University of Birmingham > Talks@bham > Geometry and Mathematical Physics seminar > Logarithmic stable maps and where to find them

Logarithmic stable maps and where to find them

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If you have a question about this talk, please contact Andrea Brini.

In enumerative geometry, we are interested in “counting” the number of curves on an algebraic variety which satisfy certain conditions. Classical examples include the 27 lines on the cubic surface, or the 12 rational cubics passing through 8 general points in the plane.

These days, enumerative geometry is centred on Gromov-Witten theory – a robust framework for formulating and studying enumerative problems, with deep and subtle connections to theoretical physics. The resulting counts are referred to as Gromov-Witten invariants, and satisfy a long (and ever expanding) list of remarkable properties.

Logarithmic Gromov-Witten theory is an enhancement of Gromov-Witten theory, which incorporates curves satisfying tangency conditions with respect to a hypersurface. In this talk, I will discuss the basics of logarithmic Gromov-Witten theory, focusing on examples and the beautiful interplay with the combinatorial world of tropical geometry. Time permitting, I will present joint work in progress with Lawrence Barrott, in which we study the behaviour of logarithmic Gromov-Witten invariants under degenerations of the hypersurface, and employ logarithmic deformation theory in order to relate the logarithmic invariants to the standard ones.

This talk is part of the Geometry and Mathematical Physics seminar series.

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