Considering the same paths in the arc and curve graph, this also shows that all curve graphs are 17-hyperbolic, including closed surfaces. </span></span></p>
  • Junior Topology and Group Theory Seminar
30 January 2013
12:00
Lukasz Grabowski
Abstract
<p><span style="font-size: x-small;"><span style="font-size: 10pt;">The eponymous result is due to Bridson and Vogtmann, and was proven in their paper "Automorphisms of Automorphism Groups of Free Groups" (Journal of Algebra 229). While I'll remind you all the basic definitions, it would be very helpful to be already somewhat familiar with the outer space. </span></span></p>
  • Junior Topology and Group Theory Seminar

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