prelim_challenges.tex

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{\bf\Large CMP 2020: Preliminary Challenges}

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{\large\bf Anthony Bordg}
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{21st January 2020}  
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\begin{enumerate}
	\item Define Lie groups
	\item Define Lie subgroups
	\item Define the type of representations of a group
	\item State theorem 2.8 in Kirillov
	\item State corollary 2.9 in Kirillov
	\item Define the Lie algebra of a Lie group
	\item Define the exponential map of a Lie group
	\item State Schur's lemma
	\item Define the differential forms on a manifold
	\item Define the exterior derivative
	\item Define the Hodge star operator
	\item Define the standard groups of matrices: the general linear groups, the special linear groups, the (special) orthogonal groups, the (special) unitary groups (Alex Hilton)
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If you decide to work on some of these challenges, please add your name in front of the challenges and coordinate your efforts on GitHub with the other contributors to avoid code duplication. \\
There are at most two places for the summer paid internship. However, every significant contributor of the project will have co-authorship of the resulting publication(s) even if he is not selected for the summer internship (he can still take part remotely anyway).


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