Date:
Tue, 06/02/202411:00-12:00
Location:
Zoom
I will discuss some applications of mirror symmetry to the study of mod 2 cohomology of some real Calabi-Yau threefolds. There are two approaches. One is via Lagrangian torus fibrations and Strominger-Yau-Zaslow (SYZ) mirror symmetry, where the real Calabi-Yau is the fixed point locus of a fibre preserving involution. The second one is via dual reflexive polytopes, where the real Calabi-Yau is given by Viro’s patchworking. It turns out that in both cases the topology of the real Calabi-Yau is related to the geometry of a “mirror” line-bundle L on the the mirror Calabi-Yau. For instance, it follows from results of Arguz-Prince and recent work of mine, that in the SYZ case, the mod-2 cohomology is determined by a ``twisted squaring of line-bundles’’ in the mirror, i.e. by the map D —> D^2 + DL, where D is a line-bundle. We can apply this to find an example of a connected (M-2)-real quintic threefold. The dual reflexive polytopes approach is work in progress with A. Renaudineau.