Prof.  Krishnaswami Alladi   		
Department of Mathematics    		
University of Florida      		

Title of colloquium talk:  Rogers-Ramanujan type partition theorems and their 
analytic representations 

ABSTRACT: A Rogers-Ramanujan (R-R) type partition identity connects 
partitions defined by difference conditions with partitions governed by 
congruence conditions. The name stems from the celebrated R-R identities 
which connect partitions into parts differing by at least 2 with partitions 
into certain residue classes mod 5. Ramanujan viewed these analytically in 
terms of a continued fraction and studied modular transformations of the 
fraction. In this talk we will discuss a hierarchy of R-R type theorems that 
can be understood by means of certain analytic key identities. The interplay 
between the analytic and combinatorial approaches leads to new perspectives 
in the theory of partitions and q-series. Some applications include new 
proofs of Jacobi's triple product identity for theta functions and some 
congruences modulo powers of 2 for certain partition functions. The talk will 
be accessible to non-experts and graduate students.