The talk will focus on manifolds with special holonomy, a class of spaces whose infinitesimal symmetries play a crucial role in M-theory compactifications. M-theory, often referred to as the "theory of everything," has emerged in recent decades as a leading candidate for unifying the four fundamental forces of nature: electromagnetism, gravity, and the weak and strong nuclear forces.

We will begin with a brief introduction to Calabi-Yau and G₂ manifolds, followed by an overview of my recent research on the connections between symplectic, contact, and calibrated structures in these manifolds.