CAPITAL REGION ALGEBRA/NUMBER THEORY SEMINAR 


Speaker:       Brenda Johnson, Union College     

Time:          Wednesday, December 1, at 4:30pm       

Place:         Bailey Hall 102, Union College 

Title:         Taylor and Lagrange polynomial approximations 
               of functors


Abstract:

We will discuss how a functor  F  from finite based sets to the
category of modules over a fixed ring  can be approximated by two
sequences of functors,
  
F(*) = P_0F --> P_1F --> P_2F --> ... ,                       (1) 
  
and
  
L_1F --> L_2F --> L_3F --> ... ,                              (2)
  
that have properties analogous to those of  Taylor and Lagrange
polynomials, respectively.  For most functors,  applying  P_1  to (2)
produces a filtration of  P_1F  which is closely related
to  a bicomplex   Xi(F)  constructed by A. Robinson and S. Whitehouse to
study  E_{\infty}  ring structures on spectra. This relationship should
shed new light on the role of certain Lie algebras in
Taylor polynomial approximations to functors.