My major research interests lie on the intersection of physics, mathematics and string theory. Compactifications of M-theory have produced a zoo of physical models and techniques allowing us to answer deep and highly non-trivial questions we usually ask of generic QFTs as instruments to describe our Universe. For example, in so called class S theories we are able to describe completely in IR regime the whole spectrum of so called BPS particles whose quantum numbers reveal a tight connection with geometry - Donaldson-Thomas invariants. One of my current interest is to exploit Hilbert spaces of BPS states in a program of categorification for various manifold invariants.