Stephan Tillmann

Geometric Structures Working Seminar

Meetings currently take place on Thursdays, 15:00–16:30.

about the seminar

This is a working seminar on geometric and topological structures on manifolds. Lectures are given by the participants. Everyone interested in participating is welcome. The focus in 2023 is on hyperbolic structures on surfaces and 3-manifolds. The focus in 2019 was on structures on 4-manifolds and trisections (Semester 1) and deformations of real projective structures (Semester 2). The focus in 2015-2016 was on moduli spaces of geometric structures on manifolds, and their connections with topology, group theory and higher Teichmüller theory.

2023 – second semester

References:

Farid Diaf and Andrea Seppi: The anti-de Sitter proof of Thurston's earthquake theorem, https://arxiv.org/abs/2306.03631
William Thurston: Earthquakes in two-dimensional hyperbolic geometry, Cambridge 1984.
Mareike Pfeil: Earthquakes in the hyperbolic plane, Master thesis, Heidelberg 2017.

Thursday, 3 August, 15:00–16:30, Carslaw 157-257: Thomas Le Fils: TBA
Thursday, 10 August, 15:00–16:30, Carslaw 157-257: Stephan Tillmann: A primer of hyperbolic geometry
Thursday, 17 August, 15:00–16:30, Carslaw 157-257: Grace Garden: Earthquake maps, I
Thursday, 24 August, 15:00–16:30, Carslaw 157-257: Sepehr Saryazdi: Earthquake maps, II
Thursday, 31 August, 15:00–16:30, Carslaw 157-257: Declan Zammit: Extending earthquakes to the boundary, I
Thursday, 7 September, 15:00–16:30, Carslaw 157-257: Grace Garden: Extending earthquakes to the boundary, II
Thursday, 14 September, 15:00–16:30, Carslaw 157-257: TBA: TBA
Thursday, 21 September, 15:00–16:30, Carslaw 157-257: TBA: TBA
Thursday, 28 September: Mid-semester break
Thursday, 5 October, 15:00–16:30, Carslaw 157-257: TBA: TBA
Thursday, 12 October, 15:00–16:30, Carslaw 157-257: TBA: TBA
Thursday, 19 October, 15:00–16:30, Carslaw 157-257: TBA: TBA
Thursday, 26 October, 15:00–16:30, Carslaw 157-257: TBA: TBA

2023 – first semester

References:

[FG1] David Futer and Francois Gueritaud: From angled triangulations to hyperbolic structures, Contemp. Math., 159-182 (2011).
[FG2] David Futer and Francois Gueritaud: Explicit angle structures for veering triangulations, AGT (2013).
Note: Everyone read the introduction of [FG1] and skim over Section 2. Talks start with Section 3.

Friday, 24 February, 14:00–16:00, Carslaw 373: James Morgan: FG1 Section 3
Friday, 3 March, 14:00–16:00, Carslaw 373: Sophie Ham: FG1 Section 3
Friday, 10 March, 14:00–16:00, Carslaw 373: Lucy Tobin: FG1 Section 3
Friday 17 March, 14:00–16:00, Carslaw 373: Youheng Yao: FG1 Section 4
Friday, 24 March, 14:00–16:00, Carslaw 373: Thomas Le Fils and Grace Garden: Milnor's work on volume and FG1 Section 4
Friday, 21 April, 14:00–16:00, Carslaw 373: Thomas Le Fils: FG1 Section 5
Friday, 28 March, 14:00–16:00, Carslaw 373: Rhuaidi Bourke: Exotic 4-d triangulations
Friday, 5 April, 14:00–16:00, Carslaw 373: Grace Garden: FG1 Section 6
Friday, 12 April, 14:00–16:00, Carslaw 373: Stephan Tillmann: Angle structures and normal surfaces after Casson
Friday, 19 May, 14:00–16:00, Carslaw 373: Sophie Ham: A result of Rivin on maxima on the boundary
Friday, 26 May, 14:00–16:00, Carslaw 373: James Morgan: Veering triangulations
Friday, 2 June, 14:00–16:00, Carslaw 373: Lucy Tobin: FG2, Section 2
Friday, 9 June, 11:00–13:00, Carslaw 373: Youheng Yao: FG2, Sections 3 & 4
Friday, 16 June, 11:00–13:00, Quad: Yossi Bokor Bleile: Applications of topological data analysis
Friday, 23 June, 11:00–13:00, Carslaw 380: Grace Garden: FG2, Section 5
Friday, 30 June, 11:00–13:00, Carslaw 380, 15min lightening talks: Reymond Akpanya (RWTH Aachen): A group-theoretic approach for constructing spherical interlocking assemblies; Thomas Le Fils: Random 3-manifolds after Thurston and Dunfield; James Morgan: The extended persistent homology transform; Youheng Yao: Parameterising PGL(3,C) representations after Zickert, Goerner and Garoufalidis
Friday, 7 July, 11:00–13:00, Carslaw 273: Thomas Le Fils: FG2, Section 6
Friday, 14 July, 11:00–13:00, Carslaw 273: Robert Tang (Xi'an Jiaotong-Liverpool University): Large-scale geometry of the Rips filtration
Friday, 28 July, 11:00–13:00, Carslaw 273: Lucy Tobin: On a combinatorial conjecture for 4-manifold triangulations

2020, 2021 and 2022

No formal meetings due to the COVID-19 pandemic.

2019 – second semester

Friday, 13 September, 11:00–13:00: Daryl Cooper: Deformations of Properly Convex Real Projective Structures I
Friday, 20 September, 10:00–12:00: Daryl Cooper: Deformations of Properly Convex Real Projective Structures II
Friday, 27 September, 10:00–12:00: Daryl Cooper: Deformations of Properly Convex Real Projective Structures III
Friday, 18 October, 10:00–12:00: Daryl Cooper: Deformations of Properly Convex Real Projective Structures IV
Friday, 1 November, 10:00–12:00: Daryl Cooper: Deformations of Properly Convex Real Projective Structures V

2019 – first semester

Friday, 6 May, 10:00–12:00: Boris Lishak: Trisections via handle decompositions
Friday, 17 May, 14:00–16:00: Behrouz Taji: Ample line bundles and the Kodeira embedding theorem
Monday, 20 May, 10:00–12:00: Behrouz Taji: Branched coverings and trisections
Monday, 3 June, 10:00–12:00 in 535A: Henry Segerman: Ray-marching and ray-tracing in hyperbolic space

2017 – first semester

References:

Joel Hass and Peter Scott: Intersections of curves on surfaces, Israel J. Math. 51 (1985), no. 1-2, 90–120.

Friday, 10 February, 10:00–12:00 (Week 1): Robert Haraway: Intersections of curves on surfaces, I
Friday, 17 February, 10:00–12:00 (Week 2): Dominic Tate: Intersections of curves on surfaces, II
Friday, 24 February, 10:00–12:00 (Week 3): Alex Casella: Intersections of curves on surfaces, III
Friday, 10 March, 10:00–12:00 (Week 4): Dickson Annor: Intersections of curves on surfaces, IV
Friday, 7 April, 10:00–12:00 (Week 5): Boris Lishak: Intersections of curves on surfaces, V
Friday, 5 May, 14:00–16:00 (Week 8): Erwan Rousseau (Aix-Marseille): On a theorem of Bogomolov
Friday, 12 May, 14:00–16:00 (Week 9): Robert Haraway: MOM-1.5 topology, part 1
Friday, 19 May, 14:00–16:00 (Week 10): Craig Westerland (Minnesota): Braid groups and shuffle algebras
Friday, 26 May, 14:00–16:00 (Week 11): Robert Haraway: MOM-1.5 topology, part 2
Friday, 2 June, 14:00–16:00 (Week 12): Montek Gill (Michigan): TBA
Friday, 9 June, 14:00–16:00 (Week 13): TBA: TBA
Friday, 16 June, 10:00–12:00, Location TBA (Week 14): Charlie Katerba (Montana): TBA

2016 – second semester

References:

Papers by Weinstein, Goldman and Fock-Goncharov

Friday, 29 July, 11:00: Robert Haraway: The MOM project
Thursday, 8 September (Week 6): Alex Casella: Basics on Symplectic and Poisson Structures
Thursday, 22 September (Week 7): Alex Casella: On Goldman’s Poisson Structure and Formula
Thursday, 6 October (Week 9): Alex Casella: Fock and Goncharov Moduli space and its Poisson Structure
Thursday, 13 October (Week 10): Alex Casella: Compatibility of Poisson Brackets I - Monodromy operator
Thursday, 20 October (Week 11): Alex Casella: Compatibility of Poisson Brackets II - Tunnels and their contribution
Thursday, 27 October (Week 12): Alex Casella: Compatibility of Poisson Brackets III - Conclusion of the proof
Thursday, 25 November (11:00–11:30): Dominic Tate: Bounded Functions on Triangulated Surfaces with Framed Convex Projective Structure
Thursday, 25 November (11:30–12:00): Alex Casella: Fock and Goncharov Moduli Space and its Poisson Structure

2016 – first semester

Tuesday, 8 March (Week 2): James Parkinson: Introduction to Euclidean buildings, I
Tuesday, 15 March (Week 3): James Parkinson: Introduction to Euclidean buildings, II
Tuesday, 22 March (Week 4): Stephan Tillmann: Degenerations of hyperbolic structures and actions on trees
Tuesday, 4 April (Week 5): Eric Chesebro (Montana): Geometry of 2-bridge links
Tuesday, 11 April (Week 6): Robert Haraway is giving a talk at UNSW
Tuesday, 18 April (Week 7): Alex Casella: More about buildings, I
Tuesday, 25 April (Week 8): Alex Casella: More about buildings, II
Tuesday, 31 May (Week 13): Discussion: Fock and Goncharov revisited
Tuesday, 14 June (Week 15): Robert Tang (Oklahoma): All about the curve complex
Tuesday, 21 June: Kate Turner (EPFL): Algorithms to compute persistent homology – cancelled
Tuesday, 30 June: Robert Tang (Oklahoma): Electrified Teichmüller space and subsurface projection

2015 – second semester

References:

"Moduli spaces of convex projective structures on surfaces" by Fock and Goncharov
"On Fock-Goncharov coordinates of the once-punctured torus group" by Yuichi Kabaya

Tuesday, 21 July (Week 0): Montek Gill: Kabaya, Sections 1–3
Tuesday, 28 July (Week 1): Montek Gill: Kabaya, Sections 3–4
Tuesday, 4 August (Week 2): Stephan Tillmann: Properly convex projective structures on surfaces
Tuesday, 11 August (Week 3): Alex Casella: Fock-Goncharov, Section 2.1
Tuesday, 18 August (Week 4): Alex Casella: Fock-Goncharov, Section 2.2
Tuesday, 25 August (Week 5): Robert Haraway: Fock-Goncharov, Section 2.3
Tuesday, 1 September (Week 6): Robert Haraway: Fock-Goncharov, Section 2.3
Tuesday, 8 September (Week 7): Robert Haraway: Fock-Goncharov, Section 2.4
Tuesday, 15 September (Week 8): Alex Casella: Fock-Goncharov, Section 2.5
Tuesday, 22 September (Week 9): Alex Casella: Fock-Goncharov, Section 2.6–2.7
Tuesday, 6 October (Week 10): Discussion
Tuesday, 13 October (Week 11): Discussion
Tuesday, 20 October (Week 12): Discussion

2015 – first semester

Tuesday, 10 March (Week 2): Stephan Tillmann: Developing map and holonomy, I
Tuesday, 17 March (Week 3): Stephan Tillmann: Developing map and holonomy, II
Tuesday, 24 March (Week 4): Montek Gill: Triangulations, fundamental group and covering spaces
Tuesday, 14 April (Week 6): Alex Casella: Thurston's hyperbolic gluing equations, I
Tuesday, 21 April (Week 7): Alex Casella: Thurston's hyperbolic gluing equations, II
Tuesday, 28 April (Week 8): Grace Garden: The mapping class group, I
Tuesday, 5 May (Week 9): Grace Garden: The mapping class group, II
Tuesday, 12 May (Week 10): Dominic Tate: The Teichmüller space of a surface, I
Tuesday, 26 May (Week 12): Dominic Tate: The Teichmüller space of a surface, II
Tuesday, 2 June (Week 13): Hemanth Saratchandran (Oxford): Kirby calculus, I
Tuesday, 9 June (Week 14): Hemanth Saratchandran (Oxford): Kirby calculus, II

references

"Invariant subspaces for some surface groups acting on A2-Euclidean buildings" by Anne Parreau
"Three-dimensional Orbifolds and Cone-Manifolds" by Daryl Cooper, Craig D. Hodgson and Steven P. Kerckhoff
"Ideals, Varieties and Algorithms" by David Cox, John Little and Donal O'Shea
"Fuchsian Groups" by Svetlana Katok
"Configurations of flags and representations of surface groups in complex hyperbolic geometry" by Julien Marche and Pierre Will
"Notes on Geometry and 3-Manifolds" by Walter Neumann
"The geometry and topology of three-manifolds" by Bill Thurston
"Higher Teichmüller Spaces: from SL(2,R) to other Lie groups" by Marc Burger, Alessandra Iozzi and Anna Wienhard