Logarithmic enumerative geometry for curves and sheaves

I will discuss ongoing work with Davesh Maulik in which we formulate a generalization of the GW/DT conjectures to the setting of simple normal crossings pairs. When the divisor in the pair is smooth, the formulation of the conjecture necessitates the study of the cohomology of the Hilbert scheme of points on a surface. The formulation of the logarithmic GW/DT conjecture requires new geometry coming from a logarithmic Hilbert scheme of points. We prove a strengthened logarithmic degeneration formula on both sides of the correspondence and prove that the new conjectures are compatible with the old ones via degeneration. I’ll discuss this circle of ideas, and explain which parts of the conjectures are within reach.

For more information see:  https://personal.math.ubc.ca/~jbryan/Zoominar-UBC-ETH/