Vincentas Mulevicius

My research explores the mathematical foundations of quantum physics by focusing on topological quantum field theories (TQFTs) through the lens of category theory. I use the Atiyah-Segal formalism, which describes TQFTs as functors mapping the geometric category of spacetime cobordisms to algebraic categories, establishing a rigorous mathematical dictionary for quantum dynamics. This research expands the functorial paradigm by introducing extended topological 'defects' – representing particles, strings, and branes – into the spacetime manifold. We investigate how new theories emerge when spacetime is saturated with a fine 'defect foam' (the so-called 'condensation' or 'generalised orbifold' construction), while also exploring dimensional reduction and the implications of extra dimensions within these emergent models. The categorical approach also provides tools for studying topological phases of matter and their applications to fault-tolerant topological quantum computation.