#### Mark McLean

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#### Research summary

I am interested in the relationship between complex analytic/algebraic geometry and symplectic geometry.
At the moment I have been using pseudo-holomorphic curves to understand this relationship.
These methods were initially introduced by Gromov and have
now developed into important tools such as Gromov-Witten invariants, Symplectic Field Theory
and Floer homology.
These are powerful tools with applications not just in symplectic and algebraic/analytic geometry but also dynamics, mathematical physics and low dimensional topology.
I have been studying smooth affine varieties and also complex singularities from this perspective. I am also interested in the relationship between symplectic geometry and birational geometry.