I work with mathematical and nonperturbative aspects of Gauge Theory, and their relations to symmetry breaking (local or global) and how the moduli space and its topology determine the quantization of the physical system at hand. I am also interested in quantum phases and the space of quantum field theories, non-linear Fredholm theory, branes and topological quantization (which is related to the previous topic via Index Theorems); noncommutative and spectral geometry, and their relation to deformation and geometric quantization; Higgs Bundles; Geometric Langlands Duality (dualities in general: AdS/CFT, modular and mirror symmetry, etc); quantum fields in curved spaces; higher gauge theory and category theory; and so on — and their relations to Quantum Gravity.
Lately, I have also been peaking at some problems in Theoreical and Computational Neuroscience, e.g., Ersätz-Brain.
Veronica Belmont - about.me user since 2010
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