# 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 AET.**Where**: Online and in-person**(Carslaw 375)**.If you would like to join or get access to a recorded talk, email bregje.pauwels@sydney.edu.au.

**News:**

In the first semester of 2022, there will also be a Machine Learning for the Working Mathematician seminar, an introduction to ways in which machine learning (and in particular deep learning) has been used to solve problems in mathematics.

The Sydney Mathematical Research Institute now has a YouTube channel. On it you can find videos from IFS's 2020 series on Hilbert schemes, Geordie Williamson's course on the Langlands correspondence and Bezrukavnikov's equivalence, and the SMRI Algebra and Geometry Online seminar.

UQ is spreading the tradition of the IFS across Australia! Check out what's happening in their new ``What is ... ? Seminar'' (WiSe) here.

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.

**Spring 2022 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****:****Friday, September****30****:****Friday,****October 7****:**Kevin Coulembier**Friday, October****14****:**Kevin Coulembier**Friday, October****21****:****Friday, October****28****:**Finn Klein**Friday, November 4:**Emilien Zabeth**Friday, November****11****:**Emilien Zabeth**Friday, November****18****:**Jonathan Spreer**November 28-December 2:**Come to Tensor Categories in Sydney!**December 6 - December 9:**Come to the 2022 AustMS Meeting at UNSW!

**Fall 2022 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 1:**~~Joe Baine~~~~, Lattices in Lie Groups~~~~(~~**online**~~)~~**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 13:**~~Chris Hone, The modularity theorem (~~**9:00-11:00am, Quad S225 or online**~~)~~**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

**Spring 2021 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**) Notes**Friday, 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**) Notes**Friday, 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**) Notes**Friday, 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**) Notes**Friday, 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**) Notes**Friday, 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**) Notes**Friday, 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**) Notes**Friday, 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!

**Fall 2021 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 16:***SEMINAR CANCELLED*~~Chris Hone, tbd (~~**9:00-11:00am, online**~~)~~**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**)

**Spring 2020 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**)

**Fall 2020 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

**Spring 2019 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**)

**Fall 2019 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**)

**Spring 2018 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*)