People_

Professor Geordie Williamson

FRS FAA

Email

[email protected]

Address

A14 - The Quadrangle

The University of Sydney

Websites

View ORCID for all publications

Geordie Williamson's web page

Biographical details

Geordie Williamson completed his PhD in 2008 at the University of Freiburg under the supervision of Wolfgang Soergel. He went on to hold an EPSRC postdoc at the University of Oxford working with Raphaël Rouquier, and was a Junior Research Fellow at St. Peter's College. He then spent five years at the Max Planck Institute in Bonn, as an Advanced Researcher (W2 research professor). He joined the Sydney University department in 2017.

Research interests

I am interested in algebra, geometry and representation theory. There are several basic questions (e.g. determining the dimensions or characters of reprentations of a Lie group or finite group of Lie type) which need extremely sophisticated techniques from algebraic geomety, Hodge theory or higher category theory to resolve. The richness and complexity contained in these simple questions is extraordinary.

My research aligns with the Faculty of Science Research Strengths - Understanding the Universe, Fundamental Laws of Nature, Complex Systems, Cultivating Scientific Capability, Brain Behaviour and Cognition, Precision and Digital Health, Decision-Making for a Sustainable Future, Data and Decisions, National Security , Quantum Frontiers.

Awards and honours

Distinguished Visiting Professor, Institute for Advanced Study (2020)

Fellow of the Australian Academy of Sciences (elected 2018)

Fellow of the Royal Society (elected 2018)

Plenary Speaker, International Congress of Mathematicians (2018)

Clay research Award (2016)

European Mathematics Society Prize (2016)

2017 New Horizons Prize (with Ben Elias), (2016)

Chevalley Prize of the American Mathematics Society (2016)

Current research students

Project title	Research student
Abstract representations of reductive groups	Nick BRIDGER
Hard Lefschetz theorem with mod p coefficients and the topology of toric and Schubert varieties	Finn KLEIN
Incompressible Tensor Categories in Positive Characteristic	Joe NEWTON
Faithfulness of braid group representations	Bailey WHITBREAD

Selected publications

Introduction to Soergel Bimodules

(Springer, 2020)

Tilting modules and the p-canonical basis

(Societe Mathematique de France, 2018)

Expand all

Books

Elias, B., Makisumi, S., Thiel, U., Williamson, G. (2020). Introduction to Soergel Bimodules. Cham: Springer. [More Information]
Riche, S., Williamson, G. (2018). Tilting modules and the p-canonical basis. Paris: Societe Mathematique de France. [More Information]

Book Chapters

Elias, B., Snyder, N., Williamson, G. (2017). On cubes of Frobenius extensions. In Henning Krause, Peter Littelmann, Gunter Malle, Karl-Hermann Neeb and Christoph (Eds.), Representation Theory—Current Trends and Perspectives, (pp. 171-186). Zurich: European Mathematical Society Publishing House.
Elias, B., Williamson, G. (2016). Kazhdan-Lusztig conjectures and shadows of Hodge theory. In W Ballmann, C Blohmann, G Faltings, P Teichner, D Zagier (Eds.), Arbeitstagung Bonn 2013: In Memory of Friedrich Hirzebruch, (pp. 105-126). Switzerland: Springer International Publishing Switzerland. [More Information]
Williamson, G. (2014). A reducible characteristic variety in type A. In Monica Nevins, Peter E. Trapa (Eds.), Representations of Reductive Groups In Honor of the 60th Birthday of David A. Vogan, Jr., (pp. 517-532). Cham: Birkhauser. [More Information]

Journals

Davies, A., Gupta, P., Racaniere, S., Swirszcz, G., Wagner, A., Weber, T., Williamson, G. (2025). Drums of high width. Proceedings of the London Mathematical Society, 130(3), e70031-32 pages. [More Information]
Williamson, G. (2024). IS DEEP LEARNING A USEFUL TOOL FOR THE PURE MATHEMATICIAN? Bulletin of the American Mathematical Society, 61(2), 271-286. [More Information]
Coulembier, K., Williamson, G. (2024). PERFECTING GROUP SCHEMES. Institute of Mathematics of Jussieu. Journal, 23(6), 2549. [More Information]
Gibson, J., Williamson, G. (2023). Calculating the p-canonical basis of Hecke Algebras. Transformation Groups, 28(3), 1121-1148. [More Information]
Elias, B., Williamson, G. (2023). Localized calculus for the Hecke category. Annales Mathématiques Blaise Pascal, 30(1), 1-73. [More Information]
Riche, S., Williamson, G. (2022). Smith–Treumann theory and the linkage principle. Institut des Hautes Etudes Scientifiques, Paris. Publications Mathematiques, 136(1), 225-292. [More Information]
Blundell, C., Buesing, L., Davies, A., Veličković, P., Williamson, G. (2022). TOWARDS COMBINATORIAL INVARIANCE FOR KAZHDAN-LUSZTIG POLYNOMIALS. Representation Theory, 26, 1145-1191. [More Information]
Davies, A., Veličković, P., Buesing, L., Blackwell, S., Zheng, D., Tomašev, N., Tanburn, R., Battaglia, P., Blundell, C., Juhász, A., Williamson, G., et al (2021). Advancing mathematics by guiding human intuition with AI. Nature, 600(7887), 70-74. [More Information]
Ciappara, J., Williamson, G. (2021). Lectures on the geometry and modular representation theory of algebraic groups. Journal of the Australian Mathematical Society, 110(1), 1-47. [More Information]
Elias, B., Williamson, G. (2021). Relative hard Lefschetz for Soergel bimodules. Journal of the European Mathematical Society, 23(8), 2549-2581. [More Information]
Achar, P., Makisumi, S., Riche, S., Williamson, G. (2019). Koszul duality for Kac-Moody groups and characters of tilting modules. Journal of the American Mathematical Society, 32(1), 261-310. [More Information]
Lusztig, G., Williamson, G. (2018). Billiards and Tilting Characters for SL_3. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 14, 1-22. [More Information]
Lusztig, G., Williamson, G. (2018). On the character of certain tilting modules. Science China Mathematics, 61(2), 295-298. [More Information]
He, X., Williamson, G. (2018). Soergel Calculus and Schubert Calculus. Academia Sinica. Institute of Mathematics. Bulletin, 13(3), 317-350. [More Information]
Webster, B., Williamson, G. (2017). A geometric construction of colored HOMFLYPT homology. Geometry and Topology, 21(5), 2557-2600. [More Information]
Libedinsky, N., Williamson, G. (2017). A non-perverse Soergel bimodule in type A | Un bimodule de Soergel non pervers de type A. Academie des Sciences. Comptes Rendus. Mathematique, 355(8), 853-858. [More Information]
Williamson, G. (2017). Algebraic representations and constructible sheaves. Japanese Journal of Mathematics, 12(2), 211-259. [More Information]
Elias, B., Williamson, G. (2017). Diagrammatics for Coxeter groups and their braid groups. Quantum Toplogy, 8(3), 413-457. [More Information]
Williamson, G. (2017). On torsion in the intersection cohomology of Schubert varieties. Journal of Algebra, 475, 207-228. [More Information]
Williamson, G. (2017). Schubert calculus and torsion explosion. Journal of the American Mathematical Society, 30(4), 1023-1046. [More Information]
Williamson, G. (2017). The Hodge theory of the decomposition theorem. Asterisque, 390, 335-367.
Jensen, L., Williamson, G. (2017). The p-canonical basis for Hecke algebras (forthcoming). Contemporary Mathematics, 683, 333-361.
Williamson, G. (2016). Local Hodge theory of Soergel bimodules. Acta Mathematica, 217(341), 341-404. [More Information]
Juteau, D., Mautner, C., Williamson, G. (2016). Parity sheaves and tilting modules. Annales Scientifiques de lEcole Normale Superieure, 49(2), 257-275.
Elias, B., Williamson, G. (2016). Soergel calculus. Representation Theory, 20(12), 295-374. [More Information]
Juteau, D., Williamson, G. (2014). Kumar's criterion modulo p. Duke Mathematical Journal, 163(14), 2617-2638. [More Information]
Riche, S., Soergel, W., Williamson, G. (2014). Modular Koszul duality. Compositio Mathematica, 150(2), 273-332. [More Information]
Williamson, G. (2014). On an analogue of the James conjecture. Representation Theory, 18(1), 15-27. [More Information]
Juteau, D., Mautner, C., Williamson, G. (2014). Parity Sheaves. Journal of the American Mathematical Society, 27(4), 1169-1212. [More Information]
Fiebig, P., Williamson, G. (2014). Parity sheaves, moment graphs and the p-smooth locus of Schubert varieties. Annales de l'Institut Fourier, 64(2), 489-536.
Libedinsky, N., Williamson, G. (2014). Standard objects in 2-braid groups. Proceedings of the London Mathematical Society, 109(3), 1264-1280. [More Information]
Elias, B., Williamson, G. (2014). The Hodge theory of Soergel bimodules. Annals of Mathematics, 180(2), 1089-1136. [More Information]
Vilonen, K., Williamson, G. (2013). Characteristic cycles and decomposition numbers. Mathematical Research Letters, 20(2), 359-366. [More Information]
Williamson, G., Braden, T. (2012). Modular intersection cohomology complexes on flag varieties. Mathematische Zeitschrift, 272(3-4), 697-727. [More Information]
Juteau, D., Mautner, C., Williamson, G. (2012). Perverse Sheaves and Modular representation theory. SÃ©minaires & CongrÃ¨s, , 313-350.
Williamson, G. (2011). Singular Soergel biomodules. International Mathematics Research Notices, 2011 (20), 4555-4632. [More Information]
Webster, B., Williamson, G. (2011). The Geometry of Markov Traces. Duke Mathematical Journal, 160(2), 401-419. [More Information]
Webster, B., Williamson, G. (2008). A geometric model for Hochschild homology of Soergel biomodules. Geometry and Topology, 12(2), 1243-1263. [More Information]

show 35 more

Conferences

Williamson, G. (2018). The Hodge theory of the Hecke category. European Congress of Mathematics (ECM 2016), Berlin: European Mathematical Society Publishing House. [More Information]
Williamson, G. (2013). Checking Lusztig's conjecture around the Steinberg weight. Representations of Finite Groups Workshop, Oberwolfach: Mathematisches Forschungsinstitut Oberwolfach. [More Information]
Williamson, G. (2012). Some examples of parity sheaves. Enveloping Algebras and Geometric Representation Theory, Oberwolfach: Mathematisches Forschungsinstitut Oberwolfach. [More Information]

Expand all

2025

Davies, A., Gupta, P., Racaniere, S., Swirszcz, G., Wagner, A., Weber, T., Williamson, G. (2025). Drums of high width. Proceedings of the London Mathematical Society, 130(3), e70031-32 pages. [More Information]

2024

Williamson, G. (2024). IS DEEP LEARNING A USEFUL TOOL FOR THE PURE MATHEMATICIAN? Bulletin of the American Mathematical Society, 61(2), 271-286. [More Information]
Coulembier, K., Williamson, G. (2024). PERFECTING GROUP SCHEMES. Institute of Mathematics of Jussieu. Journal, 23(6), 2549. [More Information]

2023

Gibson, J., Williamson, G. (2023). Calculating the p-canonical basis of Hecke Algebras. Transformation Groups, 28(3), 1121-1148. [More Information]
Elias, B., Williamson, G. (2023). Localized calculus for the Hecke category. Annales Mathématiques Blaise Pascal, 30(1), 1-73. [More Information]

2022

Riche, S., Williamson, G. (2022). Smith–Treumann theory and the linkage principle. Institut des Hautes Etudes Scientifiques, Paris. Publications Mathematiques, 136(1), 225-292. [More Information]
Blundell, C., Buesing, L., Davies, A., Veličković, P., Williamson, G. (2022). TOWARDS COMBINATORIAL INVARIANCE FOR KAZHDAN-LUSZTIG POLYNOMIALS. Representation Theory, 26, 1145-1191. [More Information]

2021

Davies, A., Veličković, P., Buesing, L., Blackwell, S., Zheng, D., Tomašev, N., Tanburn, R., Battaglia, P., Blundell, C., Juhász, A., Williamson, G., et al (2021). Advancing mathematics by guiding human intuition with AI. Nature, 600(7887), 70-74. [More Information]
Ciappara, J., Williamson, G. (2021). Lectures on the geometry and modular representation theory of algebraic groups. Journal of the Australian Mathematical Society, 110(1), 1-47. [More Information]
Elias, B., Williamson, G. (2021). Relative hard Lefschetz for Soergel bimodules. Journal of the European Mathematical Society, 23(8), 2549-2581. [More Information]

2020

Elias, B., Makisumi, S., Thiel, U., Williamson, G. (2020). Introduction to Soergel Bimodules. Cham: Springer. [More Information]

2019

Achar, P., Makisumi, S., Riche, S., Williamson, G. (2019). Koszul duality for Kac-Moody groups and characters of tilting modules. Journal of the American Mathematical Society, 32(1), 261-310. [More Information]

2018

Lusztig, G., Williamson, G. (2018). Billiards and Tilting Characters for SL_3. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 14, 1-22. [More Information]
Lusztig, G., Williamson, G. (2018). On the character of certain tilting modules. Science China Mathematics, 61(2), 295-298. [More Information]
He, X., Williamson, G. (2018). Soergel Calculus and Schubert Calculus. Academia Sinica. Institute of Mathematics. Bulletin, 13(3), 317-350. [More Information]
Williamson, G. (2018). The Hodge theory of the Hecke category. European Congress of Mathematics (ECM 2016), Berlin: European Mathematical Society Publishing House. [More Information]
Riche, S., Williamson, G. (2018). Tilting modules and the p-canonical basis. Paris: Societe Mathematique de France. [More Information]

show 2 more

2017

Webster, B., Williamson, G. (2017). A geometric construction of colored HOMFLYPT homology. Geometry and Topology, 21(5), 2557-2600. [More Information]
Libedinsky, N., Williamson, G. (2017). A non-perverse Soergel bimodule in type A | Un bimodule de Soergel non pervers de type A. Academie des Sciences. Comptes Rendus. Mathematique, 355(8), 853-858. [More Information]
Williamson, G. (2017). Algebraic representations and constructible sheaves. Japanese Journal of Mathematics, 12(2), 211-259. [More Information]
Elias, B., Williamson, G. (2017). Diagrammatics for Coxeter groups and their braid groups. Quantum Toplogy, 8(3), 413-457. [More Information]
Elias, B., Snyder, N., Williamson, G. (2017). On cubes of Frobenius extensions. In Henning Krause, Peter Littelmann, Gunter Malle, Karl-Hermann Neeb and Christoph (Eds.), Representation Theory—Current Trends and Perspectives, (pp. 171-186). Zurich: European Mathematical Society Publishing House.
Williamson, G. (2017). On torsion in the intersection cohomology of Schubert varieties. Journal of Algebra, 475, 207-228. [More Information]
Williamson, G. (2017). Schubert calculus and torsion explosion. Journal of the American Mathematical Society, 30(4), 1023-1046. [More Information]
Williamson, G. (2017). The Hodge theory of the decomposition theorem. Asterisque, 390, 335-367.
Jensen, L., Williamson, G. (2017). The p-canonical basis for Hecke algebras (forthcoming). Contemporary Mathematics, 683, 333-361.

show 6 more

2016

Elias, B., Williamson, G. (2016). Kazhdan-Lusztig conjectures and shadows of Hodge theory. In W Ballmann, C Blohmann, G Faltings, P Teichner, D Zagier (Eds.), Arbeitstagung Bonn 2013: In Memory of Friedrich Hirzebruch, (pp. 105-126). Switzerland: Springer International Publishing Switzerland. [More Information]
Williamson, G. (2016). Local Hodge theory of Soergel bimodules. Acta Mathematica, 217(341), 341-404. [More Information]
Juteau, D., Mautner, C., Williamson, G. (2016). Parity sheaves and tilting modules. Annales Scientifiques de lEcole Normale Superieure, 49(2), 257-275.
Elias, B., Williamson, G. (2016). Soergel calculus. Representation Theory, 20(12), 295-374. [More Information]

show 1 more

2014

Williamson, G. (2014). A reducible characteristic variety in type A. In Monica Nevins, Peter E. Trapa (Eds.), Representations of Reductive Groups In Honor of the 60th Birthday of David A. Vogan, Jr., (pp. 517-532). Cham: Birkhauser. [More Information]
Juteau, D., Williamson, G. (2014). Kumar's criterion modulo p. Duke Mathematical Journal, 163(14), 2617-2638. [More Information]
Riche, S., Soergel, W., Williamson, G. (2014). Modular Koszul duality. Compositio Mathematica, 150(2), 273-332. [More Information]
Williamson, G. (2014). On an analogue of the James conjecture. Representation Theory, 18(1), 15-27. [More Information]
Juteau, D., Mautner, C., Williamson, G. (2014). Parity Sheaves. Journal of the American Mathematical Society, 27(4), 1169-1212. [More Information]
Fiebig, P., Williamson, G. (2014). Parity sheaves, moment graphs and the p-smooth locus of Schubert varieties. Annales de l'Institut Fourier, 64(2), 489-536.
Libedinsky, N., Williamson, G. (2014). Standard objects in 2-braid groups. Proceedings of the London Mathematical Society, 109(3), 1264-1280. [More Information]
Elias, B., Williamson, G. (2014). The Hodge theory of Soergel bimodules. Annals of Mathematics, 180(2), 1089-1136. [More Information]

show 5 more

2013

Vilonen, K., Williamson, G. (2013). Characteristic cycles and decomposition numbers. Mathematical Research Letters, 20(2), 359-366. [More Information]
Williamson, G. (2013). Checking Lusztig's conjecture around the Steinberg weight. Representations of Finite Groups Workshop, Oberwolfach: Mathematisches Forschungsinstitut Oberwolfach. [More Information]

2012

Williamson, G., Braden, T. (2012). Modular intersection cohomology complexes on flag varieties. Mathematische Zeitschrift, 272(3-4), 697-727. [More Information]
Juteau, D., Mautner, C., Williamson, G. (2012). Perverse Sheaves and Modular representation theory. SÃ©minaires & CongrÃ¨s, , 313-350.
Williamson, G. (2012). Some examples of parity sheaves. Enveloping Algebras and Geometric Representation Theory, Oberwolfach: Mathematisches Forschungsinstitut Oberwolfach. [More Information]

2011

Williamson, G. (2011). Singular Soergel biomodules. International Mathematics Research Notices, 2011 (20), 4555-4632. [More Information]
Webster, B., Williamson, G. (2011). The Geometry of Markov Traces. Duke Mathematical Journal, 160(2), 401-419. [More Information]

2008

Webster, B., Williamson, G. (2008). A geometric model for Hochschild homology of Soergel biomodules. Geometry and Topology, 12(2), 1243-1263. [More Information]

Selected Grants

2025

Algebraic Schubert geometry and unitary reflection groups, Lehrer G, Henderson A, Williamson G, Australian Research Council (ARC)/Discovery Projects (DP)

2023

Machine learning, group theory and combinatorics, Williamson G, Australian Research Council (ARC)/Discovery Projects (DP)
Braid groups via representation theory and machine learning, Yacobi O, Williamson G, Elias B, Australian Research Council (ARC)/Discovery Projects (DP)

In the media

Maths prodigy comes home to establish $5 million world-class maths centre (Sydney Morning Herald, 13 July 2018)