## Hyperbolic Lunch

#### Next speaker

Speaker: Anton Zorich

Title: Random square-tiled surfaces and random multi-curves in large genus

Abstract: Moduli spaces of Riemann surfaces and related moduli spaces of quadratic differentials are parameterized by a genus g of the surface. Considering all associated hyperbolic (respectively flat) metrics at once, one observes more and more sophisticated diversity of geometric properties when genus grows. However, most of metrics, on the contrary, progressively share certain rules. Here the notion of “most of” has explicit quantitative meaning, for example, in terms of the Weil-Petersson measure. I will present some of these recently discovered large genus universality phenomena. I will use a count of metric ribbon graphs (after Kontsevich and Norbury) to express Masur-Veech volumes of moduli space of quadratic differentials through Witten-Kontsevich correlators. Then I will present Mirzakhani's count of simple closed geodesics on hyperbolic surfaces. We will proceed with description of random geodesic multicurves and of random square-tiled surfaces in large genus. I will conclude with a beautiful universal asymptotic formula for the Witten-Kontsevich correlators predicted by Delecroix, Goujard, Zograf and myself and recently proved by Amol Aggarwal.

Date and time: October 16, 2024, 12 pm (EDT).

#### Meeting access

The seminar will take place in room Room 210 at the fields Institute. Currently the seminar is a hybrid meeting. If you are interested in attending the seminar online, please contact me for a zoom link.

#### Description

Hyperbolic lunch is an informal talk that takes place at around noon 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.

#### 2024 Schedule

Date | Speaker | Title |
---|---|---|

October 16 | Anton Zorich | Random square-tiled surfaces and random multi-curves in large genus |

#### 2023 Schedule

Date | Speaker | Title |
---|---|---|

December 13 | Assaf Bar-Natan | Hyperbolicity of/in Big Mapping Class Groups |

November 29 | Wenyu Pan | On the dimension of limit sets on the real projective plane via stationary measures |

November 22 | Mikey Chow | Jordan and Cartan spectra in higher rank with applications to correlations |

November 15 | Daniel Litt | Mapping class group actions on the homology of covers |

November 1 | Vivian He | Random walks on groups and superlinear divergent geodesics |

October 25 | Mohammad Honari | Topologically finitely generated big mapping class groups |

October 11 | Abdul Zalloum | A cool proof of Tit's Alternative in mapping class groups |

September 27 | Pouya Honaryar | Effective counts for multicurves in surfaces |

April 7 | Barak Weiss | Horocycle flow on the moduli space of translation surfaces |

March 29 | Montse Casals | Discriminating groups and radicals |

March 22 | Tyrone Ghaswala | Small covers of big surfaces |

March 15 | George Domat | Projection Complexes and "Zooming In" |

March 8 | Sahana Balasubramanya | Actions of solvable groups on hyperbolic spaces |

March 1 | Harry Petyt | Introduction to coarse median spaces |

February 15 | Nikolay Bogachev | From geometry to arithmetic of hyperbolic orbifolds |

February 1 | Justin Tatch Moore | A more rational irrational rotation |

January 23 | Ferrán Valdez | Isometry and Veech groups of big translation surfaces |

January 11 | Alex Lubotzky | Aut(F_n) - actions on presentations and representaions |

#### 2022 Schedule

Date | Speaker | Title |
---|---|---|

December 1 | Alexander Kolpakov | Subspace stabilizers in hyperbolic lattices |

November 22 | Yvon verberne | Symmetries of surfaces |

November 17 | Danny Stoll | The Monodromy of Cycles |

November 3 | Karl Winsor | Pseudo-Anosov homeomorphisms and interval maps |

October 27 | Inhyeok Choi | Simple length spectrum of a hyperbolic surface |

October 20 | Rich Schwartz | Four coloring, continued fractions and Lagrangian subspaces |

October 6 | Abdul Zalloum | Metrics on mapping class groups |

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 | Teichmüller 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 Teichmüller distance numerically in the space of hexagons | |

Jan. 18 | Curt McMullen | ||

Jan. 11 | Yvon Verberne | How to Generate the Mapping Class Group |