SMRI Algebra and Geometry Online: Williams -- Schubert polynomials, the inhomogeneous TASEP, and evil-avoiding permutations

SMRI Algebra and Geometry Online
’Schubert polynomials, the inhomogeneous TASEP, and evil-avoiding permutations’
Lauren K. Williams (Harvard University)

Thursday 19th August 
10:00am - 11:00am (AEST) 
Register: 
https://uni-sydney.zoom.us/meeting/register/tZYkcemspz0uGtA8_BxxUMjb_d1q0dX34nRo

Abstract: The totally asymmetric simple exclusion process (TASEP) was introduced 
around 1970 as a model for translation in protein synthesis and traffic flow. It has 
interesting physical properties (e.g. boundary-induced phase transitions) and also 
beautiful mathematical properties. The inhomogeneous TASEP is a Markov chain of 
weighted particles hopping on a ring, in which the probability that two particles 
interchange depends on the weight of those particles. If each particle has a distinct 
weight, then we can think of this as a Markov chain on permutations. In many cases, 
the steady state probabilities can be expressed in terms of Schubert polynomials. 
Based on joint work with Donghyun Kim.

Biography: Lauren Williams is the Robinson professor of mathematics at Harvard and the 
Seaver Professor at the Harvard Radcliffe Institute. Her research is in algebraic 
combinatorics. Williams received her BA in mathematics from Harvard College in 2000, 
and her PhD from MIT in 2005. Subsequently, she was a postdoc at UC Berkeley and 
Harvard, then a faculty member at UC Berkeley from 2009 to 2018, before returning to 
Harvard in 2018. She is the recipient of a Sloan Research Fellowship, an NSF CAREER 
award, the AWM-Microsoft research prize, and is an Honorary member of the London 
Mathematical Society.

Note
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