From geometry to quantum gravity and back

Gastvortrag

According to general ideas in theoretical physics, effective quantum theories of particle physics or cosmology are severely constrained if one demands that they can be coupled consistently to gravity at high energies. Various physical consistency considerations have been invoked to make these constraints concrete and resulted in a web of so-called Swampland conjectures in the more recent literature. In the context of string or M-theory compactified on special holonomy geometries, these physics conjectures can be translated into very precise and general statements about the compactification spaces and their moduli spaces. Geometric insights can hence be used to quantitatively test some of the quantum gravity conjectures and, vice versa, the latter give rise to physics predictions for mathematics. We describe this research program by reviewing recent progress in quantitatively understanding the Weak Gravity Conjecture or the Emergent String Conjecture and explain, among other things, their relation to Kahler geometry and BPS state counting on Calabi-Yau varieties. If time permits, we will also motivate from string theory, along similar lines, an upper bound for the rank of the Modell-Weil group of elliptic Calabi-Yau manifolds.