Professor Geordie Williamson

FRS FAA

F07 - Carslaw Building
The University of Sydney


Website 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.

Current research students

Project title Research student
Tensor categories associated to cells in Coxeter groups Gaston BURRULL NAREDO

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)

In the media

Selected grants

2016

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

Selected publications

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Books

  • Riche, S., Williamson, G. (2018). Tilting modules and the p-canonical basis. France: Societe Mathematique de France.

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

  • Lusztig, G., Williamson, G. (2018). Billiards and Tilting Characters for SL_3. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 14, 015 -1-015 - 22. [More Information]
  • Lusztig, G., Williamson, G. (2018). On the character of certain tilting modules. Science China Mathematics, 61(2), 295-298. [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, 295-374. [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.
  • 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. Séminaires & Congrès, , 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]

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]

2018

  • Lusztig, G., Williamson, G. (2018). Billiards and Tilting Characters for SL_3. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 14, 015 -1-015 - 22. [More Information]
  • Lusztig, G., Williamson, G. (2018). On the character of certain tilting modules. Science China Mathematics, 61(2), 295-298. [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. France: Societe Mathematique de France.

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.

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, 295-374. [More Information]

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]
  • 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.
  • 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]

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. Séminaires & Congrès, , 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]

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