Geometric Structures Working Seminar

Meetings in Semester 2 of 2026 take place on Wednesdays, 14:30–16:30, in the SMRI Collaboration Space (A12.301).

about the seminar

This is a working seminar on geometric and topological structures on manifolds amnd related topics. Lectures are given by the participants. Everyone interested in participating is welcome.

2026 – second semester

The plan for this semester is to cover two different topics (one after the other): 1) Expander graphs, and applications in mathematics and theoretical computer science 2) Lattice-based cryptography Get in touch with Stephan Tillmann or Clement Canonne to be added to the outlook group and mailing list!

2026 – first semester

This semester, we continue to join a working seminar on quantum computing, following Shor's lecture notes.

2025 – second semester

This semester, we're joining a working seminar on quantum computing, following Shor's lecture notes.

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