I will present several new  3d N=2 dualities with super-potentials involving monopole operators. Some of the theories that I will discuss describe systems of D3 branes ending on pq-webs. In these cases  3d mirror symmetry is a consequence of S-duality.

 

It was discovered in the 1970s that black holes are thermodynamic objects carrying entropy, thus suggesting that they are really an ensemble of microscopic states. This idea has been realized in a remarkable manner in string theory, wherein one can describe these ensembles in a class of models. These ensembles are known, however, to contain configurations other than isolated black holes, and it remains an outstanding problem to precisely isolate a black hole in the microscopic ensemble. I will describe how this problem can be solved completely in N=4 string theory. The solution involves surprising relations to mock modular forms -- a class of functions first discovered by S. Ramanujan about 95 years ago. 

A large number of examples of compact G2 manifolds, relevant to supersymmetric compactifications of M-Theory to four dimensions, can be constructed by forming a twisted connected sum of two appropriate building blocks times a circle. These building blocks, which are appropriate K3-fibred threefolds, are shown to have a natural and elegant construction in terms of tops, which parallels the construction of Calabi-Yau manifolds via reflexive polytopes.

I will consider higher derivative corrections to the graviton 3-point coupling within a weakly coupled theory of gravity. Lorentz invariance allows further structures beyond that of Einstein’s theory. I will argue that these structures are constrained by causality, and show that the problem cannot be fixed by adding conventional particles with spins J ≤ 2, but adding an infinite tower of massive particles with higher spins. Implications of this result in the context of AdS/CFT, quantum gravity in asymptotically flat space-times, and non-Gaussianity features of primordial gravitational waves are discussed.