Dr Jeffrey Giansiracusa

Associate Professor
Mathematics
Telephone: (01792) 295087
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My research brings the powerful tools of topology to bear on fascinating objects such as moduli spaces from algebraic geometry. The tools of one field illuminate the creations of another, and a better understanding of the structure of moduli spaces leads to results in many mathematical fields, such as number theory and even theoretical physics. It is an example of the interconnectedness of the mathematical universe. The novelty and advantage of using topological tools is that topology is designed to organise and filter information; it ignores the the local structure and sees only the underlying global structure. This allows a flexibility of models that can reveal patterns and properties that were previously invisible.

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.

See more...

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

  • Moduli spaces from a topological point of view 2010 - 2015

    EP/I005908/1, £438K

Administrative Responsibilities

  • Director of Research - Department of Mathematics

    2016 - Present