l Milnor numbers of projective hypersurfaces and the chromatic polynomial of graphs
Speaker
l June Huh (허준이)
Institute
l UIUC
Date
l 2010-07-09 (Fri)
Time
l 16:00 ~ 17:00
Place
l E6-1 #1409
VodLink
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The chromatic polynomial of a graph counts the number of proper
colorings of the graph. We give an affirmative answer to the
conjecture of Read (1968) and Welsh (1976) that the absolute values of
the coefficients of the chromatic polynomial form a log-concave
sequence. We define a sequence of numerical invariants of projective
hypersurfaces analogous to the Milnor number of local analytic
hypersurfaces. Then we show log-concavity of the sequence by answering
a question of Trung and Verma on mixed multiplicities of ideals. The
conjecture on the chromatic polynomial follows as a special case.
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