The ‘What is…?’ seminar series is about an idea, concept or method that the speaker has found surprising, useful or intriguing, and which they would like to share with colleagues and students. The talk answers a question of the form “What is…?” and is directed at a broad audience of non-experts and experts alike. There is ample time for discussion, comments and questions. This talk may also serve as a prelude to a more technical talk in a specialised seminar series. Recordings can be found in the YouTube playlist.
‘What is…?’ Seminar ‘What is a Hodge module?’
Kari Vilonen, University of Melbourne
15 September 2022
Abstract: I will explain what a Hodge module is starting from Poincare.
Biography: Kari Vilonen is a professor of mathematics at the University of Melbourne. His research is in geometric aspects of representation theory and the Langlands program. He has also worked on foundational questions on perverse sheaves and D modules including the microlocal point of view.
‘What is…?’ Seminar ‘What is a moduli space?’
Kenneth Ascher, University of California, Irvine
25 August 2022
Abstract: Moduli spaces are geometric spaces which parametrize equivalence classes of algebraic varieties. I will discuss the moduli space of algebraic curves equivalently Riemann surfaces) of genus g, and use this example to motivate some interesting questions in higher dimensions. Watch the recording.
Biography: Kenneth Ascher is an assistant professor in the department of mathematics at the University of California Irvine. His research area is algebraic and arithmetic geometry, with specific focuses on moduli spaces of higher dimensional varieties and applications to questions in arithmetic. He received his PhD in 2017 from Brown University under the direction of Dan Abramovich , and was a postdoctoral fellow at the Massachusetts Institute of Technology and Princeton University.
‘What is…?’ Seminar ‘What is a virtual knot?’
Hans Boden, McMaster University
31 May 2022
Abstract: Virtual knots were introduced by Louis Kauffman in 1999 as a completion of classical knot theory in which planarity is no longer required. Virtual knots have been studied using a variety of approaches, including algebra, combinatorics, and geometric methods. They also have strong connections to quantum topology and finite type invariants. This talk will survey some fascinating results that have been established and present also open problems and directions for future research.
Biography: Dr Hans U. Boden is a professor of mathematics at McMaster University in Canada. He is visiting the University of Sydney and SMRI from May 17 to June 11. His research interests are on the geometry and topology of manifolds, especially gauge theory and low-dimensional topology. In recent years, his work has focused on developing geometric methods to understand knotting and linking in 3-dimensional manifolds. While in Sydney, he will be working closely with Dr Zsuzsi Dancso on a collaborative project related to the Tait conjectures in knot theory.
‘What is…?’ Seminar ‘What is a cohomological field theory?’
Pedram Hekmati, University of Auckland
26 April 2022
Abstract: Many interesting invariants in geometry satisfy certain glueing or factorisation conditions, that are often useful when doing calculations. Topological quantum field theories (TQFTs) emerged in the 1980s as an organising structure for invariants that are governed by bordisms. In 2 dimensions, bordisms are surfaces with boundaries and the TQFT has a simple algebraic description. By remembering the diffeomorphisms of the surfaces, one is lead to the notion of a cohomological field theory. This talk will give an overview of these ideas and be aimed at a broad audience. Watch the recording.