Dr Jeffrey Giansiracusa

Associate Professor
Mathematics
Telephone: (01792) 295087
Email: JavaScript is required to view this email address.
Room: Office - 216
Second Floor
Talbot Building
Singleton Campus

Please visit my homepage at: https://sites.google.com/view/jeffreygiansiracusa/home 

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.

Areas of Expertise

  • Tropical geometry
  • Topology and homotopy theory
  • algebraic geometry
  • Moduli spaces
  • Topological quantum field theory
  • Operads
  • Mapping class groups and diffeomorphism groups

Publications

  1. & Equations of tropical varieties. Duke Mathematical Journal 165(18), 3379-3433.
  2. & A Grassmann algebra for matroids. manuscripta mathematica
  3. & On the relation between hyperrings and fuzzy rings. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
  4. & ON THE HOCHSCHILD HOMOLOGY OF INVOLUTIVE ALGEBRAS. Glasgow Mathematical Journal, 1-12.
  5. Moduli spaces and modular operads. Morfismos 17(2), 101-125.
  6. Bertsch, G.F., Giansiracusa, J., Yabana, K. Application of time-dependent density-functional theory to electron-ion coupling in ethylene. Israel Journal of Chemistry 42
  7. Holland, J.P., Giansiracusa, J.H., Bell, S.G., Wong, L.-L., Dilworth, J.R. In vitrokinetic studies on the mechanism of oxygen-dependent cellular uptake of copper radiopharmaceuticals. Physics in Medicine and Biology 54(7), 2103-2119.
  8. & Pontrjagin–Thom maps and the homology of the moduli stack of stable curves. Mathematische Annalen 349(3), 543-575.
  9. The stable mapping class group of simply connected 4-manifolds. Journal für die reine und angewandte Mathematik (Crelles Journal) 2008(617), 215-235.
  10. The diffeomorphism group of a K3 surface and Nielsen realization. Journal of the London Mathematical Society 79(3), 701-718.
  11. & Cyclic operad formality for compactified moduli spaces of genus zero surfaces. Transactions of the American Mathematical Society 364(11), 5881-5911.
  12. & (2010). Formality of the framed little 2-discs operad and semidirect products. Presented at Contemporary Mathematics,, 115-121.AMS.
  13. & Vanishing of universal characteristic classes for handlebody groups and boundary bundles. Springer/TCMS 6(1), 103-112.
  14. The framed little 2-discs operad and diffeomorphisms of handlebodies. Journal of Topology 4(4), 919-941.
  15. & INVARIANCE PROPERTIES OF MILLER-MORITA-MUMFORD CHARACTERISTIC NUMBERS OF FIBRE BUNDLES. The Quarterly Journal of Mathematics
  16. & On the homotopy type of the Deligne–Mumford compactification. Algebraic & Geometric Topology 8(4), 2049-2062.

Teaching

  • MA-282 Game Theory and Optimization

    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).

Supervision

  • Discrete module categories (current)

    Student name:
    PhD
    Other supervisor: Dr Martin Crossley
  • Tropical Scheme theory and the tropical j-invariant (current)

    Student name:
    PhD
    Other supervisor: Dr Martin Crossley
  • 'Derived Categories and Enriched Category Theory' (current)

    Student name:
    PhD
    Other supervisor: Dr Grigory Garkusha

Key Grants and Projects

Administrative Responsibilities

  • Director of Research - Department of Mathematics

    2016 - Present