Hyperbolic Lunch

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Speaker: Lam Ngyuen

Title: Geometry of Harmonic Maps

Abstract: In this talk, we give an overview of the geometry of harmonic maps into surfaces of nonpositive curvature. Harmonic maps generalize harmonic functions in the sense that the map's domain and target are allowed to be Riemannian manifolds and the map satisfies an analogous partial differential equation. In the non-compact setting, when the targets have nonpositive curvature, the harmonic maps have a particularly rich geometry. The goal of the talk will be discussing that geometry as described in the paper of Han-Tam-Treibergs-Wan. Then we will briefly discuss a generalization of the paper in joint work with Nathaniel Sagman and Sara Maloni.

Date and time: October 22, 2025, 1 pm (EDT).

Meeting access

The seminar will take place in my office, room BA 6236 in the Bahen building. 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 weekly seminar held in my office on Wednesdays around noon. Each session lasts about an hour and is often lively, with frequent questions and discussions throughout. Participants typically bring their lunches and eat while listening. The audience usually includes graduate students and postdocs, with occasional faculty members or undergraduates interested in hyperbolic geometry and related areas such as geometry, topology, group theory and dynamics. Talks often focus on topics that someone has recently learned rather than on the speaker's own results.

If you are in Toronto and have an interesting topic to share, you are warmly encouraged to give a talk at one of our Hyperbolic Lunches. Talks should be accessible to graduate students, and we especially appreciate beautiful mathematics, even when it is elementary. We are as interested in the mathematics itself as in the stories of how it comes to be.

2025 Schedule

Date	Speaker	Title
October 28	Lam Nguyen	Geometry of Harmonic Maps
October 21	Kunal Chawla	Non-realizability of the Poisson boundary
October 15	Vivian He	Square-tiled surfaces and curve counting
October 8	Yulan Qing	Sublinearly Morse directions under first passage percolations
September 30	Nathaniel Sagman	Harmonic maps and Teichmüller theory
March 26	Richard Cao	Spheres in the Curve Complex

2024 Schedule

Date	Speaker	Title
November 27	Inhyeok Choi	Metric WPD for Homeo(S): loxodromics on the fine curve graph
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