Behrend Memorial Lectures
The School of Mathematics and Statistics at the University of Melbourne hosts a biennal public lecture in mathematics, dedicated to the memory of Felix Behrend. The event is made possible by the generosity of the Behrend family.
The 27th Behrend Memorial Lecture
Tuesday 4 August 2015, 6.00pm  7.00pm, Cuming Theatre, Chemistry Building
Linear Inequalities
MichÃ¨le Vergne
Directeur de Recherches, Classe Exceptionelle
Institut de MathÃ©matiques de Jussieu, Paris
Given several linear inequalities, it is not easy to see if this set of linear inequalities has a solution. It is even less so to find integers satisfying all given linear inequalities. I will give several examples, such as the Minkowski theorem and some other very recent ones, where we are sure that integral solutions exist. I will discuss the complexity of finding these solutions.
Finally, I will show that systems of linear inequalities arise naturally in problems related to quantum computers.
Update: Professor Vergne has allowed us to post the slides from her Behrend lecture.
Outline:

Is there a solution to some given linear inequalities?

Is there a relation between the number of solutions in integers and the volume of the set of solutions?

Quantum computing and linear inequalities for eigenvalues.
Professor Vergne will also give a colloquiumstyle lecture at La Trobe University on Wednesday 5 August, from 2pm to 3pm, in room 310 in Physical Sciences 2. The title of this talk is Integer points in polytopes.
Link to the 2013 lecture page