Speaker: Professor Askold Khovanskii 
Affiliation: University of Toronto


Newton{Okounkov bodies relate Algebraic geometry with Convex geometry via semigroups of integral
points in the lattice Zn. In general, sub-semigroups of the lattice Zn are very complicated objects. It turns
out that asymptotic behavior of such semigroups is simple enough. It has a nice description via Convex
geometry (via its convex Newton{Okounkov cone and Newton{Okounkov bodies).
Let me present a high school problem, which provides a simplest example of asymptotic behaviour of a
Problem. Let G Z be an additive semigroup generated by 3; 5 2 Z. Prove that G contains all natural
numbers n 8.
One can construct a Zn valued valuation on the multiplicative group of nonzero rational functions on any
irreducible n-dimensional algebraic variety. Such valuation relates algebraic geometry with subsemigroups
in Zn.
Newton{Okounkov bodies allow to provide an elementary proof of isoperimetric type inequalities in Al-
gebraic geometry.

About Pure mathematics seminars

We present regular seminars on a range of pure mathematics interests. Students, staff and visitors to UQ are welcome to attend, and to suggest speakers and topics.

Seminars are usually held on Tuesdays from 2 to 3pm.

Talks comprise 45 minutes of speaking time plus five minutes for questions and discussion.

Information for speakers

Researchers in all pure mathematics fields attend our seminars, so please aim your presentation at a general mathematical audience.

Contact us

To volunteer to talk or to suggest a speaker, email Ole Warnaar or Ramiro Lafuente.


Physics Annexe (06)
Room: 407