Sayan Chattopadhyay

Mirror to the Logarithmic hilbert scheme of points on P^2 (joint with P.Bousseau) - The Gross-Siebert program gives a recipe to construct mirrors to log Calabi-Yau varieties. We apply their program to the Logarithmic Hilbert Scheme of two points on P2 and explicitly describe the canonical scattering diagram. We also identify an specific family in this mirror which is isomorphic to the spherical part of the GL2 DAHA.

Here is a poster concering these ideas which was presented at SRI.

2. Enumerativity of Tevelev Degrees of blowups of projective spaces (With U.Dutta) - It is a common theme in Gromov-Witten theory of having to perform virtual counts of curves rather than actual geometric ones. A standard question then becomes, when are said "virtual" counts actually representing geometric curve counts.

In this project we try to answer such questions in the context of Tevelev degrees for blowups of Projective spaces.

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