**The commensurability criterion for arithmeticity (after Margulis)**

March-April 2019 at the University of Virginia

PDF file

**Lattices in Lie groups**

January 2019 at CIRM (Luminy, France)

PDF
file

Introduction to arithmetic groups

February 2020 at University of Auckland, New Zealand

PDF
file

another series of talks on a similar subject:

January
2010 at KAIST in Daejeon, Korea (three 1.5-hour lectures)

PDF
file

a more elementary talk on a similar subject:

** Introduction to arithmetic groups**

December 2014 at University of Lethbridge

PDF
file

Cayley graphs of order *kp*
are hamiltonian for *k* < 48

October 2018 at U of Lethbridge

PDF file

**Quasi-isometric bounded generation by Q-rank-one subgroups**

February 2020 at U of Auckland, New Zealand

March 2019 at U of Manitoba

May 2018 at U of Virginia

May 2018 at U of Chicago

January 2018 at IPAM (UCLA)

PDF file version
1

PDF file
version 2

What does the first row of an
invertible matrix look like?

March 2018 at Wesleyan University

PDF file

Strictly convex norms on amenable
groups

July 2017 at the University of Regensburg (Germany)

April 2016 at the University of Virginia November 2013 at
University of Utah

March 2013 at South Padre Island, Texas (*Geometric Groups on the Gulf
Coast*)

April 2012 at University of Lethbridge

March 2012 at University of Chicago

March 2012 at Indiana University

March 2012 at Purdue University

Lecture 1: *Strictly convex norms on abstract
groups* (PDF file)

Lecture 2: *Strictly convex norms on amenable
groups* (PDF file)

Condensed version (PDF
file)

**Groups of polynomial growth** (after Gromov, Kleiner, and
Shalom-Tao)

May 2017 at the University of Virginia

April 2016 at the University of Virginia

PDF
file

**Introduction to model-theoretic methods for proofs of bounded
generation**

April 2017 at the University of Virginia

PDF file

**Hamiltonian paths in projective checkerboards**

October 2016 at the University of Lethbridge

PDF
file

**Infinitely many nonsolvable groups whose Cayley graphs are
hamiltonian**

June 2016 at Canadian Math Society in Edmonton

PDF file

**Horospherical limit points of locally symmetric spaces**

June 2016 at Newcastle University, UK

PDF
file

**Arithmetic subgroups whose representations all map into GL(n,Z)
**August 2015 at the Wasatch Topology Conference (Park
City, Utah)

May 2015 at Stanford University

May 2015 at the University of Chicago

February 2015 at Institute for Pure and Applied Mathematics (UCLA)

PDF file

February 2015 at MSRI (Berkeley)

June 2010 at Ohio State University

March 2010 at the University of British Columbia

April 2009 at the University of Virgina

PDF file

**Hamiltonian cycles in some easy Cayley graphs**

June 2014 at

PDF file

June 2014 at the University of Waterloo (

PDF file

**Vanishing of first cohomology for arithmetic subgroups of
higher real rank
(after G. A. Margulis)**

May 2014 at University of Chicago

PDF file

**What is a Coxeter Group?**

October 2013 at University of Lethbridge

PDF file

**Introduction to Bruhat-Tits buildings**

October 2013 at University of Chicago

PDF file

**Arithmetic subgroups of SL( n,R)**

August 2013 in Jeonju, South Korea (

May 2013 at University of Chicago

PDF file

SL(n,Q) has no volume-preserving
actions on (n-1)-dimensional compact manifolds

August 2013 at Seoul National University

May 2013 at the University of Chicago

March 2013 at Rice University

July 2012 at Oberwolfach

PDF file

Introduction to vertex-transitive
graphs of prime-power order

March 2013 at the University of Lethbridge

PDF
file

Hamiltonian paths in solvable
Cayley digraphs

October 2012 at the University of Lethbridge

July 2011 in Regina

June 2011 in Bled (7th Slovenian International Conference on Graph
Theory)

PDF
file

July 2012 at Park City Mathematics Institute

Lecture 1: Introduction (PDF file)

Lecture 2: Proof using bounded generation (PDF file)

Lecture 3: What is an amenable group? (PDF file)

Lecture 4: Introduction to bounded cohomology (PDF file)

On interactions of amenability with left orderings

February 2012 at workshop in Banff

PDF file

How to make infinitely large numbers from two-player games

December 2011 at University of Lethbridge

PDF file

Does every Cayley graph have a hamiltonian cycle?

March 2011 at University of Western Australia

PDF file

another talk on a similar subject (and others can be found below):

When do subsets of {0,1}

December 2010 in Vancouver (Canadian Mathematical Society)

PDF file

Why arithmetic groups are lattices

June 2010 at the University of Chicago

PDF file

Survey of invariant orders on arithmetic groups

September 2014 at conference on

September 2011 in AMS Sectional meeting at Cornell

June 2011 at Oberwolfach

June 2010 at the University of Chicago

October 2009 in AMS Sectional meeting at Penn State

PDF file

What is the Congruence Subgroup Property?

September 2009 at Carleton-Ottawa Algebra Day

PDF file

other talks on a similar subject:

The Congruence Subgroup Property and bounded generation

May 2008 at the University of Chicago

May 2008 at the University of Chicago

Lecture 1: Introduction to the Congruence Subgroup Property

Lecture 2: Proof that SL(3,Z) has the Congruence Subgroup Property

Lecture 3: Bounded generation

A lattice with no torsion-free subgroup of finite index (after P.Deligne)

June 2009 informal discussion at the University of Chicago

PDF file

Two lectures on bounded cohomology

June 2009 at the University of Chicago

PDF file

Locally symmetric subspaces of locally symmetric spaces

(joint work with Vladimir Chernousov and Lucy Lifschitz)

January 2009 at AMS meeting in Washington, DC

September 2008 at Oberwolfach

April 2008 at Indiana University

February 2008 at the University of Chicago

PDF file of slides from recent talk

PDF file of lecture notes from older talk

other talks on the same subject:

Minimal
isotropic simple Q-groups of higher real rank

February 2008 at the University of Virginia

PDF file

February 2008 at the University of Virginia

PDF file

Using left-invariant orders to study actions on 1-manifolds

June 2008 at CIRM, Luminy, France

Lecture 1: Left-invariant orders and local indicability

Lecture 2: Amenability and Ghys-Burger-Monod Theorem

Lecture 3: Ghys-Burger-Monod Theorem and a theorem of Navas

Proof of the Margulis Normal Subgroups Theorem

February 2008 at the University of Chicago

Lecture
1: Introduction to Amenable Groups (PDF file)

Lecture 2: Statement and Most of the Proof (PDF file)

Lecture 3: Proof of the 'Black Box' Result (PDF file)

Lecture 2: Statement and Most of the Proof (PDF file)

Lecture 3: Proof of the 'Black Box' Result (PDF file)

Amenable groups that act on the line

April 2008 at University of Illinois, Chicago

April 2008 at Northwestern University

April 2008 at AMS meeting in Bloomington, Indiana

February 2008 at Ohio State University

March 2007 at the University of British Columbia

November 2006 at the University of Alberta

October 2006 at the University of Karlsruhe

PDF file

a more elementary talk on the same subject:

Using recurrence to study symmetries of the real line

March 2012 at the University of Virginia

PDF file

Dani's contributions to ergodic
theory on homogeneous spaces

December 2007 at Tata Institute in Mumbai, India

PDF file

(a lecture in a course given by B.Farb and M.Kisin)

October 2007 at the University of Chicago

PDF file

Some discrete groups that cannot

at Schrodinger Institute in Vienna

Part 1: Actions of amenable groups (PDF
file)

Part 2: Actions of arithmetic groups (PDF file)

Part 3: 3 Major Theorems of Margulis (PDF file)

(Theorems in Part 3 are not part of the announced topic,

but are important and use methods similar to Part 2)

Part 2: Actions of arithmetic groups (PDF file)

Part 3: 3 Major Theorems of Margulis (PDF file)

(Theorems in Part 3 are not part of the announced topic,

but are important and use methods similar to Part 2)

**Which circulant digraphs are hamiltonian?
**June 2007 in Koper, Slovenia

PDF file

**Bounded generation of special linear groups (after
Carter, Keller, and Paige)
**April 2008 at Vanderbilt University

June 2005 at workshop in Banff

PDF file

**Actions of arithmetic groups on the circle
**April 2005 at the University of Illinois,
Chicago

PDF file

Some arithmetic groups that cannot act on the line(joint work with

Lucy Lifschitzand Vladimir Chernousov)Alternate titles:

Some arithmetic groups that cannot act on the circle,

Some arithmetic groups that cannot act on 1-manifolds,

Some arithmetic groups that cannot be right ordered

March 2012 at Purdue University

April 2010 at the University of Virginia

December 2009 at the University of Lethbridge

April 2008 at Vanderbilt University

February 2008 at the University of Virginia

January 2008 at Mississippi State University

January 2008 at the University of Texas

July 2007 at the University of Minnesota, Duluth

March 2007 at the University of British Columbia

July 2006 at Oberwolfach, Germany

March 2006 at the University of Hawaii

November 2005 at Texas A&M University

March 2005 at AMS meeting in Lubbock, Texas

March 2005 at Princeton University

March 2005 at AMS meeting in Newark, Delaware

March 2005 at Rice University

February 2005 in Auckland, New Zealand

November 2004 at the University of Alberta

November 2004 at Lorentz Dynamics Workshop in Banff

August 2004 at Alberta Topology Seminar in Banff

June 2004 at Caltech

April 2004 at the University of Regina

PDF file

Some arithmetic groups that cannot act on the circle

(alternate title:Arithmetic groups that cannot be right-ordered)

December 2001 at Tata Institute (Mumbai, India)

February 2002 at Case Western Reserve University and Virginia Tech

PDF fileSome arithmetic groups that cannot act on the circle

March 2002 at Les Diablerets, Switzerland

PDF file

SL(3,Z) cannot act continuously on the circle

October 1998 at the Ecole Normale Superieure - Lyon (France)

PDF file

Actions of semisimple Lie groups on circle bundles

(joint work withRobert J. Zimmer)

May 2000 at the Newton Institute (Cambridge, UK)

March 2000 at the University of Manchester, England

PDF file

**Cocompact Lattices
**January 2006 in Workshop
on Property RD

at the American Institute of Mathematics, Palo Alto

PDF file

**Hamiltonian checkerboards
**November 2011 at the University of Lethbridge

May 2010 at the University of Manitoba

(Prairie Discrete Mathematics Conference)

PDF file

other talks on related subjects:

**Hamiltonian cycles in Cayley graphs
**August 2005 at the University of Winnipeg

(Prairie Discrete Mathematics Conference)

PDF file

**Open problems on hamiltonian cycles in Cayley graphs
**June 2006 in Minisymposium in SIAM conference

at University of Victoria

PDF file

**Hamiltonian cycles in circulant graphs and digraphs
**May 2004 at the University of Lethbridge

(Combinatorics Day)

PDF file

May 2003 at Simon Fraser University

(conference for Brian Alspach's 65th birthday)

PDF file

**Which flows are sums of
hamiltonian cycles in abelian Cayley graphs?
**(joint work with

May 2003 in Koper, Slovenia (

PDF file

(joint work with

March 2002 at Southeastern Combinatorics Conference in Boca Raton, Florida

PDF file

**Hamiltonian paths in cartesian powers
of directed cycles**

(joint work with **David Austin** and **Heather Gavlas**)

November 2002 at the University of Lethbridge

PDF file

March 2008 at the University of Michigan

April 2002 at the University of Lethbridge, Canada

November 2001 at Oklahoma State University

PDF file

**Geometric interpretation of the Q-rank of a locally symmetric
space
**May 2004 at AMS/SMM Meeting in Houston

(joint work with Pralay Chatterjee)

PDF file

another talk on a related subject:

**Orbits of Cartan subgroups
on homogeneous spaces
(after George Tomanov and Barak Weiss)
**December 2001 at Tata Institute (Mumbai,
India)

PDF file

**Real representations of sp(n) have Q-forms
**April 2003 at the University of North Carolina

PDF file

another talk on a related subject:

Q-forms of real representations of compact semisimple Lie groups

(after Raghunathan and Eberlein)

October 2001 at OSU

PDF file

**Gromov and Piatestski-Shapiro's Nonarithmetic**** Lattices in
**SO(1,n)

September 2002 at Oklahoma State University

PDF file

**Some ideas in the proof of Ratner's Theorem**

(alternate title: **An Introduction to Unipotent Flows**)

September 2007 at Pennsylvania State University

January 2007 at University of Calgary

July 2002 at ETH, Zurich

June 2002 at the University of Chicago

February 2000 at the Newton Institute (Cambridge, UK)

previously at a few other universities

PDF file

**Ergodic actions of semisimple Lie groups on compact
principal bundles**

(joint work with **Robert J. Zimmer**)

April 2001 at the University of Illinois, Chicago

PDF file

**Rigidity of some characteristic-p nillattices**

(joint work with **Lucy Lifschitz**)

June 2000 at the Newton Institute (Cambridge, UK)

PDF file

**What is a superrigid subgroup?**

(alternate title: **Superrigid
subgroups of solvable Lie groups**)

September 2015 at the
University of Lethbridge

November 2013 at U of Utah and Idaho State U

April 2002 at the University of Regina, Canada

February 2002 at Virgina Tech

May 2000 at the University of Birmingham, England

PDF file

Other talks on the same subject:

More elementary: What
is a superrigid subgroup? (August 1997 at the MAA Mathfest, Atlanta)

More advanced: Superrigid
subgroups of solvable Lie groups (April 1999 at the U of Chicago)

**Tessellations of homogeneous spaces of SU(2,n)**

(joint work with **Alessandra Iozzi** and **Hee Oh**
)

March 2000 at the Newton Institute (Cambridge, UK)

PDF file

**Cartan-decomposition subgroups**

(joint work with **Hee Oh** and **Alessandra Iozzi**
)

September 1999 at the University of Michigan

PDF file

**Transitive permutation groups of prime-squared degree**

(joint work with **Edward Dobson**)

May 1999 Group Theory Junior Seminar at the University of
Chicago

PDF file

**Foliation-preserving maps between solvmanifolds**

(joint work with **Holly Bernstein**)

March 1998 at Kansas State University AMS meeting

PDF file

**Simple groups of real rank at least two have Kazhdan's
property T**

January 28, 1998 Lie Groups Seminar at Oklahoma State
University

PDF file

**Introduction to Kazhdan's property T**

January 21, 1998 Lie Groups Seminar at Oklahoma State
University

PDF file