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\ufcdSetVars{
  backaddress  = \universityname\\79085 Freiburg,
  division     = Mathematisches Institut,
  department   = Abteilung f\"ur Reine Mathematik,
  fromname     = Prof. Dr. W. Soergel,
  signature    = Prof. Dr. W. Soergel,
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  fromaddress  = {Eckerstr. 1\\79104 Freiburg},
  fromphone    = 0761/203-5540 -5604,
  fromfax      = 0761/203-5541,
  fromemail    = Wolfgang.Soergel@math.uni-freiburg.de,
  fromurl      = home.mathematik.uni-freiburg.de/soergel/,
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\begin{document}
\begin{letter}{%
}[
  subject={\bf Nomination for the Chevalley Prize of the AMS}
]
\opening{\vspace{-1cm}}
I write to nominate my former student 
Geordie Williamson for the Chevalley Prize in 
Lie Theory of the AMS in view
of his groundbreaking work on irreducible characters \cite{EW, WiST}.

In joint work with Ben Elias \cite{EW} he showed how to
establish the conjectures of Kazhdan and Lusztig \cite{KL-C} 
concerning the 
characters of irreducible admissible representations 
of a complex reductive group like
$\operatorname{GL} (n ; \mathbb C)$ in an elementary 
way. This led to a great
simplification of the whole theory as well as to new 
results, in particular a proof of the positivity of 
coefficients of Kazhdan-Lusztig polynomials for 
arbitray Coxeter groups also conjectured in \cite{KL-C}, 
which has been open for more than thirty years. 

In his work on modular representations
\cite{WiST} he used similar methods to construct counterexamples to the 
description of characters of irreducible rational 
representations of $\operatorname{GL} (n; \mathbb F_p)$ 
conjectured by Lusztig \cite{Lu-PC}.
He even shows that for any $r$ there are counterexamples with $p > n^r$.
Up to then it was only known that given $n$, 
Lusztig's conjecture is true all primes $p$
with at most finitely many exceptions.
In the same paper Williamson finds the first counterexamples 
to a conjecture of James  \cite{Jam} about characters of irreducible
representations of symmetric groups over finite fields, which 
has been open for more than twenty years.

I think each one of these  works constitutes a breakthrough in central 
questions of Lie theory. I therefore nominate Geordie Williamson 
for the Chevalley prize of the AMS. 

\hfill Wolfgang Soergel
% \closing{\vspace{-20cm}}

 \vspace{10 mm}
\textit{REFERENCES}
\bibliographystyle{amsalpha}
\bibliography{geordie} 
% \begin{thebibliography}{Jam90}

% \bibitem[EW14]{EW}
% Ben Elias and Geordie Williamson, \emph{The {H}odge theory of {S}oergel
%   bimodules}, Ann. of Math. (2) \textbf{180} (2014), no.~3, 1089--1136.

% \bibitem[Jam90]{Jam}
% Gordon James, \emph{The decomposition matrices of $\op{GL}_n(q)$ for $n\leq
%   10$}, Proc. London Math. Soc. (3) \textbf{60} (1990), 225--265.

% \bibitem[KL79]{KL-C}
% David Kazhdan and George Lusztig, \emph{Representations of {C}oxeter groups and
%   {H}ecke algebras}, Inventiones \textbf{53} (1979), 191--213.

% \bibitem[Lus80]{Lu-PC}
% George Lusztig, \emph{Some problems in the representation theory of finite
%   {C}hevalley groups}, Proceedings of Symposia in Pure Mathematics 37, AMS,
%   1980, pp.~313--317.

% \bibitem[Wil13]{WiST}
% Geordie Williamson, \emph{{S}chubert calculus and torsion}, arXiv:1309.5055,
%   2013.

% \end{thebibliography}
%\bibliographystyle{amsalpha}\bibliography{geordie}

\end{letter}




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