MaPSS: Maths Postgraduate Seminar Series: Gaston Burrull -- Towards the p-canonical basis in \tilde{A}_1

Hello all, 

The next MaPSS talk of this semester will be at 17:00 on Mon 27th August in Carslaw
535.  It’s a great opportunity to meet fellow postgrads, listen to an interesting
talk, and of course get free food! 

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Speaker: Gaston Burrull 

Title: Towards the p-canonical basis in \tilde{A}_1 

Abstract: In this talk, we will introduce the diagrammatic category of Soergel bimodules
and our formula for the intersection forms in \tilde{A}_1.  This talk will begin with a
little review about Coxeter groups and historical motivation.  

For a universal Coxeter system (W,S) and a realization, we give a topological formula
for the local intersection forms I_{w,x}, where w is a reduced expression and x is an
element of W.  This formula is given in terms of the generalized Cartan matrix
determined by the realization.  For this purpose, we calculate compositions modulo lower
terms of degree zero Libedinsky’s light leaves.  In fields k of characteristic p>0,
ranks of local intersection forms over k are used to define the p-canonical basis of the
Hecke algebra.  Furthermore, these numbers govern the direct sum decomposition of
Soergel bimodules over k.  

This is a joint work with Paolo Sentinelli.  

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See you there! 

Details can also be found on the school’s new Postgraduate Society website:
http://www.maths.usyd.edu.au/u/MaPS/mapss.html 

Cheers, 
Alex