Talks

N=8 supergravity in 4 dimensions exhibits a surprisingly favorable UV behavior -- it is known from explicit computations that the 4-point amplitudes in N=8 supergravity are finite up to 4-loop order. I explain how a "matrix-element approach" can be used to study candidate counterterms for UV divergences in this theory. This approach both demystifies the finiteness found in previous computations, and predicts finiteness of arbitrary n-point amplitudes in N=8 supergravity below the 7-loop order. It also points to the 7-loop 4-point amplitude as the first amplitude whose finiteness is not guaranteed by any known symmetry of the theory.

Quantum mechanics does not allow us to measure all possible combinations of observables on one system. Even in the simplest case of two observables we know, that measuring one of the observables changes the system in such way, that the other measurement will not give us desired precise information about the state of the system. Prominent examples of such observables are measurement of position and momentum of a particle, or measuring spin along two orthogonal directions. However, once we accept the possibility of imprecise measurements, we can consider to perform such measurement within one experiment. This is the basis of the notion of coexistence. I will present the basics of coexistence by showing how to perform the spin measurement in two directions, while considering the imprecision of the measurement described by POVMs. We can also go a little further and consider coexistence of instruments, i.e. measurements, where on the output besides classical information we are also left out with quantum post-measurement state.

Recent observations first made in string theory led to the realization that introducing various ``deformations" (finite volume, appropriate double-trace operators...) allows for an analytic study of many nonperturbative aspects of arbitrary four-dimensional gauge theories. Notably, the confinement mechanism, the generation of mass gap, and, in some cases, chiral symmetry breaking can be studied in a theoretically controlled manner. In this talk, I will review: i.) the ideas and tools involved, ii.) the main results obtained so far in this approach (and its limitations), iii.) our understanding of its relation to other approaches to (non-)supersymmetric gauge dynamics, iv.) ongoing and possible future work.