\( \newcommand{\Sp}{\operatorname{Sp}} \newcommand{\SL}{\operatorname{SL}} \newcommand{\GL}{\operatorname{GL}} \newcommand{\PGL}{\operatorname{PGL}} \newcommand{\SO}{\operatorname{SO}} \newcommand{\SU}{\operatorname{SU}} \newcommand{\PU}{\operatorname{PU}} \newcommand{\Pin}{\operatorname{Pin}} \newcommand{\Vol}{\operatorname{Vol}} \newcommand{\Aut}{\operatorname{Aut}} \newcommand{\Out}{\operatorname{Out}} \newcommand{\vcd}{\operatorname{vcd}} \newcommand{\Id}{\operatorname{Id}} \newcommand{\Flat}{\operatorname{Flat}} \newcommand{\CP}{\mathbb{CP}} \newcommand{\CC}{\mathbb{C}} \newcommand{\EE}{\mathbb{E}} \newcommand{\HH}{\mathbb{H}} \newcommand{\RR}{\mathbb{R}} \newcommand{\QQ}{\mathbb{Q}} \newcommand{\ZZ}{\mathbb{Z}} \newcommand{\calG}{\mathcal{G}} \newcommand{\calO}{\mathcal{O}} \newcommand{\from}{\colon} \newcommand{\cross}{\times} \)

Geometry and Topology Seminar

Warwick Mathematics Institute, Term II, 2017-2018

Please contact Saul Schleimer if you would like to speak or to suggest a speaker.


Thursday January 11, 15:00, room MS.03

TBA (TBA)

TBA

Abstract: TBA


Thursday January 18, 15:00, room MS.03

Chris Leininger (UIUC)

TBA

Abstract: TBA


Thursday January 25, 15:00, room MS.03

TBA (TBA)

TBA

Abstract: TBA


Thursday February 1, 15:00, room MS.03

Viveka Erlandsson (Bristol)

TBA

Abstract: TBA


Thursday February 8, 15:00, room MS.03

Michael Shapiro (Bath)

The Heisenberg group has rational growth in all generating sets

Abstract: Given a group \(G\) and a finite generating set \(\calG\) the (spherical) growth function \( f_\calG(x) = a_0 + a_1 x + a_2 x^2 + \ldots\) is the series whose coefficients \(a_n\) count the number of group elements at distance \(n\) from the identity in the Cayley graph \(\Gamma_\calG(G)\). For hyperbolic groups and virtually abelian groups, this is always the series of a rational function regardless of generating set. Many other groups are known to have rational growth in particular generating sets.

In joint work with Moon Duchin, we show that the Heisenberg group also has rational growth in all generating sets.

The first ingredient in this result is to compare the group metric, which we can see as a metric on the integer Heisenberg group with a metric on the real Heisenberg group. This latter is induced by a norm in the plane which is in turn induced by a projection of the generating set. The second ingredient is a wondrous theorem of Max Bensen regarding summing the values of polynomical over sets of lattice points in families of polytopes. We are able to bring these two ingredients together by showing that every group element has a geodesic whose projection into the plane fellow-travels a well-behaved set of polygonal paths.


Thursday February 15, 15:00, room MS.03

Stergios Antonakoudis (Cambridge)

TBA

Abstract: TBA


Thursday February 22, 15:00, room MS.03

Bert Wiest (Rennes)

TBA

Abstract: TBA


Thursday March 1, 15:00, room MS.03

Marko Berghoff (Humboldt)

TBA

Abstract: TBA


Thursday March 8, 15:00, room MS.03

Rodolfo Gutierrez (Jussieu)

TBA

Abstract: TBA


Thursday March 15, 15:00, room MS.03

Ruth Charney (Brandeis)

TBA

Abstract: TBA


Information on past talks. This line was last edited Monday, October 2, 2017 02:30:50 PM BST