I work across several areas of mathematics, broadly under the heading of Topology and Geometry, covering both pure and applied aspects. I am involved in research in topological data analysis, the foundations of tropical geometry and algebraic geometry over the so-called field with one element, and homotopy theory in low-dimensional topology.
Please visit my homepage at: https://sites.google.com/view/jeffreygiansiracusa/home
Geometry, communication in mathematics, game theory, mathematical modelling
An introduction to Euclidean geometry and the axiomatic method, as a basis for developing general mathematical skills including logic and communication.
Game theory is about strategies for making decisions, in cases where there are two or more players. The complication is that the possible choices for the other players may influence a particular player's choice of strategy. Economics has many examples of the application of game theory, but it has also been applied to areas as diverse as global politics (e.g. the Cuban missile crisis) and evolutionary biology (e.g. the hawks and doves game). Optimisation is about finding the optimum strategy (e.g. maximising profit for a company) by maximising or minimising a function in a specified domain. Again it has applications in economics, but it has also been used in engineering design (e.g. genetic algorithms were used to design the superconducting magnets in the CERN particle accelerator) and molecular biology (modelling shapes of molecules by minimising energy).
Funded by EPSRC grant EP/R018472/1, “New approaches to data science: application-driven topological data analysis”, with Pawel Dlotko, Ulrike Tillmann, Heather Harrington, Vitaliy Kurlin, £2.6M
, with Joint project with Prof. Andrea Pulita (Grenoble), £85k
Funded by EPSRC grant EP/I005908/1, £438k
2011 - Present
2010 - 2011
2007 - 2010
2006 - 2007
I am enthusiastic about public engagement. I’ve reached thousands of Welsh primary and secondary school students through Master Classes and other activities, and I’ve appeared as a guest on the BBC RadioWales programme Science Café.
