The Mahler lectures are a biennial activity organised by the Australian Mathematical Society. In 2009 we have partnered with the Clay Mathematical Institute to combine the Mahler Lectures and the Clay Lectures into the 2009 Clay–Mahler Lecture Tour, with funding also from the Australian Mathematical Sciences Institute.

• 6th October, in Russell Love Theatre, Richard Berry Building, Melbourne University, 12:00pm;
  colloquium talk by Mohammed Abouzaid (MIT): Understanding hypersurfaces through tropical geometry.
• 7th October, in Babel Middle Theatre (106), 2:15pm;
  colloquium talk by Mohammed Abouzaid (MIT):
  String topology and the Fukaya category of cotangent bundles.
• 7th October, in Babel Middle Theatre (106), 3:30pm;
  colloquium talk by Mohammed Abouzaid (MIT):
  A topological model for the Fukaya category of plumbings.

Abstract: Understanding hypersurfaces through tropical geometry

Given a polynomial in two or more variables, one may study the zero locus from the point of view of different mathematical subjects (number theory, algebraic geometry, ...). I will explain how tropical geometry allows to encode all topological aspects by elementary combinatorial objects called tropical varieties.

Abstract: String topology and the Fukaya category of cotangent bundles

The most interesting version of the Fukaya category of cotangent bundles includes Lagrangians which are allowed to be non-compact. I will explain how this category is essentially equivalent to the category of modules over the based loop space. The classical equivalence between symplectic homology and the homology of the based loop space (with the pair of pants product on one side and the Chas–Sullivan product on the other) follows from this story.

Abstract: A topological model for the Fukaya category of plumbings

The simplest examples of symplectic manifolds beyond cotangent bundles are obtained by plumbings of these. I will explain a topological model for the Fukaya categories of these manifolds; the model is given in terms of classical invariants from algebraic topology (the cochain complexes on the skeleta ...).

For More Information: contact: Arun Ram (A.Ram@ms.unimelb.edu.au)