Problems in the Theory of Partitions and Q- Series

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9400191 Alladi This award funds the research of Professor Krishnaswami Alladi in partition theory. Prof. Alladi will try to apply a new technique that he developed in joint work with Prof. Basil Gordon to five problems. He will study a partition theorem mf Gollnitz, a recent result of Capparelli, the q-Gauss identities, and the quintuple product identity. This work is in the general field of analytic number theory and in particular partition theory. At its most basic level partition theory studies the question, how many different ways can one number be written as the sum of smaller numbers? This question becomes a part of analytic number theory when answers to this question are encoded into mathematical functions. This allows mathematicians to apply the analysis techniques of calculus. The idea of using continuous methods to investigate discrete objects is two centuries old, but with the work of the modern analytic number theorists, the field has had a new rebirth and led to a deeper understanding of partitions of the whole numbers.