Séminaires : Géométrie énumérative

Equipe(s) : aa,
Responsables :Penka Georgieva, Ilia Itenberg.
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Orateur(s) Kendric Schefers - UT Austin,
Titre Microlocal perspective on homology
Horaire14:00 à 15:00

The difference between the homology and singular cohomology of a space can be seen as a measure of the singularity of that space. This difference as a measure of singularity can be made precise in the case of the special fiber of a map between smooth schemes by introducing the so-called "microlocal homology" of such a map, an object which records the singularities of the special fiber as well as the codirections in which they arise. In this talk, we show that the microlocal homology is in fact intrinsic to the special fiber—independent of its particular presentation by any map—by relating it to an object of -1-shifted symplectic geometry: the canonical sheaf categorifying Donaldson-Thomas invariants introduced by Joyce et al. Time permitting, we will discuss applications of our result to ongoing work relating to the singular support theory of coherent sheaves.