Week starting Monday 24 September 2018
We briefly recall the classical highest weight categories theory (following Cline-Parshall-Scott, Donkin and Ringel) for finite dimensional algebras in a language which allows generalizations to stratified algebras and infinite situations. In particular we formula aspects of tilting theory and Ringel duality in a semi-infinite setting. If time allows we will mention some explicit examples for this construction related to diagram algebras and categorifications.
In this talk we will try to make a little tour from the classical theory of singularities in the sense of Felix Klein to modern developments in representation theory.
The main idea behind it is the concept of categorification. This idea will not be explained in detail, but illustrated by an example. The so called Kleinian singularities arise from finite subgroups of SL(2,C) and have beautiful explicit descriptions. We will present a generalization of them (certain special examples of Springer fibres) and indicate their role in symplectic geometry and Fukaya categories.
As an application we will sketch a construction of Khovanov homology, which is a knot invariant categorifying the Jones polynomial.
Mathematics is the study of the order and patterns that structure the universe. Since the 1970s, computers allowed new understanding of complex and chaotic systems, and resulted in new geometries being discovered such as fractals.
Singapore-based artist and architect Richard Hassell discusses tessellation art, the recurrent tropes of his practice, and the interconnectivity between nature, mathematics, art and architecture.
Richard Hassell is a Founding Director of WOHA, the practice which designed PARKROYAL on Pickering, Oasia Hotel Downtown and the School of the Arts in Singapore. He has served on advisory panels for URA, BCA and DesignSingapore Council. He has taught at the National University of Singapore and is currently an Adjunct Professor at the University of Western Australia. His last solo exhibition “Strange Creatures Complex Tessellations” was on show at Arndt Fine Art in Singapore in 2016. His new exhibition “Knots and Nets” will open in Taipei in October 2018.