Speaker: Professor Askold Khovanskii 
Affiliation: University of Toronto


A beautiful isoperimetric inequality was known to the Ancient Greeks claiming that the circle has the largest area amongst all planar domains with a fixed boundary length. This inequality has many interesting geometric generalizations. One of them is the famous Brunn-Minkowsky inequality which relates volumes of convex bodies and the volume of their Minkowsky sum. One can define the mixed volume of n-convex bodies in n-dimensional real vector space. Another one, the more general Alexandrov-Fenchel inequality relates certain mixed volumes of dierent n-tuples of convex bodies. Quite surprisingly, there are analogous inequalities in algebra. First of all, the BKK (Bernstein-Khovanskii-Koushnirenko) theorem computes the number of solutions of n generic polynomial equations with given Newton polyhedra in (C*)n in terms of the mixed volume of their Newton polyhedra. Indeed, such inequalities, known as Khovanskii-Teissier inequality, were eventually found. Furthermore, a group of mathematicians, in connection with Field's Laureate June Huh, has recently discovered multiple fascinating applications for these inequalities.

In this talk, I will discuss such inequalities and other relations between Algebraic and Convex Geometries. The talk will be accessible to a broad mathematical audience.

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