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Abstract: Let p(n) denote the number of partitions of n (for example, 3=2+1=1+1+1, so we have p(3)=3). This function plays a basic role in such diverse areas of mathematics as Combinatorics, Number Theory, Representation Theory, and Mathematical Physics. Its arithmetic properties have been studied for a century, with many breakthroughs in the last decade. These properties can be viewed as "footprints" of the deeper theory of modular forms, and I will describe some recent results which this theory has produced.
This talk will be accessible to graduate students.
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