Hyperbolic Lunch

Next speaker

Speaker: Asha McMullin

Title: Billiards in hyperbolic polygons and symbolic coding

Abstract: A billiard trajectory in a polygon in the hyperbolic plane is the path of a particle in the polygon, following a geodesic line until it hits the side, reflects off, and continues. This trajectory gives rise to a symbolic coding, its "bounce sequence", which is (generically) a biinfinite sequence recording the sides encountered (which we assume are labeled). In joint work with Erlandsson and Sadanand, we prove that generically the "bounce spectrum" (i.e. the set of all bounce sequences of biinfinite trajectories), determines the shape of the polygon. The "non-generic" case is also completely understood, and we can completely determine when two polygons have the same bounce spectrum. In the talk, I'll explain this theorem, using the case of billiards in Euclidean polygons as motivation (which was a result of earlier work with Duchin, Erlandsson, and Sadanand).

Date and time: July 20, 2022, 12pm (EDT).

Meeting access

Currently the seminar is a hybrid meeting. If you are interested in attending the seminar online, please contact me for a zoom link.


Hyperbolic lunch is an informal talk that takes place at 12pm in my office (BA 6236). They generally last around 60 minutes and the talks are often interrupted by many questions. People bring their lunches to my office and eat as they listen to the talk. The audience consists of graduate students and postdocs and an occasional faculty or undergraduate interested in hyperbolic geometry or related topics in geometry, topology, group theory and dynamics. The topics are often what someone has learned recently and not necessarily a result by the speaker.

If you are in Toronto and have a fun topic you can talk about, you should consider doing one of these lunches. The talks should be accessible to graduate students. We appreciate beautiful math even when it is elementary and would like to know about math as much as about stories of how math gets done.

2022 Schedule

Date Speaker Title
July 20 Chris Leininger Billiards in hyperbolic polygons and symbolic coding
July 13 Asha McMullin Quasi Isometries on Baumslag Solitar Groups
July 6 Vivian He Generalizing the Gromov Boundary
June 29 Alex Wright Random surfaces of large genus
June 22 Assaf Bar-Natan Geodesic Envelopes in the Thurston Metric on Teichmüller Space
June 8 Kunal Chawla A dynamical characterization of hyperbolic groups
June 1 Yulan Qing The Gromov boundary expanded
May 25 Pouya Honaryar The growth of a fixed conjugacy class in negative curvature

2021 Schedule

Date Speaker Title
April 14 Yael Algom-Kfir Nielsen realization for big Out(F_n)
April 7 Kasia Jankiewicz A generalization of the Tits Conjecture for Artin groups
March 31 Assaf Bar-Natan The Thurston Metric -- Geodesics and their Envelopes
March 17 Sander Kupers E_2-algebras and the unstable homology of mapping class groups (Notes)
March 10 Dragomir Saric Train tracks and measured laminations on infinite surfaces (slides)
March 3 Dave Futer Infinitely many virtual geometric triangulations
February 24 Cagri Sert Large deviations and concentration for random walks on hyperbolic spacess
February 10 Aaron Abrams Area relations in square triangulations
February 3 Anders Karlsson From linear to metric
Janurary 27 Christopher Cashen Hyperbolicity in one-relator groups
Janurary 20 Michelle Chu SL(2,C)-character variety of 3-manifold groups

2020 Schedule

Date Speaker Title
December 2 Tarik Aougab Thermodynamic metrics on outer space
November 25 Stephen Cantrell Counting limit theorems for dominated representations
November 18 Wouter van Limbeek Infinite expander graphs and random walks
November 4 Viveka Erlandsson Rigidity and flexibility of hyperbolic cone surfaces
October 28 Jing Tao Genericity of pseudo-Anosov mapping classes (slides)
October 21 Federica Fanoni Big mapping class groups acting on homology (slides)
October 14 Vincent Delecroix Simple closed curves are typically non-separating on high genus surfaces (slides)
October 7 Katie Mann Reconstructing maps out of groups (slides)
September 30 Bram Petri Random 3-manifolds with boundary
September 23 Jacqueline Warren Effective equidistribution of horospherical flows in infinite volume
September 16 Kirill Lazebnik Bers slices in families of univalent maps
July 22 Maxime Fortier Bourque Beurling's criterion and systolic inequalities (slides)
July 15 Saul Schleimer From veering triangulations to Cannon-Thurston maps (slides)
July 8 Anschel Schaffer-Cohen Graphs of curves and arcs quasi-isometric to big mapping class groups (slides)
July 1 Mary He The many facets of Basmajian's identity (slides)
June 24 Matt Clay McMullen's approach to minimal volume entropy of graphs (slides)
June 17 Giulio Tiozzo Shannon's theorem and Poisson boundaries for locally compact groups (slides)
June 10 (10 am) Wenyuan Yang Counting conjugacy classes in groups with contracting elements (slides)
June 3 Joe Chen Big mapping class groups and rigidty of the simple cicle (slides)
May 27 Lei Chen Actions of homeomorphism groups and diffeomorphism groups on manifolds (slides)
May 20 Dylan Thurston From curves to currents (slides)
May 13 Sang-Hyun Kim Algebraic structures of circle diffeomorphism groups
May 6 Alan McLeay Homeomorphic subsurfaces and the omnipresent arcs (slides)
April 29 Mark Greenfield Isometric submersions of Teichmuller spaces
April 22 Radhika Gupta Currents for free groups
April 15 Edgar Bering Special covers of alternating links
April 8 Mark Hagen Tricks with Ramsey's theorem and Dilworth's theorem in CAT(0) cube complexes
April 1 Abdul Zalloum Sublinearly-contracting geodesics in CAT(0) cube complexes
Mar. 25 Ian Frankel L^2 meromorphic functions on flat surfaces
Mar. 16 (Cancelled) Merlin Incerti-Medici A Survey on Topologies of the Morse Boundary
Mar. 11 Petr Kosenko On Random Walks on Word-hyperbolic Groups and Hitting Measures
Mar. 4 Adriano Pacifico Cremona Group II
Feb. 26 Adriano Pacifico Cremona Group I
Feb. 12 Mary He Anosov Prepresentation 102
Feb. 5 Mary He Anosov Representation 101
Jan. 27 Rylee Lyman Outer Automorphisms of Free Products of Finite Groups
Jan. 22 Kasra Rafi Large Scale Geomety of Big Mapping Class Groups

2019 Schedule

Date Speaker Title
Dec. 4 Camillie Horbez Measure equivalence rigidity of mapping class groups, after Y. Kida
Nov. 27 Remi Coulon Automorphisms with exotic growth
Nov. 13 Catherine Pfaff Typical Trees: An Out(F_r) Excursion
October 30 Thomas Ng Finding free subgroups using non-positive curvature
October 23 Igor Belegradek Centers of disks in Riemannian manifolds
October 18 Heejoung Kim Algorithms detecting stability and Morseness for finitely generated groups
October 9 Jacopo De Simoi Spectral rigidity and determination in dynamical billiards
Sept. 25 Anton Petrunin Dimension of CAT(k) spaces
Sept. 18 Yvon Verberne Constructing pseudo-Anosov Mapping Classes Using Positive Twists
Sept. 4 Diaaeldin Taha The Distribution of the Largest Coefficient in Continued Fraction Expansions
April 4 Kathryn Lindsey Iterated function systems & stretch factors
March 28 Yvon Verberne Strong contractibility of geodesics in the mapping class group (Version 4.3)
March 21 Jaccob Kewarth Categories of translation surfaces
Jananan Arulseelan
March 14 Thomas Dykes Sum of squares property in groups
March 7 Assaf Bar-Natan The Earth is Flat in the Eyes of the Law
Feb. 28 Yulan Qing Sublinear boundary of a CAT(0) group
Feb. 21 Zachary Schutzman Shape Analysis for Redistricting
Feb. 14 Ivan Telpukhovskiy On normalizations of Thurston measure on the space of measured laminations
Feb. 7 Chris Karg Infiinite regular translation surfaces
Jan. 31 Ilya Gekhtman Invariant random subgroups and their growth rates
Jan. 24 Adriano Pacifico The desingularization Theorem
Jan. 17 Keivan Mallahi Karai Spectral independence and random walks on products of compact groups

2018 Schedule

Date Speaker Title
July 4 Jordan Hofmann Hyperbolic Isometries and the Double cover SU(2) to SO(3) (see notes)
June 14 Ivan Telpukhovskiy Arithmetic hyperbolic surfaces: without cusps
June 7 Ivan Telpukhovskiy Arithmetic hyperbolic surfaces: with cusps
May 17 Ruth Charney Artin groups: what are they and why are they interesting?
May 30 Adriano Pacifico Thurston Stretch Paths
May 10 Maxime Fortier Bourque Local maxima of the systole function
May 3 Ivan Telpukhovskiy Masur's criterion does not hold in Thurston metric
April 4 Yvon Verberne Strong Contractibility in the Mapping class group.
March 28 Bram Petri Random surfaces
March 22 Giulio Tiozzo Generating functions and counting in RAAGs
March 15 Assaf Bar-Natan How we tried to fix redistricting, and ended up doing group theory
March 7 Dmitri Gekhtman Dynamics in the space of bounded holomorphic functions on the polydisk
March 1 Jeffrey Carlson Commensurability of surface automorphisms
Feb. 15 Justin Martel Kantorovich Singularity Functor and Homotopy-Reductions
Feb. 8 Maxime Fortier Bourque The Art Gallery Problem
Feb. 1 Yulan Qing Guirardel core and relative twisting
Jan. 25 Keivan Mallahi Oppenheim conjecture, and its generalization to the S-arithmetic case
Jan. 18 Tanran Zhang Hyperbolic-type distance on punctured spheres

2017 Schedule

Date Speaker Title
Dec. 13 Funda Gültepe Cannon-Thurston map
Dec. 8 Maxime Scott Teichm├╝ller theorems for topological branched covers
Nov. 15 Camille Hornez Automorphisms of hyperbolic groups and growth
October 31 Maxime Fortier Bourque Scissors congruences and Dehn's dissection theorem
October 25 Jeff Carlson Accidental Isomorphisms between Lie groups
October 11 Joseph Maher Generic foliations via electrification
October 4 Yulan Qing Efficient geodesic in the curve complex
Sept. 27 Giulio Tiozzo Dimension of invariant subsets of the circle
Sept. 20 Pat Hooper Maximal square tiled surface with regular cylinder patterns
Sept. 8 Howard Masur Ergodic theory and interval exchange transformations
August 8 Yulan Qing Convexity of the Outer Space
August 1 Eko Hironaka The minimum dilatation for pseudo-Anosov mapping classes
July 26 Adriano Pacifico Maximal stretch over simple closed curves
July 19 Kasra Rafi Limit sets of Teichmüller geodesics in PML
July 12 Anja Randecker Siegel-Veech constants and the diameter of translation surfaces
June 28 March 8 Jonah Gaster
March 1 Aaron Fenyes Shearing Coordinates
Feb. 8 Maxime Fortier Bourque How to compute Teichm├╝ller distance numerically in the space of hexagons
Jan. 18 Curt McMullen
Jan. 11 Yvon Verberne How to Generate the Mapping Class Group