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About MeI am a postdoctoral research fellow in the Faculty of Mathematics of the NRU Higher School of Economics in Moscow, Russia. I am a native of Christchurch, New Zealand. After completing an MSc at Canterbury University, I accepted a Fulbright scholarship to attend Indiana University in the USA. There I completed a PhD in mathematics under the advisorship of Paul Kirk.
Note that my full name is Ashley Charles Lightfoot. |
Research |
My research interests lie in low dimensional topology, the aim of which is to understand three- and four-dimensional manifolds. Classical knot theory is a principal tool in studying 3-manifolds, and its generalizations illustrate interesting properties of manifolds of higher dimension. Generalized link homotopy is one instance of this, and my work has addressed problems in that subject in the four-dimensional setting, drawing largely from the study of surface braids in 4-space and immersed surfaces in 4-manifolds. Certain Vassiliev (or finite-type) knot invariants arise in this study, and an active part of my research is to explore their applications.
Invariants are an indispensable tool for obtaining classification results, and a recurring theme in my research is to address the applicability of various invariants in low-dimensional topology. |
Contact |
Room 309
Faculty of mathematics NRU Higher school of Mathematics Usacheva str. 6, Moscow, Russia 119048 |
