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Coulomb Phases and Anomalies: Geometric Approach to 5d/6d Theories

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I will review the geometric approach to the description of Coulomb branches and Chern-Simons terms of gauge theories coming from compactifications of M-theory on elliptically fibered Calabi-Yau threefolds. Mathematically, this involves finding all the crepant resolutions of a given Weierstrass model and understanding the network of flops connecting them together with computing certain topological invariants. I will further check that the uplifted theory in 6d is anomaly-free using Green-Schwartz mechanism. I will give examples on the theory with semi-simple gauge groups such as SU(2)xG2, which plays a major role in the classification of 6d superconformal theories, and SU(2)xSU(3), which describes the non-abelian sector of the standard model.