Stefan Dawydiak

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I am a postdoctoral fellow at the University of Glasgow, under the supervision of Dinakar Muthiah. Previously I was an NSERC postdoctoral fellow at the Mathematical Institute of the University of Bonn and a postdoctoral fellow at the Max Planck Institute for Mathematics in Bonn. I obtained my PhD in 2022 from the University of Toronto, under the supervision of Alexander Braverman. I work on the representation theory of reductive p-adic groups, geometric representation theory, and related problems. I am particularily interested in Lusztig's asymptotic Hecke algebra J and its recent generalizations, affine Hecke algebras, and interactions between Kazhdan-Lusztig theory and the local Langlands correspondence. In particular, I am interested in using this interaction to relate classical notions of temperedness with more algebraic notions arising from geometric perspectives on the local Langlands correspondence. This leads me to think about (derived) algebraic geometry on one hand, and about harmonic analysis and Harish-Chandra's Plancherel Theorem on the other. I am interested in affine Hecke algebras with unequal parameters as they appear via type theory. I have also recently started working with p-adic loop groups.

Before Toronto, I was an undergraduate at UBC, where I developed a continuing interest in real groups, thanks to Julia Gordon.

Papers and Preprints:

  1. On Braverman-Kazhdan's asymptotic Hecke algebra for unequal parameters and the p-adic unitary group U_3. In preparation, draft available upon request.
  2. On Braverman-Kazhdan's asymptotic Hecke algebra for inner forms of GL_n arxiv.
  3. Standard modules of affine Hecke algebras arxiv. Submitted.
  4. A positivity property in the based ring of the lowest two-sided cell arxiv, Int. Math. Res. Not. IMRN.
  5. The asymptotic Hecke algebra and rigidity, with an appendix by D. Rumynin, arxiv (Updated September 2025, Submitted)
  6. A coherent categorification of the based ring of the lowest two-sided cell, arxiv (Updated August 2024, Submitted)
  7. Denominators in Lusztig's asymptotic Hecke algebra via the Plancherel formula arxiv J. Inst. Math. Jussieu
  8. On the structure of the affine asymptotic Hecke algebras, with R. Bezrukavnikov and G. Dobrovolska and an appendix by R. Bezrukavnikov, A. Braverman, and D. Kazhdan. arxiv Transform. Groups
  9. Lusztig's asymptotic Hecke algebra for SL_2 arxiv Proc. Amer. Math. Soc.

    10. stefan dot dawydiak at glasgow dot ac dot uk