Festival Speakers 19822018
1982
 E. Thomas, Hilbert Modular Varieties
 W. Metzler, Simplehomotopy in Low Dimensions and Group Presentations
 T. Petrie, Smith Equivalence of Representations
 S. Ferry, Fibered Triangulations of Qmanifold Bundles
 R. Hamilton, ThreeManifolds with Positive Ricci Curvature
 D. Johnson, Finite Generation of the Torelli Subgroup of the Mapping Class Group
 R. Charney, Cohomology of Satake Compactifications
 M. Davis, Groups Generated by Reflections and Aspherical Manifolds Not Covered by Euclidean Space
1983
 J. Milnor, InfiniteDimensional Lie Groups: A Survey
 F. Peterson, Loop Spaces and the Dickson Algebra
 K. Igusa, Parametrized Morse Theory and Pseudoisotopy
 M. Steinberger, Equivariant Fiber Properties
 F. Quinn, Recent Progress in 4manifolds
 K.H. Dovermann, Smith Equivalence of Representations
 H. Miller, Recent Work on the Homotopy Theory of Classifying Spaces of Finite Groups
 P. Scott, Least
Area Surfaces in 3manifolds
1984
 J. Morgan, Degeneration of Hyperbolic Structures and Groups Acting on Trees
 S. Weinberger, Symmetry and Homology
 M. Culler, A Space of Moduli for the Free Group
 D. Davis, A Strong NonImmersion Theorem for Real Projective Spaces
 G. Katz, Integrality Theorems and Witt Analogues of Burnside Rings
 K. Brown, Finiteness Properties of Groups of Tree Derangements
 R. Fintushel, SO(3)Connections
and the Topology of 4Manifolds
1985
 W. Neumann, Volumes of Hyperbolic 3Manifolds
 J. Birman, Jones' New Link Invariants
 K. Orr, A General Framework for Link Cobordism Implying the SatoLevine Invariants Vanish
 D. DeTurck, Music on Manifolds
 M. Gage, A Curve Shortening Process in the Plane
 M. Steinberger, Equivariant Topological Torsion
 E. Devinatz, On Ravenel's Nilpotence Conjecture
 D. Gabai, Foliations and the Topology of 3Manifolds
1986
 W. Kazez, Maps of Surfaces and Some Conjectures of Berstein and Edmonds
 L. Kaufmann, State Models for Knot Polynomials
 J. Harper, CoGroups which are not Suspensions
 C. Rourke, A Proof of the Poincare Conjecture I
 S. Plotnick, Growth Functions and Fuchsian Groups
 P. Hilton, Failures of Cancellation in Group Theory and Homotopy Theory
 A. Edmonds, Group Actions on 4Manifolds
 C. Rourke, A Proof of the Poincare
Conjecture II
1987
 M. Handel, ZeroEntropy Surface Diffeomorphisms
 J. Shaneson, Smooth Nontrivial 4Dimensional sCobordisms
 C. Wilkerson, Smith Theory and the Sullivan Conjecture
 M. Scharlemann, Link Genus and the Conway Skein Tree
 P. Shalen, Trees and Continued Fractions
 G. Carlsson, Applications of the Burnside Ring Conjecture
 J. West, Nonlinear Similarity Begins in Dimension 6
 B. Lawson, The Topological Structure of the Space of Algebraic Varieties
1988
 D. Fried, Homology of Free Abelian Covers
 S. Ferry, EpsilonTopology and Novikov's Conjecture
 J. Luecke, The Knot Complement Problem
 P. Peterson, Bounding Homotopy Types by Geometry
 W. Dwyer, Wreath Products and Iterated Fibrations
 W. Metzler, The Distinction between Homotopy Type and SimpleHomotopy Type for 2Complexes
 M. Bestvina, Train Tracks for Free Group Automorphisms and a Conjecture of Peter Scott
1989
 F. T. Farrell, A Topological Analogue of Mostow's Rigidity Theorem
 E. Miller, Generalizations of Casson's Invariant for 3Manifolds
 D. Ravenel, The Chromatic Point of View in Homotopy Theory
 C. Frohman, Unitary Representation of Knot Groups
 R. Skora, Splitting of Surfaces
 W.C. Hsiang, The KTheoretic Novikov Conjecture
 L. Jones, A Counterexample to Smooth Rigidity
 C. McMullen, 3Manifolds and Riemann Surfaces
1990
 B. Eckmann, The Euler Characteristic of Spaces and Groups  Theme and Variations
 J. Morgan, Applications of Gauge Theory to Smooth 4Manifolds
 A. Dranishnikov, Cohomological Dimension Theory and its Applications
 T. Cochran, New Linking Phenomena: The Land Beyond Massey Products
 T. Petrie, The Equivariant Serre Conjecture and Algebraic Actions on Complex nSpace
 M. Feighn, Combining Negatively Curved Groups
 A. Adem, Cohomology and Actions of Finite Groups
 M. Culler, Paradoxical Decompositions and Margulis Numbers
1991
 S. Stolz, SimplyConnected Manifolds of Positive Scalar Curvature
 J. Cao, Almost Visible Manifolds of Nonpositive Curvature
 W. Menasco, The Tait Conjecture and the Classification of Alternating Links
 T. Goodwillie, Loops and the KTheory of Group Rings
 M. Lustig, Tunnels, Bridges and K_1
 M. Kapranov, On a Conjecture of Baues in the Theory of Loop Spaces
 A. Casson, The SeifertFiberedSpace Conjecture
1992
 P. Hilton, The Life and Work of Israel Berstein
 Z.X. He, On "Energy" of Knots and Unknots
 C. Wilkerson, Estimating Homotopy by Cohomology
 M. Bridson, The Flat Torus Theorem and Semihyperbolic Groups
 W. Goldman, Building Polyhedra in Variable Curvature
 A. Hatcher, Sphere Complexes of 3Manifolds and Aut(F_n)
 J. Bryant, A NonResolvable Generalized Manifold
 E. Pedersen, On the Sphere Cross Euclidean Space Form Problem
 J. Franks, Geodesics on the 2Sphere and Periodic Points of Annulus Homeomorphisms
1993
 R. Schoen, Harmonic Maps and Actions of Discrete Groups
 J. Shaneson, Counting Lattice Points and Singularities of Functions
 I. Rivin, Deformation Theory of Singular Hyperbolic Metrics on 3Manifolds
 A. Dranishnikov, Cohomological Dimension Type and the Mapping Intersection Problem
 U. Oertel, Spaces which are not Negatively Curved
 G. Carlsson, Some Remarks on the Assembly Map in Algebraic KTheory
 C. Curtis, Generalized Casson Invariants
 M. Bestvina, The Boundary of Outer Space
1994
 K. Kuperberg, Counterexamples to the Seifert Conjecture
 P. Thurston, The 4Dimensional Busemann Conjecture: Recognizing Manifolds in Synthetic Geometry
 L. Mosher, Mapping Class Groups are Automatic
 S. Ferry, InfiniteDimensional Phenomena in FiniteDimensional Topology
 S. Gersten, Subgroups of Hyperbolic Groups
 R. Charney, Hyperplane Complements Associated to Infinite Reflection Groups
 M. Feighn, On the Tits Alternative for Out(F_n)
 R. Gompf, On the Topology of Symplectic 4Manifolds
1995
 R. Fintushel, Introduction to SeibergWitten Invariants
 B. Farb, Coarse Geometry and Rigidity
 D. Chase, Fixed Point Sets of Involutions on Spheres
 J. Cannon, Thompson's Group: Fordham's Algorithm for Minimal Representatives
 R. MacPherson, The Topological Trace Formula
 D. Burago, Asymptotic Invariants of Riemannian Tori
 J. Morgan, Applications of SeibergWitten Invariants to the Topology of 4Manifolds
1996
 D. Gabai, Geometric and Topological Rigidity of Hyperbolic 3Manifolds
 Y. Minsky, The Complex of Curves on a Surface: Hyperbolicity Lost and Found in Teichmueller Space
 M. Weiss, Index Theory Without Operators
 M. Brin, Automorphisms of Some Small Homeomorphism Groups
 N. Brady, Branched Coverings of Cubical Complexes and Subgroups of Hyperbolic Groups
 R. Lee, The Spherical Space Form Problem
 M. Davis, Boundaries of Coxeter Groups
1997
 B. Kleiner, The LargeScale Geometry of Spaces with Nonpositive Curvature
 M. Hopkins, Topological Modular Forms
 L. Carbone, NonUniform Lattices on Uniform Trees
 Z. Szabo, Disproving the Minimal Conjecture
 M. Sageev, JSJSplittings for Finitely Presented Groups
 W. Dwyer, Homology Decompositions for Classifying Spaces
 Z. Sela, LowDimensional Topology, Algebraic Geometry over Groups, and the Elementary Theory of Free Groups
1998
 D. Cooper, Some Surface Subgroups Survive Surgery
 J. Stasheff, From Operads to String Theory
 J. McCammond, General Versions of Small Cancellation Theory
 M. Hutchings, Reidemeister Torsion in Generalized Morse Theory (with an Application to SeibergWitten Theory)
 A. Reid, Thue Equations and Dehn Surgery
 M. Handel, The Mapping Torus of a Free Group Automorphism is Coherent
 W. Thurston, ThreeManifolds that Slither around the Circle
1999
 Y. Eliashberg, Introduction to Symplectic Field Theory
 P. Shalen, Boundary Slopes of Knots, and 3Manifolds with Cyclic Fundamental Group
 C. Woodward, Eigenvalue Inequalities and Quantum Cohomology of the Grassmannian
 W. Ziller, Curvature and Symmetry of Milnor Spheres
 S. Boyer, A Proof of the Finite Filling Conjecture
 M. Kapovich, Group Actions on Coarse Poincare Duality Spaces
 D. Wise, Subgroup Separability of the Figure 8 Knot
 R. Edwards, Cantor Groups, their Classifying Spaces, and their Actions on ENR's
2000
 R. Geoghegan, SL(2) Actions on the Hyperbolic Plane
 C. Connell, Volume Growth Rigidity
 M. Sapir, Some Applications of Higman Embeddings
 J. Roe, Amenability and Assembly Maps
 K. Whyte, Large Scale Geometry of Graphs of Groups
 M. Bridson, Subgroups of Semihyperbolic Groups
 S. Bigelow, Braid Groups are Linear
2001
 G. Tian, Symplectic Surfaces in Rational Complex Surfaces
 P. Teichner, LTheory of Knots
 J. Rognes, TwoPrimary Algebraic KTheory of Pointed Spaces
 D. Sinha, The Topology of Spaces of Knots
 D. Calegari, Promoting Essential Laminations
 M. Abreu, The Topology of Symplectomorphism Groups
 D. Allcock, Reflection Groups on the Octave Hyperbolic Plane
 R. Forman, The Differential Topology of Combinatorial Spaces
2002
 M. Bestvina, Measured Laminations and Group Theory
 D. Biss, The Combinatorics of Smooth Manifolds: Oriented Matroids in Topology
 S. Gersten, Isoperimetric Inequalities for Nilpotent Groups
 D. McDuff, The Topology of Groups of Symplectomorphisms
 Y. Minsky, On Thurston's Ending Lamination Conjecture
 P. Ozsvath, Holomorphic Disks and Lowdimensional Topology
 G. Yu, The Novikov Conjecture and Geometry of Groups
2003
 D. BarNatan, The Unreasonable Affinity of Knot Theory and the Algebraic Sciences
 J. Birman, Stabilization in the Braid Groups
 F. Cohen, Braid Groups, the Topology of Configuration Spaces, and Homotopy Groups
 B. Farb, Hidden Symmetries of Riemannian Manifolds
 G. Levitt, Automorphisms of Canonical Splittings
 J. Meier, Asymptotic Cohomology for the Motion Group of a Trivial nComponent Link
 J. Roberts, RozanskyWitten Theory
 D. Thurston, How Efficiently Do 3Manifolds Bound 4Manifolds?
 U. Tillmann, The Topology of the Space of Strings
 A. Valette, Vanishing Results for the First L^{2} Betti Number of a Group
 K. Vogtmann, Graph Homology and Outer Space
2004
 I. Agol, Tameness of Hyperbolic 3Manifolds
 J. Brock, Ending Laminations and the WeilPetersson Visual Sphere
 N. Dunfield, Does a Random 3Manifold Fiber Over the Circle?
 J. Etnyre, Invariants of Embeddings Via Contact Geometry
 R. Grigorchuk, Groups of Branch Type and Finitely Presented Groups
 P. Kronheimer, Property P for Knots
 Y. Rudyak, Category Weight and the Arnold Conjecture on Fixed Points of Symplectomorphisms
 R. Schwartz, Spherical CR Geometry and Dehn Surgery
 D. Sullivan, String Background in Algebraic Topology
 Z. Szabo, Heegaard Diagrams and Holomorphic Disks
 W. Thurston, What Next?
2005
 Denis Auroux, Symplectic 4Manifolds, Mapping Class Groups, and Fiber Sums
 Augustin Banyaga, Some Invariants of Transversally Oriented Foliations
 Paul Biran, Algebraic Families and Lagrangian Cycles
 Thomas Delzant, Fundamental Groups of Kaehler Manifolds
 Yakov Eliashberg, Geometry of Contact Transformations: Orderability vs. Squeezing
 Étienne Ghys, Minimal Sets of Holomorphic Foliations on the Complex Projective Plane: A Survey
 Yael Karshon, Tori in Symplectomorphism Groups
 John Morgan, Ricci Flow and Topology of 3Manifolds
 Shahar Mozes , Lattices in Products of Trees
 Yann Ollivier, A Panorama of Random Groups
 Brendan Owens, Unknotting Information from Heegaard Floer Theory
2006
 Noel Brady, University
of Oklahoma
PerronFrobenius Eigenvalues, Snowflake Groups and Isoperimetric Spectra  Gunnar Carlsson,
Stanford University
Algebraic Topology and High Dimensional Data  Thomas Farrell,
Binghamton University
Some Applications of Topology to Geometry  Soren Galatius,
Stanford University
Stable Homology of Automorphisms of Free Groups  Robert Ghrist,
University of Illinois at UrbanaChampaign
Homological Sensor Networks  Jesper Grodal,
University of Chicago
From Finite Groups to Infinite Groups via Homotopy Theory  Maurice Herlihy,
Brown University
Topological Methods in Distributed and Concurrent Computing  Tara Holm, Connecticut
and Cornell University
Orbifold Cohomology of Abelian Symplectic Reductions  Martin Kassabov,
Cornell University
Kazhdan Property T and its Applications  Lee Mosher, Rutgers
University
Axes in Outer Space  Nathalie Wahl,
University of Chicago
Mapping Class Groups of Nonorientable Surfaces
2007
 Danny Calegari,
California Institute of Technology
Curvature and stable commutator length  Ralph Cohen,
Stanford University
Surfaces in a background manifold and the homology of mapping class groups  Cornelia Drutu,
Université des Sciences et Technologies de Lille I
Relatively hyperbolic groups: geometry and quasiisometric invariance  Alex Eskin,
University of Chicago
Counting problems in Teichmüller space  Mark Feighn,
Rutgers University at Newark
Definable subsets of free groups  Ilya Kapovich,
University of Illinois at UrbanaChampaign
Geodesic currents and outer space  Chris Leininger,
University of Illinois at UrbanaChampaign
The boundary of the curve complex  Tim Riley,
Cornell University
The geometry of discs spanning loops in groups and spaces  Juan Souto,
University of Chicago
Heegaard splittings and hyperbolic geometry  Gang Tian,
Princeton University
Geometrization of low dimensional manifold
2008
 Andrew Dancer,
Oxford University
Symplectic Versus Hyperkahler Geometry  Hansjörg
Geiges, University of Cologne
Contact Dehn Surgery  Viktor
Ginzburg, University of California at Santa Cruz
Leafwise Coisotropic Intersections  Rebecca
Goldin, George Mason University
Equivariant Cohomology in Symplectic Geometry  Richard
Kenyon, Brown University
The Configuration Space of Branched Polymers  Ian Leary,
Ohio State University
Infinite Smith Groups  Kaoru Ono,
Hokkaido University
Floer Theory for Lagrangian Submanifolds  Peter Ozsváth,
Columbia University
Heegard Diagrams and Holomorphic Disks  Katrin
Wehrheim, Massachusetts Institute of Technology
Construction of Topological Invariants Via Decomposition and Representation in a Symplectic Category  Shmuel Weinberger,
University of Chicago
Manifolds Whose Universal Covers Have Finite Type
2009
 PierreEmmanuel Caprace, University of Louvain
Isometry Groups of Proper CAT(0) Spaces  Benson Farb, University of Chicago
Some Universality Phenomena for PseudoAnosov Dilations  Tom Farrell, Binghamton University
Bundles with Negatively Curved Fibers  Cameron Gordon, University of Texas
Surface Subgroups of Doubles of Free Groups  Bruce Kleiner, Courant Institute
A New Proof of Gromov's Theorem on Groups of Polynomial Growth  Seonhee Lim, Cornell University
Volume Entropy of Buildings  Robert MacPherson, Institute for Advanced Study
The Geometry of Crystal Decompositions in Materials  Kasra Rafi, University of Chicago
Counting Closed Geodesics in a Stratum  Bertrand Rémy, University of Lyon
Rigidity and Quasiisomorphism Classes of Simple Twin Building Lattices  Anna Wienhard, Princeton University
Domains of Discontinuity
2010
 Miklos Abert,
University of Chicago
Graph Limits, Covering Towers, and the Dynamics of Profinite Actions
 Indira Chatterji, Ohio State University and Université d'Orléans
Subgroup Distortion and Bounded Cohomology  Karsten Grove, University of Notre Dame
Positive Curvature in the Presence of Symmetries  Jeremy Kahn, Stony Brook University
Essential Immersed Surfaces in Closed Hyperbolic 3Manifolds  Dan Margalit, Tufts University
Problems and Progress on Torelli Groups  Nikolay Nikolov, Imperial College London
Rank Gradient of Groups and Applications  Doug Ravenel, University of Rochester
The ArfKervaire Invariant Problem  Ed Swartz, Cornell University
Counting Faces Since Poincaré  Daniel Wise, McGill University
The Structure of Groups with a Quasiconvex Hierarchy  Robert Young, IHES
The Dehn Function of SL(n;Z)
2011

Matthew Foreman, University of California at Irvine
Classifying Measure Preserving Diffeomorphism of the Torus 
Rostislav Grigorchuk, Texas A&M University
Manifestations of the Lamplighter 
Olga Kharlampovich, McGill University
Algebraic Geometry for Groups 
Darren Long, University of California at Santa Barbara
Some Algebraic Applications of Real Projective Manifolds 
Jason Manning, State University of New York at Buffalo
Hyperbolic Dehn Filling of Spaces and Groups 
Yair Minsky, Yale University
Dynamics of Automorphism Groups: Ergodicity, Stability, and Topology 
Justin Moore, Cornell University
Amenability and Ramsey Theory 
Alexandra Pettet, Oxford University
Abstract Commensurators of the Johnson Filtration 
Slawek Solecki, University of Illinois at UrbanaChampaign
Fixed Points, Ramsey Theorems, Concentration of Measure, and Submeasures 
Simon Thomas, Rutgers University
The Complexity of the QuasiIsometry Relation for Finitely Generated Groups
2012

Ian Agol, University of California at Berkeley
The Virtual Haken Conjecture 
Francis Bonahon, University of Southern California
Hitchin Representations 
David Gabai, Princeton University
Volumes of Hyperbolic 3Manifolds 
Allen Hatcher, Cornell University
A 50Year View of Diffeomorphism Groups 
Jacob Lurie, Harvard University
The Siegel Mass Formula, Tamagawa Numbers, and Nonabelian Poincaré Duality 
Peter May, University of Chicago
What Is Equivariant Cohomology and What Is It Good For? 
Dusa McDuff, Barnard College / Columbia University
Embedding Questions in Symplectic Geometry 
John Milnor, Stony Brook University
Small Denominators: Adventures Through the Looking Glass 
Tom Mrowka, Massachusetts Institute of Technology
Instantons and Knots 
Walter Neumann, Barnard College / Columbia University
Local Metric Geometry of Complex Varieties 
Hee Oh, Brown University
Circle Packings and Ergodic Theory 
John Pardon, Stanford University
Totally Disconnected Groups (Not) Acting on ThreeManifolds 
Ronald Stern, University of California at Irvine
Pinwheels, Smooth Structures, and 4Manifolds with Euler Characteristic 3 
Peter Teichner, University of California at Berkeley / MPI Bonn
Iterated Disk Constructions in 4Manifold Topology  William Thurston, Cornell University
2015
 Mladen Bestvina, University of Utah
Boundaries of Hyperbolic Spaces (Friday Introductory Talk)
Boundaries of Some $Out(F_n)$Complexes  Matthew Strom Borman, Stanford University and IAS
Overtwisted Contact Structures  Cornelia Drutu, Oxford University
Fixed Point Properties and Proper Actions on Nonpositively Curved Spaces and on Banach Spaces  Talia Fernos, University of North Carolina Greensboro
The Roller Boundary and CAT(0) Cube Complexes  Koji Fujiwara, Kyoto University
Geometry of Contracting Geodesics (Friday Introductory Talk)
Handlebody Subgroups In A Mapping Class Group  Bob Gilman, Stevens Institute
Universal Groups of Prees  John Hubbard, Cornell University
Parabolic Blowups  Denis Osin, Vanderbilt University
Highly Transitive Actions, Mixed Identities, and Acylindrical Hyperbolicity  Ori Parzanchevski, Princeton University and IAS
High Dimensional Expanders  Ana Rita Pires, Fordham University
The Topology of Toric Origami Manifolds
2016
 Karim Adiprasito, Hebrew University of Jerusalem
Combinatorial Hodge Theory of Manifolds, Geometries, and Minkowski Weights  Laura Anderson, Binghamton University
Phased Matroids and Matroids Over Hyperfields  Anders Björner, Royal Institute of Technology (KTH)
Topological Combinatorics — an Introduction and Retrospective  Florian Frick, Cornell University
Intersection Patterns of Finite Sets and of Convex Sets  Patricia Hersh, North Carolina State University
Representation Stability and $S_n$Module Structure in the Homology of the Partition Lattice  Matthew Kahle, Ohio State University
Topology of Random Simplicial Complexes (introductory talk)
A Bouquet of Spheres (research talk)  Greg Kuperberg, University of California at Davis
Geometric Topology Meets Computational Complexity  Ciprian Manolescu, University of California at Los Angeles
The Triangulation Conjecture  Emmy Murphy, Massachusetts Institute of Technology
Flexibility in High Dimensional Contact Geometry  Bena Tshishiku, Stanford University
Obstructions to Nielsen Realization  Günter Ziegler, Freie Universität Berlin
Geometry vs. Topology: On 4Polytopes and 3Spheres
2017
 David Ayala, Montana State University
Factorization Homology and TQFTs  Andrew Blumberg, University of Texas at Austin
The Kunneth Theorem for Topological Periodic Cyclic Homology  Moira Chas, Stonybrook University
Computer Driven Questions, Pretheorems and Theorems in Geometry  Dan Freed, University of Texas at Austin
Remarks About the Interface of Topology and Physics (introductory talk)
Bordism and Topological Phases of Matter  Leonard Gross, Cornell University
The Ground State Transformation  Kathryn Hess, École Polytechnique Fédérale de Lausanne
Configuration Spaces of Products  Vlad Markovic, California Institute of Technology
Caratheodory's Metrics on Teichmüller Spaces  Kate Poirier, The City University of New York
Fatgraphs for String Topology  Hiro Lee Tanaka, Harvard University
Bringing More Homotopy Theory to Symplectic Geometry  Susan Tolman, University of Illinois at Urbana
NonHamiltonian Circle Actions with Isolated Fixed Points  Jonathan Weitsman, Northeastern University
On the Geometric Quantization of (Some) Poisson Manifolds
2018
 Tara Brendle, University of Glasgow
Normal Subgroups of Mapping Class Groups  Thomas Church, Stanford University
New Methods for Finite Generation  Kazuo Habiro, Kyoto University
HochschildMitchell Homology of Stratified Linear Categories  David Jordan, University of Edinburgh
Braided Tensor Categories and the Cobordism Hypothesis  Liat Kessler, Cornell University
Equivariant Cohomology Distinguishes Circle Actions on a Symplectic FourManifold  Mikhail Khovanov, Columbia University
Categorification in Topology and Representation Theory and
How to Category the Ring of Integers with Two Inverted  Ajay Ramadoss, Indiana University
Representation Homology of Spaces  Brooke Shipley, University of Illinois at Chicago
Coalgebras, coTHH, and KTheory  Vladimir Turaev, Indiana University
Introduction to TQFTs and HQFTs and
Brackets, Cobrackets, and Double Brackets in the World of Loops  Helen Wong, Carleton College
Representations of Kauffman Bracket Skein Algebras of a Surface
2019
 Jonathan Barmak, Universidad de Buenos Aires
The Winding Invariant and the AndrewsCurtis Conjecture  Ruth Charney, Brandeis University
Beyond Hyperbolicity: Boundaries of NonHyperbolic Spaces  Steve Ferry, Rutgers University and Binghamton University
Counterexamples to the BingBorsuk Conjecture  Dave Futer, Temple University
Special Covers of Alternating Links  Anthony Genevois, Université d'Orsay
Cubical Geometry of Braided Thompson's Group brV  Chris Kapulkin, University of Western Ontario
Homotopy Type Theory and Internal Languages of Higher Categories  Alexander Kupers, Harvard University
Diffeomorphisms of Disks  Mona Merling, University of Pennsylvania
Equivariant hCobordisms and Algebraic KTheory  Alan Reid, Rice University
Profinite Rigidity  Inna Zakharevich, Cornell University
Quillen's Devissage in Geometry
2020
Festival cancelled due to COVID19 crisis.
2021
 Agnes Beaudry, University of Colorado Boulder
Homotopy theory and phases of matter  Lvzhou Chen, University of Texas, Austin
Stable torsion length  Jeremy Hahn, Massachusetts Institute of Technology
Manifolds with at most three homology groups  Sebastian Hensel, University of Munich
Rotation Sets and Fine Curve Graphs  Sarah Koch, University of Michigan
Exploring Dynamical Moduli Spaces  Kate Ponto, University of Kentucky
Mortia equivalence and traces (and induction for characters and Euler characteristics for fibrations and ....)  Manuel Rivera, Purdue University
A quadratic equation which determines the fundamental group  Federico Rodriguez Hertz, Pennsylvania State University
Rigidity via potentials  Nick Salter, Columbia University
Topology of strata of translation surfaces: an unfortunately comprehensive survey  Richard Schwartz, Brown University
The spheres of Sol  Matthew Stover, Temple University
A geometric characterization of arithmeticity  Steve Trettel, Stanford University
What do 3manifolds look like?
2022
Tarik Aougab, Haverford College
Detecting covers, simple closed curves, and Sunada's construction
▾ Given a pair of finite degree (not necessarily regular) covers (p,X),(q,Y) of a finite type surface S, we show that the covers are equivalent if and only if the following holds: for any closed curve gamma on S, some power of gamma admits an embedded lift to X if and only if some power of gamma admits an embedded lift to Y. We apply this to study the wellknown construction of Sunada which yields pairs of hyperbolic surfaces (X,Y) that are not isometric but that have the same unmarked length spectrum. In particular we show that the lengthpreserving bijection from closed geodesics on X to those on Y arising from the Sunada construction never sends simple closed geodesics to simple closed geodesics. We also show that lengthisospectral surfaces arising from several of the most wellknown manifestations of the construction are not simple length isospectral. Even more, we construct lengthisospectral hyperbolic surfaces so that for each finite n, the set of lengths corresponding to closed geodesics with at most n self intersections disagree. This represents joint work with Maxie Lahn, Marissa Loving, and Nicholas Miller. 
Ian Biringer, Boston College
The space of subgroups of PSL(2,R)
▾ We’ll describe some features of the global topology of the space Sub(G) of all closed subgroups of G=PSL(2,R), equipped with the Chabauty topology. The quotient of the hyperbolic plane by the action of a discrete subgroup of G is a hyperbolic 2orbifold, and we will mostly focus on sets of subgroups where the quotient orbifold has a fixed finite topological type, and their closures in Sub(G). 
Aaron Calderon, Yale University
Long curves on hyperbolic surfaces
▾ In her thesis, Maryam Mirzakhani counted the number of simple closed curves on a (real) hyperbolic surface of bounded length. This breakthrough theorem and the subsequent explosion of related results use techniques and draw inspiration from Teichmüller theory, symplectic geometry, surface topology, and homogeneous dynamics. In this talk, I’ll survey these connections as well as discuss answers to some qualitative strengthenings: what do long curves look like on a hyperbolic surface? And what do hyperbolic surfaces with long curves look like? Answers to these questions represent joint work with Francisco AranaHerrera and James Farre, respectively. 
Josh Greene, Boston College
Peg problems
▾ I will talk about joint work with Andrew Lobb related to Toeplitz's square peg problem, which asks whether every (continuous) Jordan curve in the Euclidean plane contains the vertices of a square. Specifically, we show that every smooth Jordan curve contains the vertices of a cyclic quadrilateral of any similarity class. I will describe the context for the result and its proof, which involves symplectic geometry in a surprising way. 
Sara Maloni, University of Virginia
dPleated Surfaces
▾ Pleated surfaces are an important tool introduced by Thurston to study hyperbolic 3manifolds and can be described as piecewise totally geodesic surfaces immersed in the 3manifold and bent along a geodesic lamination. Bonahon generalized this notion to representations of surface groups in PSL_2(C) and described a holomorphic parametrization of the resulting open chart of the character variety in term of shearbend cocycles. In this talk I will discuss joint work with Martone, Mazzoli and Zhang, where we generalize this theory to surface group representations in PSL_d(C). In particular, I will discuss the notion of dpleated surfaces, and their holomorphic parametrization. 
Dusa McDuff, Barnard College
Symplectic embeddings and recursive patterns
▾ One of the simplest measurements you can make of the "size" of a compact symplectic manifold X is its Gromov width that measures the capacity of the largest ball that embeds into it. More generally, one can study the size of the largest ellipsoid of a given eccentricity that embeds into X. This function of the eccentricity has been (partially) calculated for certain 4dimensional targets, such as the 4ball or its onepoint blowup, and turns out to have intricate arithmetic properties. This talk, which will be aimed at a nonspecialized audience, will describe some recent work with Nicki Magill and Morgan Weiler about the properties of this function when the target is a ball that has been blown up once with weight b. 
Arpon Raksit, Massachusetts Institute of Technology
Motivic filtrations on topological Hochschild homology
▾ Topological Hochschild homology (THH) is an invariant of associative ring spectra, closely related to algebraic Ktheory. Bhatt–Morrow–Scholze defined a "motivic filtration" on the THH of ordinary commutative rings, after completion at a prime number p, relating it to invariants (new and old) in padic Hodge theory. These new structures have led to many advancements in the study of algebraic Ktheory and in arithmetic geometry. In this talk, I will try to give an accessible overview of this landscape of invariants, and then discuss a new construction of the motivic filtration on THH, with the advantages that it is quite simple to state and applies not only to ordinary commutative rings but a broad class of commutative ring spectra; the new work is joint with Jeremy Hahn and Dylan Wilson. 
Emily Riehl, Johns Hopkins University
Absolute lifting diagrams and formal category theory
▾ Left and right lifting diagrams, like the dual left and right (Kan) extensions, can be defined in any 2category. In this talk, we'll make the case that absolute lifting diagrams are particularly expedient for formal category theory, using them to provide a streamlined version of the classical proof that left adjoints preserve colimits and right adjoints preserve limits. This is joint work with Dominic Verity. 
Genevieve Walsh, Tufts University
Planar boundaries and parabolic subgroups
▾ Relatively hyperbolic groups generalize geometrically finite Kleinian groups acting on real hyperbolic space H^3. The boundaries of relatively hyperbolic groups generalize the limit sets of Kleinian groups. Since the boundary of H^3 is S^2, the limit set of every Kleinian group is planar. Can every relatively hyperbolic group with planar boundary be realized a Kleinian group? The answer is no, and we will give illustrative examples to show the many ways this can fail. However, we prove that if G is oneended, (G,P) is relatively hyperbolic, and the boundary of (G,P) is planar and without cut points, then all the peripheral subgroups are surface groups. This is consistent with G being a Kleinian group. We also formulate a conjecture about the general situation (which is an extension of the Cannon Conjecture). This is joint work with Chris Hruska. 
Jenny Wilson, University of Michigan
The highdegree rational cohomology of the special linear group
▾ In this talk I will describe some current efforts to understand the highdegree rational cohomology of SL_n(Z), or more generally the cohomology of SL_n(R) when R is a number ring. Although the groups SL_n(R) do not satisfy Poincare duality, they do satisfy a twisted form of duality, called (virtual) BieriEckmann duality. Consequently, their highdegree rational cohomology groups are governed by an SL_n(R)representation called the Steinberg module. The key to understanding these representations is through studying the topology of certain associated simplicial complexes. I will survey some results, conjectures, and ongoing work on the Steinberg modules, and the implications for the cohomology of the special linear groups. This talk includes work joint with Brück, Kupers, Miller, Patzt, Sroka, and Yasaki. The talk is geared for topologists and will not assume prior expertise on the cohomology of arithmetic groups! 
2023
David Gay, University of Georgia, Malott 251
On the smooth mapping class group of the 4sphere
▾ I will talk about a group which might be the trivial group, in which case either the results I will discuss are pointless or are a useful step in the direction of proving triviality! But the group might not be trivial, which is one of the many examples of how little we really understand about dimension 4. The group in question is the smooth mapping class group of the 4sphere, namely the group of smooth isotopy classes of orientationpreserving selfdiffeomorphisms of S^4. Using ideas going back to Cerf I will explain why every element of this group can be described by loops of 2spheres in connected sums of S^2XS^2's, that under favorable conditions (which might always hold), this description can be reduced to a loop of circles in S^1XS^3 and that the subgroup of the smooth mapping class group that arises under these favorable conditions is at worst a cyclic group of order 2. The last part involves finding explicit generators and relations for the subgroup in question. 
Robert E. Gompf, University of Texas at Austin, Malott 251
Contact and Engel Topology
▾ Contact structures, like foliations, are intimately sensitive to the topology of their ambient manifolds, and have been used to prove deep results in 3manifold topology. The contact condition is an example of a "topologically stable" condition for kplane distributions on nmanifolds. Such conditions were classified by Cartan at the turn of the previous century. The one topologically stable condition that is still poorly understood is the Engel condition. Engel structures are 2plane fields that only exist on 4manifolds. It is still unknown what, if anything, they might tell us about 4manifold topology. After discussing background, we will take a first step in this direction by exploring an Engel analogue of transverse knots in contact 3manifolds. 
Thomas Haettel, IUT Montpellier, Malott 251
Group actions on injective metric spaces
▾ A metric space is called injective if any family of pairwise intersecting balls has a nonempty global intersection. Such injective metric spaces enjoy many properties typical of nonpositive curvature, notably the existence of a convex geodesic bicombing. We will show that many groups of geometric nature have an interesting action by isometries on an injective metric space, including Gromovhyperbolic groups, braid groups, lattices in Lie groups and mapping class groups of surfaces. 
Jean Lafont, Ohio State University, Malott 251
Cubulating strict hyperbolizations
▾ The strict hyperbolization process developed by Charney and Davis inputs a simplicial complex, and outputs a piecewise hyperbolic, locally CAT(1) space. This process has been used to produce aspherical manifolds with various interesting properties. I'll briefly review the strict hyperbolization process, and then explain how to construct an action of the fundamental group of the resulting space on a CAT(0) cube complex with controlled cell stabilizers. This is joint work with Lorenzo Ruffoni (Tufts). 
Maggie Miller, Stanford University, Malott 251
Slice obstructions from genus bounds in definite 4manifolds
▾ Minimum genus bounds for surfaces representing specific homology classes in some 4manifolds can be used to show that certain knots in S^3 are not slice. For example, one genus bound due to Bryan in the 1990s can be used to show that the (2,1)cable of the figure eight knot is not slice, recovering a result of Dai—Kang—Mallick—Park—Stoffregen from last summer based on Heegaard Floer (and related) homology. I’ll talk about this construction, underlying motivation, and some interesting open questions. This is joint work with Paolo Aceto, Nickolas A. Castro, JungHwan Park and András Stipsicz. 
Paige North, University of Pennsylvania, Malott 251
The univalence principle
▾ The Equivalence Principle is an informal principle asserting that equivalent mathematical objects have the same properties. For example, group theory has been developed so that isomorphic groups have the same grouptheoretic properties, and category theory has been developed so that equivalent categories have the same categorytheoretic properties (though sometimes other, ‘evil’ properties are considered). Vladimir Voevodsky established Univalent Foundations as a foundation of mathematics (based on dependent type theory) in which the Equivalence Principle for types (the basic objects of type theory) is a theorem. Later, versions of the Equivalence Principle for setbased structures such as groups and categories were shown to be theorems in Univalent Foundations. In joint work with Ahrens, Shulman, and Tsementzis, we formulate and prove versions of the Equivalence Principle for a large class of categorical and higher categorical structures in Univalent Foundations. Our work encompasses bicategories, dagger categories, opetopic categories, and more. Early versions and our generalization of the Equivalence Principle in Univalent Foundations rely on the fact that the basic objects  the types  can be regarded as spaces. That is, Univalent Foundations can be viewed as an axiomatization of homotopy theory and as such is closely related to Quillen model category theory. Univalent Foundations can also be viewed as a foundation of mathematics based not on sets, but on spaces. It is only the homotopical content of this foundation of mathematics that allows us prove something like the Equivalence Principle, something which is not possible in setbased foundations of mathematics, such as ZFC. 
Margaret Symington , Mercer University, Malott 251
From K3 surfaces to spheres and back
▾ I will describe the beginnings of a project to understand and visualize singular integral affine structures on the twosphere via rational polyhedra, integral affine unfoldings of them, and integral affine coordinate charts. Integral affine structures on the twosphere are induced by special Lagrangian fibrations of K3 surfaces, which are studied in the context of mirror symmetry in dimension four. (The polyhedral presentations are motivated the GrossSiebert approach to mirror symmetry on K3 surfaces.) More generally, the integral affine geometries are induced by almost toric structures on a symplectic K3 surface (symplectic fourmanifold diffeomorphic to a quartic surface in CP3). I will explain how the integral affine structures arise, what some of them look like, and what they reveal about the fibered fourmanifolds that produced them. 
Liam Watson, University of British Columbia, Malott 251
Khovanov homology and Conway sphere
▾ I will describe some of my joint work with Claudius Zibrowius and Artem Kotelskiy, which recasts BarNatan’s invariants for Conway tangles in terms of immersed curves. This gives rise to some unexpected structural results, and I will attempt to place these in context by explaining what they tell us about Khovanov homology for knots admitting an essential Conway sphere. 