Papers and preprints

For Mathematicians / Papers and preprints

Standard objects in 2-braid groups

Joint with Geordie Williamson, Proceedings of the London Mathematical Society 109 (2014), no. 5, 1264-1280. We introduce the concept of Δ-exact complexes for any Coxeter system. With that, we establish the existence of analogues of standard and costandard objects in 2-braid groups, thus proving the conjecture that Rouquier stated in the ICM 2006. This result was a key step for the proof by Elias and Williamson of Kazhdan-Lusztig conjectures

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January 1, 2014
For Mathematicians / Papers and preprints

New bases of some Hecke algebras via Soergel bimodules 

Advances in Mathematics 228 (2011) 1043-1067. I introduce a new set of bases for Hecke algebras related to extra-large Coxeter groups, coming from the theory of Soergel bimodules. I believe that they have a deep meaning related to the Hecke category and the p-canonical basis. This is related to my "Forking Path conjecture" that is false as stated, as proved by Gonzalo Jimenez. Nonetheless, in all generality, there seems to be an extremely strange phenomenon that I would love to understand better. 

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June 29, 2011
For Mathematicians / Papers and preprints

Presentation of right-angled Soergel categories by generators and relations

Journal of Pure and Applied Algebra 214 (2010) no. 12, 2265-2278. This was the first time that a "presentation of Soergel bimodules by generators and relations" was attempted. This revolutionary idea (explained to me by Rouquier) was the key of all the impressive subsequent development of the theory.

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January 27, 2009
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For Mathematicians / Papers and preprints

My Ph.D thesis

Chapter 1 is essentially a version of the paper that one could call "Soergel bimodules explained by Soergel" with explanations of the obscure points. Sections 2.4 and 2.5 are original and are not included in any other paper. I give a different (and easier) proof of the fact that Rouquier complexes satisfy the braid relations.

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November 17, 2008