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I am an NSERC postdoctoral fellow at the Mathematical Institute of the University of Bonn. Previously I was 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 the Schwartz space of the basic affice space, with the aim of relating 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 various categories of *l*-adic sheaves on the other, and also about harmonic analysis and Harish-Chandra's Plancherel Theorem. I am recently more interested in various extensions of methods of Hecke algebras beyond the principal block.

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

**Papers and Preprints:**

- Lusztig's asymptotic Hecke algebra for SL_2 arxiv Journal
- 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 Journal
- Denominators in Lusztig's asymptotic Hecke algebra via the Plancherel formula arxiv (Updated August 2024, Submitted)
- A coherent categorification of the based ring of the lowest two-sided cell, arxiv (Updated August 2024, Submitted)
- The asymptotic Hecke algebra and rigidity, arxiv
- On a theorem of Steinberg, In preparation

dawydiak **at** math **dot** uni-bonn **dot** de