RESEARCH IN PAIRS
Floer and Symplectic Homology and Contact Loci in Arc Spaces (2574)
Homologie de Floer et homologie symplectique et .......
Dates: 13-24 September 2021 
​Place: CIRM (Marseille Luminy, France)
DESCRIPTION
In [?] McLean constructs a spectral sequence which converges to Floer Homology, and whose E1 page is formed by ordinary homology groups of spaces that are constructed using an embedded resolution of singularities. Bobadilla, Budur, Lê Quy Thuong and Honc Duc Nguyen [1] have found a connection of this theory with the study of arc spaces connected with motivic integration and the Monodromy Conjecture. Denef and Loeser proved that the Euler characteristic of the m-th contact loci of a complex polynomial coincides with the Lefschetz number of the m-th iterate of its monodromy. Answering questions of Seidel and McLean, the four authors mentioned above have found a spectral sequence converging to the cohomology of the m-th contact loci, and whose E1-page coincides with McLean’s.

In this Research in Pairs event, we aim to advance towards the solution of the conjecture.
PARTICIPANTS (list to be completed)
References
[1]  N. Budur, J. Fernandez de Bobadilla, Quy Thuong Lê, Hong Duc Nguyen. Cohomology of contact loci. arXiv:1911.08213
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