CAPITAL REGION ALGEBRA/NUMBER THEORY SEMINAR 


Speaker:       Professor Matthias Beck, SUNY-Binghamton   
Time & Place:  Wednesday, November 15, at 4:30pm, in ES 152A  
Title:         Lattice point enumeration in rational polytopes 


Abstract: 

We use generating functions and analytic methods to count integer 
("lattice") points in polytopes with rational vertices. More precisely, we
study the number of lattice points as the polytope gets dilated by an
integer factor. This expression is known as the Ehrhart quasipolynomial. 

Even in basic examples, we can see that the building blocks of these
counting functions are Dedekind sums and their various generalizations. 
This work generalizes well-known formulas for the `Mordell tetrahedron'.  

Finally, we show how to apply our methods to two old counting problems: 
enumeration of magic squares, and the 'coin-exchange' problem of 
Frobenius.   



Refreshments at 4:15 pm in ES 152.