Presented by: 
Richard Brak (The University of Melbourne)
Mon 23 May, 2:00 pm - 3:00 pm
Hawken Engineering Building (50), room N202

The enumeration of lattice paths is a classical topic in combinatorics with many applications. I will talk about the enumeration of different paths on a lattice with various boundary walls and the connection with Weyl groups. Along the way we will discover how Pascal’s triangle can be generalized to multidimensional pyramids and how paths in tubes are related to affine Weyl groups. The bimodal property of binomial coefficients arrises from a reflection symmetry. This symmetry generalises to the pyramid coefficients. Two path problems (Kreweras and Gessel) have proved particularly difficult to solve despite the simplicity of the final result. We will get an understanding of this difficulty from the geometry of the associated Weyl chambers.