The following talks are available to download in pdf
format.

**Warning:** There were some typos found
during the presentations that I have not yet corrected (reader
beware).

**Mountain View, California **

In October, 2007 I gave a talk at Google Headquarters during the Bay
Area Discrete Math day. This is a summary version of a series of
papers on hypertrees and loop groups with various coauthors.

- Points in the plane and loops in space (pdf)

In August, 2007 I gave a talk at MSRI in Berkeley based on recent work by my graduate student Rena Levitt.

- Triangles, Squares and Biautomaticity (pdf)

In June, 2007 I gave a talk at the Mathematics Institute in Bedlewo, Poland based on recent work by my graduate student Rena Levitt.

- Instability in Triangle-Square Complexes (pdf)

In May, I gave a series of three talks at Southern Oregon University as their Kieval Lecturer for 2007. Two talks had slides and the third was chalk-based. Talk 1 played a double role as the address following the Sigma Xi banquet for their local chapter. I discussed a sample of some of the surprises that arise when things are repeated. The second talk was based on my monthly article, "Noncrossing partitions in surprising locations."

During the 4th week on geometric group theory in Luminy (February 2007), I gave a series of four talks on Coxeter groups and Artin groups. The first two talks were about Coxeter groups and virtually all of the material is classical. The second pair of talks were about the on-going research program to understand all Artin groups by using a newly developed continuous geometry. (The content of these slides is similar to the short course I gave in Ottawa in June 2006, for which no slides were produced.)

- Day 1: Polytopes and Reflection Groups (pdf)
- Day 2: Symmetric Spaces and Simple Groups (pdf)
- Day 3: Pulling Apart Orthogonal Groups (pdf)
- Day 4: Affine Isometries and Artin Groups (pdf)

In a special session on geometric combinatorics during the AMS sectional meeting (October 2006) I gave a talk on a generalization of the combinatorial Gauss-Bonnet theorem that allows one to choose arbitrary angles in high dimensional polytopal complexes.

- Moebius inversion and combinatorial curvature (pdf)

At the AMS special session on curvature in group theory and combinatorics held in Santa Barbara, California (April 2005), I gave a short talk on new (and pretty) geometric presentations of the pure braid group (joint work with Dan Margalit).

- Square-dancing in the pure braid group (pdf)

At the Institute for Advanced Studies / Park City Summer Institute on Geometric Combinatorics in Park City, Utah (July 2004), I gave a talk on the generalization of non-crossing partitions to arbitrary Coxeter groups. This is a project with Noel Brady and John Crisp. The first half of the talk is an overview of Garside structures formulated for geometric combinatorialists.

- Non-crossing partitions for arbitrary Coxeter groups (pdf)

At the geometric group theory conference in Poland (April 2004), I gave a status report on the Garside structures for Artin groups project with Noel Brady and John Crisp. (expanded version of the talk from October listed below)

- Garside structures for (some more) Artin groups (pdf)

At the AMS sectional meeting (March 2004) I gave another version of the talk on hypertrees, including some new results with John Meier and Craig Jensen at the end.

- Hypertrees and the l
^{(2)}betti numbers of the pure symmetric automorphism groups (pdf)

At the AMS sectional meeting (October 2003) I gave a short talk on recent joint work with Anton Kaul, Noel Brady, and John Crisp.

- Garside structures for free groups (and other Artin groups) (pdf)

During the Durham symposium on geometric and cohomological group theory (July 2003) I gave a short course on constructing non-positively curved spaces and groups.

**Day 1:**Basic definitions, curvature conjecture, decidability, length spectra (pdf)**Day 2:**Algorithms, dimension 3, computers, 5/6* 3-manifolds, positive curvature (pdf)**Day 3:**Special shapes, Artin groups, small cancellation grouups, ample twisted face pairings (pdf)**Day 4:**Angles in polytopes, Gauss-Bonnet, conformal CAT(0), one-relator groups (pdf)

At a semigroup conference in Braga, Portugal (June, 2003) I talked on joint work with John Rhodes on geometrically defined expansions of finite semigroups.

- Expansions of semigroups (pdf)

At the Joint AMS-RSME conference (June 2003) I gave a short talk on research carried out by my graduate student Woonjung Choi.

- CAT(0) structures for Artin groups (pdf)

During the Cannonfest (June 2003) I gave two talks. The first on a recent result with John Meier, and the second, a general interest talk on the various ways the noncrossing partition lattice arises in geometric group theory, enumerative combinatorics, and non-commutative geometry.

- Hypertrees, the pure symmetric automorphism groups, and their
l
^{(2)}betti numbers (pdf) - Noncrossing partition lattice (pdf)