# Informal Friday Seminar

The Informal Friday Seminar is a space where members of our research group can explain interesting things to each other in a casual setting.

The rules of the seminar are the following:

Any question/additional explanation from the audience is allowed.

Ego out the window.

Examples, examples, examples.

The seminar is intended to be conversational, so come ready to engage. If you choose to give an IFS talk, it's important to know that part of the IFS philosophy is that learning is not linear. In other words, it if perfectly acceptable to give a talk that is a prerequisite for a talk that already happened.

When: Fridays, 9:00-11:00am AEST.

Where: In-person (SMRI Seminar Room at Macleay Building (A12) Room 301).

If you would like to join, email june.park@sydney.edu.au.

2024 Semester 2 Schedule:

Friday, August 9: Andrej Bauer, What is type theory?

Friday, August 16: Andrej Bauer, The anatomy of a proof assistant.

Friday, August 23: Ashvni Narayanan, TBA.

Friday, August 30: Ashvni Narayanan, TBA.

Friday, September 6: Pieter Roffelsen, A multi-valued perspective on Hilbert's 21st problem (Part I).

Friday, September 13: Pieter Roffelsen, A multi-valued perspective on Hilbert's 21st problem (Part II).

Friday, September 20: TBD.

Friday, September 27: TBD.

Friday, October 4: TBD.

Friday, October 11: TBD.

Friday, October 18: TBD.

Friday, October 25: TBD.

Friday, November 1: TBD.

Friday, November 8: TBD.

Friday, November 15: TBD.

Friday, November 22: TBD.

2024 Semester 1 Schedule:

Friday, 8 March: Grace Garden, Character varieties and essential surfaces. (Notes)

Friday, 15 March: Chris Hone, Six functor formalism and geometric extensions. (Notes)

Friday, 22 March: Finn Klein, Schubert Calculus in Grassmannian by examples. (Notes)

Friday, 5 April: Finn Klein, Schubert Calculus in Grassmannian by examples.

Friday, 12 April: James Morgan, Introduction to Hyperbolic Knots. (Notes)

Friday, 19 April: James Morgan, Introduction to Hyperbolic Knots.

Friday, 26 April: Jeremie Guilhot, Hecke Algebras and Kazhdan-Lusztig theory in the unequal parameter case.

Friday, 3 May: Jeremie Guilhot, Hecke Algebras and Kazhdan-Lusztig theory in the unequal parameter case.

Friday, 10 May: Alan Stapledon, Unimodality via anisotropy: Characteristic 2'eys, too right!

Friday, 17 May: Alan Stapledon, Unimodality via anisotropy: Characteristic 2'eys, too right!

Friday, 24 May: Sam Jeralds, Conformal blocks and fusion products of Lie algebra representations. (Notes)

Friday, 31 May: Sam Jeralds, Conformal blocks and fusion products of Lie algebra representations. (Notes)

Friday, 7 June: Tasman Fells, Quantisation (Notes)

Friday, 14 June: Tasman Fells, Quantisation (Notes)

Friday, 21 June: Joe Newton, Computations in unusual tensor categories. (Notes)

Friday, 28 June: Matthew Emerton, Localizing modules over non-commutative rings, (derived) Morita theory, and related topics

2023 Semester 2 Schedule:

Friday, August 4: Roman Bezrukavnikov, Center and Cohomology.

Friday, August 11: Daniel Tubbenhauer, Matrix problems (Part I).

Friday, August 18: Daniel Tubbenhauer, Matrix problems (Part II).

Friday, August 25: Alex Sherman, Kac-Moody algebras: To affinity and beyond!

Friday, September 1: Alex Sherman, Kac-Moody algebras: To affinity and beyond!

Friday, September 8: Thomas Le Fils, Introduction to Teichmüller spaces.

Friday, September 15: Dominic Williamson, Quantum codes from Homology.

Friday, September 22: Dominic Williamson, Quantum codes from homology.

Friday, October 6: Oded Yacobi, Categorical dynamics.

Friday, October 13: Oded Yacobi, Categorical dynamics.

Friday, October 20: Bregje Pauwels, Representability.

Friday, October 27: Bregje Pauwels, Representability.

Friday, November 3: Tasman Fell, Representation theory and quantum mechanics. Notes

Friday, November 10: Gus Lehrer, The fundamental Theorems of Invariant Theory.

Friday, November 17: Don Taylor, Finite groups of Lie type.

Friday, November 24: Hannah Bryant, Introduction to Egyptian Hieroglyphs: Basic history and translation.

2023 Semester 1 Schedule:

Friday, February 24: Ivan Angiono, Hopf, Hopf, Hopf.

Friday, March 3: Catharina Stroppel, Approaching Springer fibers following the old Greeks.

Friday, March 10: Dominic Williamson, What's the deal with quantum computing? Part I.

Friday, March 17: Dominic Williamson, What's the deal with quantum computing? Part II.

Friday, March 24: Alex Sherman, What drives us to derive I

Thursday, March 30 (!): Alex Sherman, What drives us to derive II (Carslaw 273)

Friday, April 7: No IFS (Good Friday)

Friday, April 14: No IFS (mid-semester break)

Friday, April 21: Daniel Tubbenhauer, A primer on computer algebra (Quad S223)

Friday, April 28: Alistair Savage, When bosons think they're fermions (and vice versa) I

Friday, May 5: Alistair Savage, When bosons think they're fermions (and vice versa) II

Friday, May 12: Joe Baine, The moduli space of algebraic curves I (Quad: SMRI Terrace)

Friday, May 26: Anne Thomas, Bass-Serre theory I

Friday, June 2: Anne Thomas, Bass-Serre theory II

Friday, June 9: Joe Baine, The moduli space of algebraic curves II

2022 Semester 2 Schedule:

Friday, August 5: Chris Hone, What are modular forms and why are they useful? Notes

Friday, August 12: Chris Hone, Taniyama-Shimura and the modular symmetry of point counting for rational elliptic curves. Notes

Friday, August 19: Geordie Williamson, What are polytopes like?

Friday, August 26: Geordie Williamson, How many vertices, edges, faces, ... can a polytope have?

Friday, September 2: Joel Gibson, GCT Part I: An introduction to complexity theory. Notes, Colab Notebook, Karp's problems

Friday, September 9: Alan Stapledon, Part 1: The local h-polynomial rises.

Friday, September 16: Joel Gibson, GCT Part 2: Complexity Theory and Representation Theory.

Friday, September 23: Alan Stapledon, Part 2: The local h-polynomial rises.

Friday, September 30: Break

Friday, October 7: Bregje Pauwels: Lorentzian polynomials I (the combinatorics). Notes

Friday, October 14: No IFS (due to strike)

Friday, October 21: Bregje Pauwels: Lorentzian polynomials II (the geometry). Notes

Friday, October 28: Finn Klein: Toric Varieties I. Notes

Friday, November 4: Emilien Zabeth: Jantzen's Generic Decomposition Patterns and periodic polynomials. Notes

Friday, November 11:

Emilien Zabeth: Jantzen's Generic Decomposition Patterns and periodic polynomials II. (9:00-11:00am). Notes

Finn Klein: Toric Varieties II. (3:00-5:00pm). NotesFriday, November 18: Jonathan Spreer: Triangulating Manifolds

Friday, November 25: Geordie Williamson: Total positivity for beginners like me

November 28-December 2: Come to Tensor Categories in Sydney!

December 6 - December 9: Come to the 2022 AustMS Meeting at UNSW!

2022 Semester 1 Schedule:

Friday, March 4: Alex Bishop, An introduction to geometric group theory I (9:00-11:00am, Quad S225 or online)

Friday, March 11: Alex Bishop, An introduction to geometric group theory II (9:00-11:00am, Quad S225 or online)

Friday, March 18: Daniel Tubbenhauer, In and around the origin of quantum groups I (9:00-11:00am, Quad S225 or online) Notes

Friday, March 25: Daniel Tubbenhauer, In and around the origin of quantum groups II (9:00-11:00am, Quad S225 or online) Notes

Friday, April 8, 15, 22: No IFS. Come to the Farewell conference for Anthony Henderson instead!

Friday, April 29: Joe Baine, Lattices in Lie Groups I (online) Notes

Friday, May 6: Chris Hone, The modularity theorem (9:00-11:00am, Quad S225 or online) Notes

Friday, May 20: Daniel Tubbenhauer, Subfactors in a nutshell (9:00-11:00am, Quad S225 or online) Notes

Friday, May 27: Joe Baine, Lattices in Lie Groups II (online) Notes

Friday, June 3: Leonardo Maltoni, Introduction to Discrete Hodge Theory I (9:00-11:00am, Quad S225 or online) Notes

Friday, June 10: Leonardo Maltoni, Introduction to Discrete Hodge Theory II (9:00-11:00am, Quad S225 or online) Notes

2021 Semester 2 Schedule:

Friday, August 27: Bregje Pauwels, Spectra for beginners (9:00-11:00am, online) Notes

Friday, September 3: Chris Hone, Topological K-theory (9:00-11:00am, online) Notes

Friday, September 10: Bregje Pauwels, Spectra for beginners II (9:00-11:00am, online) Notes

Friday, September 17: Joshua Ciappara, Model categories (9:00-11:00am, online) Notes

Friday, September 24:

Bregje Pauwels, Brave new rings (9:00-11:00am, online) Notes

Geordie Williamson, Motives for beginners (3:00-5:00pm, online) NotesFriday, October 1: No IFS. Come to the conference Representation theory's hidden motives instead!

Friday, October 8:

Chris Hone, Cobordism and MU (9:00-11:00am, online) Notes

Gaston Burrull, Introduction to Schubert calculus and flag varieties (3:00-5:00pm, online) NotesFriday, October 15: Bregje Pauwels, K-theory, spectra and the Riemann-Roch theorem (9:00-11:00am, online) Notes

Friday, October 22:

Chris Hone, MU and formal group laws (9:00-11:00am, online) Notes

Geordie Williamson, Moment maps and moment graphs (3:00-5:00pm, online) NotesFriday, October 29:

Joshua Ciappara, Atiyah-Hirzebruch spectral sequence (9:00-11:00am, online) Notes

Joe Baine, Combinatorial Geometries, Convex Polyhedra and Schubert Cells (4:00-6:00pm, online) NotesFriday, November 5:

Bregje Pauwels, Localisations and completions at primes (9:00-11:00am, online) Notes

Gaston Burrull, Hard Lefschetz and the shape of Bruhat intervals (3:00-5:00pm, online) NotesFriday, November 12:

Chris Hone, Computing with the Serre spectral sequence and localisation (9:00-11:00am, online) Notes

Geordie Williamson, Examples in the geometry of Schubert varieties (3:00-5:00pm, online)Friday, November 19:

Bregje Pauwels, Cohomology operations (9:00-11:00am, online) Notes

Joel Gibson, Sheaves on moment graphs and the Braden-MacPherson algorithm (3:00-5:00pm, online) NotesFriday, November 26:

Aleksandra Utiralova, Harish-Chandra bimodules in complex rank (9:00-11:00am, online) Notes

Geordie Williamson, More singularities for Schubert varieties (3:00-5:00pm, online) NotesFriday, December 3: Geordie Williamson, The combinatorial invariance conjecture (9:00-11:00am, Quad S227 or online) Notes

Friday, December 10: No IFS. Come to the AUSTMS conference!

2021 Semester 1 Schedule:

Friday, March 6: Anthony Henderson, Slodowy slices for large nilpotent orbits in simple Lie algebras (9:00-11:00am, Quad S225)

Friday, March 12: Anna Romanov, Affine Whittaker modules and twisted D-modules on the affine flag variety (9:00-11:00am, Quad S225)

Friday, March 19: Joe Baine, p-Kazhdan-Lusztig polynomials for minuscule and cominuscule Schubert varieties (9:00-11:00am, online)

Friday, March 26: Bregje Pauwels, Fields! (9:00-11:00am, Quad S225)

Friday, April 2: public holiday, no IFS

Friday, April 9: Giulian Wiggins, When is a category of perverse sheaves a highest weight category? (9:00-11:00am, Quad S225)

Friday, April 23: Oded Yacobi, Cyclic Sieving and Categorification (9:00-11:00am, Quad S225)

Friday, April 30: Edmund Heng (ANU), A new (categorical) look on generalised braid groups (9:00-11:00am, Quad S225)

Friday, May 7: Chris Hone, The Dold Kan theorem (9:00-11:00am, Quad S225)

Friday, May 14: Emily Cliff, Smooth 2-groups and moduli spaces of principal 2-group bundles (9:00-11:00am, online)

Friday, May 21: Josh Ciappara, Actions of the Hecke category via Smith--Treumann theory (9:00-11:00am, online)

Friday, May 28: Geordie Williamson, Spectra in representation theory (9:00-11:00am, Quad S225)

Friday, June 4: Kevin Coulembier, Tensor products of modular representations (9:00-11:00am, Quad S225)

Friday, June 11: Joel Gibson, Computation in affine Weyl groups and reflection subgroups (9:00-11:00am, Quad S225)

2020 Semester 2 Schedule:

Friday, July 31: Ting Xue, Derived Satake equivalence (3:00-5:00pm, ONLINE)

Friday, August 7: Anna Romanov, Vogan duality II (3:00-5:00pm, ONLINE)

Friday, August 14: Linyuan Liu, The equivariant derived category, part I (3:00-5:00pm, ONLINE)

Friday, August 21: Linyuan Liu, The equivariant derived category, part II (3:00-5:00pm, ONLINE)

Friday, August 28: Elijah Bodish, Generators and relations for Rep(G) (3:00-5:00pm, ONLINE)

Friday, Sept 4: no IFS

Friday, Sept 11: Anthony Henderson, Hilbert schemes, Part I (Introduction)(9:00am-11:00am, ONLINE)

Friday, Sept 18: Anthony Henderson, Hilbert schemes, Part II (H is smooth) (9:00am-11:00am, Carslaw 453 + ONLINE)

Friday, Sept 25: Emily Cliff, Hilbert schemes, Part III (The universal family on H) (9:00am-11:00am, ONLINE)

Friday, October 2: Anthony Henderson, Hilbert schemes, Part IV (Kleinian singularities 1) (9:00am-11:00am, Carslaw 453 + ONLINE)

Friday, October 9: Joe Baine , Hilbert schemes, Part V (Quotients and GIT) (9:00am-11:00am, ONLINE)

Friday, October 16: Emily Cliff, Hilbert schemes, Part VI (GIT stability, quiver representations, & Hilbert schemes) (9:00am-11:00am, ONLINE)

Friday, October 23: Tony Licata, Hilbert schemes, Part VII (Kleinian singularities 2) (9:00am-11:00am, Carslaw 453 + ONLINE)

Friday, October 30: Emily Cliff, Hilbert schemes, Part VIII (Heisenberg algebras, Fock space representations and vertex algebra structure) (9:00am-11:00am, ONLINE)

Friday, November 6: Anthony Henderson, Hilbert schemes, Part IX (Correspondences in homology) (9:00am-11:00am, Carslaw 453 + ONLINE)

Friday, November 13: Josh Ciappara, Hilbert schemes, Part X (Representations of Heisenberg algebras on homology of Hilbert schemes) (9:00am-11:00am, ONLINE)

Friday, November 20: Emily Cliff, Hilbert schemes, Part XI (Geometric construction of vertex operators) (9:00am-11:00am, ONLINE)

Friday, November 27: No IFS

Friday, December 4: Peter McNamara, Preprojective Algebras (9:00am-11:00am, Carslaw 453 + ONLINE)

2020 Semester 1 Schedule:

Friday, January 31: Hannah Bryant, Ancient Egypt (2:00-3:00pm, SMRI common room)

Friday, February 7: Joel Gibson, How to compute and visualise characters of modular representations of rank 2 groups (3:00-4:00pm, Quad S227)

Friday, February 14: No IFS. Come to the New Connections in Representation Theory conference in Mooloolaba instead!

Friday, February 21: Laurentiu Maxim, Topological applications of nearby and vanishing cycles (3:00-5:00pm, Quad S227)

Friday, February 28: Laurentiu Maxim, Topological applications of nearby and vanishing cycles (3:00-5:00pm, Quad S224)

Friday, March 6: Emily Cliff, Beilinson-Drinfeld Grassmannian and fusion, part I (3:00-5:00pm, Quad S224)

Friday, March 13: Emily Cliff, Beilinson-Drinfeld Grassmannian and fusion, part II (3:00-5:00pm, Quad S224)

Friday, March 20: Giulian Wiggins, Rickard’s Morita Theory for Derived Category (This talk will take place ONLINE via Zoom. If you would like to attend, please email Anna Romanov at anna.romanov@sydney.edu.au.)

Friday, March 27: William Hardesty, Introduction to coherent Springer theory (3:00-5:00pm, ONLINE)

Friday, April 3: Emily Cliff, Beilinson-Drinfeld Grassmannian and fusion, part III (3:00-5:00pm, ONLINE)

Friday, April 10: Bregje Pauwels, Koszul duality (3:00-5:00pm, ONLINE)

Friday, April 17: Leonardo Maltoni, Deriving dg categories (after B. Keller) (4:00-6:00pm, ONLINE) Note unusual time!

Friday, April 24: Masoud Kamgarpour, Global Langlands correspondence for function fields: an overview of V. Lafforgue’s work, Part I: Understanding the statement (12:00-2:00pm, ONLINE) Note unusual time!

Friday, May 1: Masoud Kamgarpour, Global Langlands correspondence for function fields: an overview of V. Lafforgue’s work, Part II: Pseudo-representations (3:00-5:00pm, ONLINE)

Friday, May 8: Masoud Kamgarpour, Global Langlands correspondence for function fields: an overview of V. Lafforgue’s work, Part III: Hecke modifications and Shtukas (3:00-5:00pm, ONLINE)

Friday, May 15: Linyuan Liu, One dimensional global Langlands correspondence for function fields: the class field theory, part I (3:00-5:00pm, ONLINE)

Friday, May 22: Joel Gibson, The Robinson-Schensted correspondence via the Steinberg variety (3:00-5:00pm, ONLINE)

Friday, May 29: Linyuan Liu, One dimensional global Langlands correspondence for function fields: the class field theory, part II (3:00-5:00pm, ONLINE)

Friday, June 5: Linyuan Liu, One dimensional global Langlands correspondence for function fields: the class field theory, part III (3:00-5:00pm, ONLINE)

Friday, June 12: Kevin Coulembier, Galois theory of Riemann Surfaces (3:00-5:00pm, ONLINE)

Friday, June 19: Joe Baine, Trace in categories (3:00-5:00pm, ONLINE)

Friday, June 26: Peter McNamara, Perverse sheaves for the canonical basis for affine sl_2 (3:00-5:00pm, ONLINE)

Friday, July 3: Josh Ciappara, A problem for the topologists or geometers (3:00-5:00pm, ONLINE)

Friday, July 10: Anna Romanov, Vogan duality I (3:00-5:00pm, ONLINE)

Friday, July 17: No IFS

Friday, July 24: No IFS

2019 Semester 2 Schedule:

Friday, July 26: Gaston Burrull, The Bruhat graph of a Coxeter group (2:30-4:30pm, Quad S225)

Friday, August 2: Emily Cliff, On the Kirwan map for moduli stacks of Higgs bundles (2:30-4:30pm, Quad S422)

Friday, August 9: No IFS, come to the Flags, Galleries, and Reflection Groups conference instead!

Friday, August 16: Anna Romanov, The Kazhdan-Lusztig conjectures: history, statement, "proof" (2:30-4:30pm, SMRI terrace)

Friday, August 23: Boris Lishak, Group cohomology (2:30-4:30pm, Quad S225)

Friday, August 30: Geordie Williamson, Intersection cohomology over rings (2:30-4:30pm, Quad S225)

Friday, September 6: Geordie Williamson, An introduction to geometric Satake (2:30-4:30pm, Quad S225)

Friday, September 13: Geordie Williamson, An introduction to geometric Satake (3:00-5:00pm, Quad S422)

Friday, September 20: Emily Cliff, An introduction to sheaves on stacks (2:30-4:30pm, Quad S225)

Friday, September 27: Yusra Naqvi, An introduction to buildings (2:30-4:30pm, Quad S225)

Friday, October 4: Lin Yuan Liu, Introduction to cohomology of line bundles on flag varieties, part I (2:30-4:30pm, Quad S225)

Friday, October 11: Lin Yuan Liu, Introduction to cohomology of line bundles on flag varieties, part II (2:30-4:30pm, Quad S225)

Friday, October 18: Emily Cliff, Vanishing cycles (2:30-4:30pm, Quad S225)

Friday, October 25: Josh Ciappara, Combinatorial actions of Soergel bimodules, Part I (2:30-4:30pm, Quad S225)

Friday, November 1: Josh Ciappara, Combinatorial actions of Soergel bimodules, Part II (2:30-4:30pm, Quad S225)

Friday, November 8: Anna Romanov, The Lusztig-Vogan module of the Hecke algebra (2:30-4:30pm, Quad S225)

Friday, November 15: Anna Romanov, The Lusztig-Vogan module of the Hecke algebra (2:30-4:30pm, SMRI terrace or common room)

Friday, November 22: Lin Yuan Liu, The Brylinski-Kostant filtration (2:30-4:30pm, SMRI common room)

Friday, November 29: Joe Baine, Some characters for simple G-modules (2:30-4:30pm, SMRI terrace or common room)

2019 Semester 1 Schedule:

Friday, February 8: Will Donovan, Perverse schobers on mirror moduli spaces (3pm)

Friday, February 15: Søren Galatius, $E_\infty$-cells and general linear groups of finite fields (1:30-3:30pm) Note the irregular time!

Friday, February 22: Kevin Coulembier, Tannakian categories in positive characteristic (3pm)

Friday, March 1: Anna Romanov, Representation theory of SL(2,R) (3-5pm)

Friday, March 8: Anna Romanov, The local Langlands correspondence for SL(2,R) (3-5pm)

Friday, March 15: James Parkinson, Hecke algebras with unequal parameters I: Cells (3-5pm)

Friday, March 22: James Parkinson, Hecke algebras with unequal parameters II: Plancherel Theorems (3-5pm)

Friday, March 29: Gwyn Bellamy, Symplectic singularities and their quantizations (3-5pm)

Friday, April 5: Gwyn Bellamy, Symplectic singularities and their quantizations (3-5pm)

Friday, April 12: Gwyn Bellamy, Symplectic singularities and their quantizations (3-5pm)

Friday, April 19: Holiday, no seminar

Friday, April 26: Joe Baine, Representations of SL_2(F_q) (2:15-4:15pm)

Friday, May 3: Joe Baine, Representations of SL_2(F_q) (2:15-4:15pm)

Friday, May 10: Ivan Losev, Modular representations of semisimple Lie algebras (3-4 pm)

Monday, May 13: Ivan Losev, Modular representations of semisimple Lie algebras (3-5 pm) Note the irregular day of the week!

Friday, May 17: Gaston Burrull, The Bernstein presentation of the Hecke algebra (2:15-4:15pm)

Friday, May 24: Leonardo Maltoni, Categorification of the loop presentation of the affine Hecke algebra for SL2 (2:15-4:15pm)

Friday, May 31: Josh Ciappara, Tensor products of finite and infinite dimensional representations of semisimple Lie algebras (2:15-4:15pm)

Friday, June 7: Josh Ciappara, Tensor products of finite and infinite dimensional representations of semisimple Lie algebras (2:15-4:15pm)

Friday, June 14: Anna Romanov, Equivariant cohomology, part I (2:15-4:15pm)

Friday, June 21: Anna Romanov, Equivariant cohomology, part II (2:15-4:15pm)

2018 Semester 2 Schedule:

Friday, October 5: Xun Xie, Boundedness of the a-function

Friday, October 12: Xun Xie, Boundedness of the a-function, continued

(with supplementary 3-4pm lecture by Geordie on background on why the a-function is so interesting)

Friday, October 19: Anna Romanov, Unitary representations of real reductive groups: the abelian case

Friday, October 26: Anna Romanov, Unitary representations of real reductive groups, continued

Friday, November 2: Minhua Liu, The decomposition theorem

Friday, November 9: Josh Ciappara, Perverse sheaves and the weak Lefshetz theorem

Friday, November 16: Joel Gibson, Abelian Hodge theory (3pm) and Geordie Williamson, Mixed Hodge theory (4pm)

Friday, November 23: Joel Gibson, Higgs bundles (3pm) and Anna Romanov, the Hitchin fibration and the Springer resolution (4pm)

Friday, November 30: No seminar

Friday, December 7: Joe Baine, counting points on character varieties (3pm) (canceled, didn't meet quorum)

News:

The Sydney Mathematical Research Institute has a YouTube channel.

In November 2018, we spent some time preparing for Luca Migliorini's lecture series on the P=W conjecture at the MATRIX institute in Creswick, Victoria. We found this survey on the P=W conjecture helpful in our preparations, and as a group, we put together these lecture notes from the workshop.