March 14, Wednesday, 15:30, room 211

Valeriya Ignatovskaya

Three-dimensional Generalizations of Pick’s Formula and the Khovanskii-Pukhlikov theorem

It is known that classical Pick’s formula can not be transferred to higher dimensions. In the first part of my talk, I will show another approach to express the area of convex integer polygons. This way can be easily generalized to higher dimensions so the volume of 3-dimensional polytopes can be found. After that, I will introduce the Todd operator and prove the Khovanskii-Pukhlikov theorem about relations between the continuous and discrete volume of an integral polytope.
No prerequisites required.