During past 25 years there has been intensive interaction between string theory and geometry which has led to a creation of entirely new mathematical areas. String theory has suggested that "conventional" geometry emerges from the quantum theory at certain limits. Then various string dualities give equivalent but mathematically very different descriptions of the same physical quantities. A beautiful and deep example illustrating all these ideas is mirror symmetry.
The M-Center supports and promotes research in mathematical questions arising from string theory, in which mirror symmetry and tropical geometry play a central role.
The Strominger-Yau-Zaslow conjecture has led to work by Kontsevich, Soibelman, Gross, Siebert, Zharkov and others to view mirror symmetry in terms of integral affine manifolds and tropical data on them. On the other hand, Mikhalkin's pioneering work on holomorphic curve counting using tropical geometry demonstrated that Gromov-Witten invariants were accessible by tropical methods, and increasingly, tropical methods are being seen as a tool for studying algebraic varieties. Some of the current research directions pursued at the M-Center include: