CAPITAL REGION ALGEBRA/NUMBER THEORY SEMINAR 


Speaker:       Professor Pedro Teixeira, Union College 

Time:          Wednesday, October 22, at 4:30pm 

Place:         Bailey Hall 100, Union College 

Title:         p-Fractals and the Rationality of Certain Hilbert-Kunz Series 
 


Abstract:

Hilbert-Kunz functions are interesting and mysterious, and a source of 
many open problems---one of the main such problems being the question 
of whether its associated generating function, the Hilbert-Kunz series, 
is always a quotient of polynomials. In this talk I'll present some of 
the tools used in the calculation of the Hilbert-Kunz function. I'll 
indicate how its calculation leads naturally to certain real valued 
functions, while the proof of the rationality of the Hilbert-Kunz 
series depends on proving that these functions have certain 
self-similarity properties, formalized through the introduction of the 
notion of p-fractals.  This is joint work with Paul Monsky.


Refreshments at 4:15 pm in the Math. Dept. lounge, 2nd floor.