727 research outputs found
Representation Growth and Rational Singularities of the Moduli Space of Local Systems
We relate the asymptotic representation theory of and
the singularities of the moduli space of -local systems on a smooth
projective curve, proving new theorems about both. Regarding the former, we
prove that, for every d, the number of n-dimensional representations of
grows slower than , confirming a conjecture of
Larsen and Lubotzky. Regarding the latter, we prove that the moduli space of
-local systems on a smooth projective curve of genus at least 12 has
rational singularities. Most of our results apply more generally to semi-simple
algebraic groups.
For the proof, we study the analytic properties of push forwards of smooth
measures under algebraic maps. More precisely, we show that such push forwards
have continuous density if the algebraic map is flat and all of its fibers have
rational singularities.Comment: preliminary version, comments are welcome. v2. Revised version, now
covering all semi simple group
A Unifying Framework for Deciding Synchronizability
Several notions of synchronizability of a message-passing system have been introduced in the literature. Roughly, a system is called synchronizable if every execution can be rescheduled so that it meets certain criteria, e.g., a channel bound. We provide a framework, based on MSO logic and (special) tree-width, that unifies existing definitions, explains their good properties, and allows one to easily derive other, more general definitions and decidability results for synchronizability
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