Talks

This page is an archive of slides and videos for talks that I have given, as well as some talks by my collaborators. See here for a list of all recent talks I have given.

Boone–Higman Embeddings

I have been working with Collin Bleak, Francesco Matucci, and Matthew Zaremsky on embeddings of groups into finitely presented simple groups. My most recent talk on this subect was in the fall of 2023, at the GoTh workshop at Otto-von-Guericke-Universität Magdeburg. Here are the slides:

• Slides — Hyperbolic Groups Satisfy the Boone–Higman Conjecture, September 2023, Magdeburg (PDF)

I gave a similar talk in the summer of 2023 at the Algebra, Geometry, and C*-Algebras workshop at the ICMS, but directed at a C*-algebras audience. Here are the slides and video for the that talk:

• Slides — Embeddings into Topological Full Groups, June 2023, ICMS (PDF)
• Video — Embeddings into Topological Full Groups, June 2023, ICMS (YouTube)

Finally, in the fall of 2022 I gave talks at the Dame Kathleen Ollerenshaw Workshop (Modern advances in geometric group theory) at the University of Manchester, the Geometry & Topology seminar at the University of Glasgow, the Al@Bicocca seminar at the University of Milano–Bicocca, and at the ENS Group Theory Seminar. Here are the slides for these talks:

• Slides — Embeddings into Finitely Presented Simple Groups, ENS, December 2022 (PDF)
• Video — Embeddings into Finitely Presented Simple Groups, ENS, December 2022 (YouTube)
• Slides — Embeddings into Finitely Presented Simple Groups, Milan, December 2022 (PDF)
• Slides — Embeddings into Finitely Presented Simple Groups, Glasgow, September 2022 (PDF)
• Slides — Embeddings into Finitely Presented Simple Groups, Manchester, September 2022 (PDF)

Finally, here is a video of my collaborator Collin Bleak giving a talk on the same research:

• Video — Collin Bleak — Embeddings into Finitely Presented Simple Groups, ESI, July 2023 (YouTube)

Finite Germ Extensions

I have an upcoming paper with Francesco Matucci and In the spring of 2023 I gave a talk at the Groups and Topology workshop at the University of Lancaster, and in the summer of 2023 I gave a similar talk at the Al@Bicocca Flash Workshop at the University of Milan–Bicocca. Here are the slides for the talk:

• Slides — Finite Germ Extensions, Milan, July 2023 (PDF)
• Slides — Finite Germ Extensions, Lancaster, April 2023 (PDF)

Maximal Subgroups of V

I have been working on classifying maximal subgroups of Thompson's group V with Collin Bleak, Martyn Quick, and Rachel Skipper. Here are videos of two talks that Rachel Skipper has given on this research:

• Video — Rachel Skipper — Maximal Subgroups of Thompson's Group V, ENS, October 2022 (YouTube)
• Video — Rachel Skipper — Maximal Subgroups of Thompson's Group V, Newcastle, October 2020 (YouTube)

Quasisymmetries of Finitely Ramified Fractals

I've been working on quasisymmetries of fractals with Bradley Forrest. I've given talks on this research on several occasions, including in the University of Glasgow Analysis Seminar, the Cornell Topology & Geometric Group Theory seminar, and the St Andrews Analysis Seminar. Here are the slides and video:

• Slides — Quasisymmetries of Finitely Ramified Fractals, Glasgow, May 2023 (PDF)
• Slides — Quasisymmetries of Finitely Ramified Fractals, Cornell, September 2021 (PDF)
• Slides — Quasisymmetries of Finitely Ramified Julia Sets, St Andrews, March 2021 (PDF)
• Video — Quasisymmetries of Finitely Ramified Julia Sets, St Andrews, March 2021 (YouTube)

Twisted Brin–Thompson Groups

I have given several talks on my work with Matt Zaremsky on quasi-isometric embeddings of finitely generated groups into simple groups (arXiv). The most recent was at the University of Milano-Bicocca (via Zoom), but I also gave talks on the same subject here at St Andrews and at Heriot-Watt University. Here is the most recent version of the slides for this talk:

• Slides — Twisted Brin–Thompson Groups (PDF)

The version of this talk at the University of Milano-Bicacca was recorded on Zoom:

• Video — Twisted Brin–Thompson Groups, Milan, June 2020 (MP4, 177 MB)

Finitely Presented Groups that Contain Q

I have given several talks on my recent work with James Hyde and Francesco Matucci on embeddings of Q into finitely presented groups (arXiv). The most recent was at Ohio State University (via Zoom), but I also gave talkes at Groups and Geometry in the South East at the University of Southampton, and at the Workshop on Groups, Generalisations and Applications here at St Andrews. Here is the most recent version of the slides for this talk:

• Slides — Finitely Presented Groups that Contain Q (PDF)

Here is a video of my collaborator James Hyde giving a talk on this subject:

• Video — James Hyde — Embedding Q into a Finitely Presented Group (YouTube)

Tree Lifting

I have given several talks on my work with Justin Lanier, Dan Margalit, and Becca Winarski (arXiv). The most recent version of this talk was at the Geometry and Topology Seminar at the University of Glasgow:

• Slides — Recognizing Topological Polynomials by Lifting Trees (PDF)

I gave an earlier talk on the same material for experts at the Algorithms in Complex Dynamics and Mapping Class Groups workshop at ICERM. Here are the slides for that talk:

• Slides — The Tree Lifting Algorithm (PDF)

You can view a video of this talk on the ICERM web page:

• Video — The Tree Lifting Algorithm — ICERM, Brown University, 2 November 2019 (streaming)

This was the second of two talks on our paper at the workshop. The first was given by Becca Winarski:

• Video — Rebecca Winarski — ICERM — Mapping Class Groups and Twisted Rabbits (streaming)

I also gave a couple of earlier talks on this work before the main theorem was proven, one at the University of Michigan (slides) and one here at St Andrews (slides). You can also see an earlier talk by Dan Margalit at the 2017-2018 Warwick EPSRC Symposium on Geometry, Topology and Dynamics in Low Dimensions:

• Video — Dan Margalit — Warwick — Mapping Class Groups in Complex Dynamics (YouTube)

Rational Embeddings of Hyperbolic Groups

I have given several talks on my work with Collin Bleak and Francesco Matucci on the embedding of arbitrary hyperbolic groups into the rational group (arXiv). The most recent version of this talk was at the University of Aberdeen, but I also spoke on this subject here at St Andrews, at Georgia Tech, and at the Geometric Group Theory in Campinas 2018 ICM satellite conference at the University of Campinas. Here is the most recent version of my slides for this talk:

• Slides — Rational Actions of Hyperbolic Groups (PDF)

Here is a short clip of me giving this talk in Campinas:

• Video Clip — Rational Embeddings of Hyperbolic Groups — Campinas 30 July 2018 (MP4, 197 MB)

Embedding RAAG's into Brin–Thompson Groups

I gave a short talk on my paper with Collin Bleak and Francesco Matucci on embedding right-angled Artin groups into Brin–Thompson groups (arXiv) at the 52nd Spring Topology and Dynamical Systems Conference at Auburn University. Here are the slides for this talk:

• Embedding Right-Angled Artin Groups into Brin–Thompson Groups (PDF)

Rearrangement Groups of Fractals

I gave several talks on my paper on rearrangement groups of fractals with Bradley Forrest (arXiv), including one at the Workshop on the Thompson Groups at the University of Southern Denmark in 2016 and a talk at Binghamton University in 2015.

• Rearrangement Groups of Fractals (Mathematica notebook, 44 MB)

Torsion in 2V

Here are the slides for my talk on the torsion problem in $2$V and the undecidability of the finiteness problem for groups of asynchronous automata, which is based on my paper with Collin Bleak (arXiv). I gave this talk at several different seminars in the fall of 2013, and I recently gave this talk in the Logic Seminar at Cornell:

• Slides — Turing Machines, Automata, and the Brin-Thompson Group $2$V (PDF, 8 MB)

Here are the slides for a slightly different version of this talk that I gave at the Workshop on the Extended Family of R. Thompson Groups at the University of St Andrews in May 2014. They include some extra material on subshifts from my joint work with Francesco Matucci, Brita Nucinkis, and Conchita Martínez-Pérez, but do not include any introductory material on Thompson's groups.

• Slides — Dynamics and Decidability in the Brin-Thompson Group $2$V (Mathematica notebook)

Thompson-Like Groups Acting on Julia Sets

Here are the slides for my talk on Thompson-like groups acting on Julia sets, based on my first paper with Bradley Forrest (arXiv). I gave this talk at the St Andrews in October 2013, and I also gave shorter versions of this talk at Groups St Andrews 2013, as well as the Workshop on the Extended Family of R. Thompson Groups conference at St Andrews in 2014.

• Slides — Thompson-Like Groups Acting on Julia Sets (PDF, 7.5 MB)

(This PDF was created from images of the original Mathematica slides. It includes a few still frames of the original animations.)

Here is a PDF of the shorter, 20-min. version of this talk that I gave at Groups St Andrews 2013. The PDF includes a few of my Mathematica animations:

• Slides — Groups St Andrews Talk (PDF)

Finally, Here are the slides for the older talk I gave on the basilica Thompson group. I gave this talk at the University of Virginia and at Binghamton University in April 2012.

• Slides — A Thompson Group for the Basilica (Mathematica Notebook, 30 MB)