Prof. dr. Sinai Robins: Polyhedral cones, their theta functions, and what they tell us about polytopes

Sinai Robins 

 

Nanyang Technological University, Singapur 

 

First, we will give a general introduction to some ideas in polyhedral combinatorics. Then we will see that the result of J. Gram gives us a way to relate the solid angles of each face of a polytope to each other, a result that extends (to all dimensions) the 2-dimensional elementary school theorem about sums of angles of a triangle adding up to 180 degrees. Finally, we give a further extension of Gram's theorem, using polyhedral theta functions.