I will discuss various operator algebras in supersymmetric quantum field theories in various dimensions. The operator algebras are induced and classified by generalised topological twists. Omega deformation plays an important role in connecting different sectors. This talk is based on previous works and a work in progress with Junya Yagi.

In this talk I will present an optical theorem for perturbative CFTs, which directly computes the double discontinuity of CFT correlators in terms of the discontinuities of correlators at lower loops or lower points, in analogy to the optical theoreom for scattering amplitudes. I will then discuss the application of this theorem to high-energy scattering of type IIb strings in AdS at one loop and finite 't Hooft coupling. Tidal excitations are taken into account and shown to be efficiently described by an AdS vertex function. The result is related to the 1987 flat space result of Amati, Ciafaloni and Veneziano via the flat space limit in impact parameter space.

We will discuss recent progress in understanding (ordinary and generalized) symmetries, dualities and classification of superconformal field theories in 5d and 6d, which involves the study of M-theory and F-theory compactified on Calabi-Yau threefolds.

In view of the recent observations of gravitational-wave signals from black-hole mergers, classical black-hole scattering has received considerable interest due to its relation to the classical bound-state problem of two black holes inspiraling onto each other. In this talk I will discuss the link between classical scattering of spinning black holes and quantum scattering amplitudes for massive spin-s particles. Considering the first post-Minkowskian (PM) order, I will explain how the spin-exponentiated structure of the relevant tree-level amplitude follows from minimal coupling to Einstein's gravity and in the s → ∞ limit generates the black holes' complete series of spin-induced multipoles. The resulting scattering function will be shown to encode in a simple way the classical net changes in the black-hole momenta and spins at 1PM order and to all orders in spins. I will then comment on the results and challenges at 2PM order and beyond.
 

A vast class of 4d SCFTs can be engineered by wrapping a stack of M5-branes on a Riemann surface. These SCFTs can exhibit a variety of global symmetries, continuous or discrete, including both ordinary (0-form) symmetries, as well as generalized (higher-form) symmetries. In this talk, I will focus on discrete and higher-form symmetries in setups with M5-branes on a smooth Riemann surface. Adopting a holographic point of view, a crucial role is played by topological mass terms in 5d supergravity (similar to BF terms in four dimensions). I will discuss how the global symmetries of the boundary 4d theory are inferred from the 5d topological terms, and how one can compute 4d ‘t Hooft anomalies involving discrete and/or higher-form symmetries.

All five-dimensional non-abelian gauge theories have a U(1)U(1)I​U(1) global symmetry associated with instantonic particles. I will describe a mixed ’t Hooft anomaly between this and other global symmetries of  the theory, namely the one-form center symmetry or ordinary flavor symmetry for theories with fundamental matter. I will explore some general dynamical properties of the candidate phases implied by the anomaly, and apply our results to supersymmetric gauge theories in five dimensions, analysing the symmetry enhancement patterns occurring at their conjectured RG fixed points.

For 20 years we have known that average values of characteristic polynomials of random unitary matrices provide a good model for moments of the Riemann zeta function.  Now we consider moments of the logarithmic derivative of characteristic polynomials, calculations which are motivated by questions on the distribution of zeros of the derivative of the Riemann zeta function.  Joint work with Emilia Alvarez. 

We analyse the eigenvectors of the adjacency matrix of a critical Erdös-Rényi graph G(N,d/N), where d is of order \log N. We show that its spectrum splits into two phases: a delocalized phase in the middle of the spectrum, where the eigenvectors are completely delocalized, and a semilocalized phase near the edges of the spectrum, where the eigenvectors are essentially localized on a small number of vertices. In the semilocalized phase the mass of an eigenvector is concentrated in a small number of disjoint balls centred around resonant vertices, in each of which it is a radial exponentially decaying function. The transition between the phases is sharp and is manifested in a discontinuity in the localization exponents of the eigenvectors. Joint work with Johannes Alt and Raphael Ducatez.

Daniel M. Anderson

Department of Mathematical Sciences, George Mason University

Applied and Computational Mathematics Division, NIST

Binary and multicomponent alloy solidification occurs in many industrial materials science applications as well as in geophysical systems such as sea ice. These processes involve heat and mass transfer coupled with phase transformation dynamics and can involve the formation of mixed phase regions known as mushy layers.  The understanding of transport mechanisms within mushy layers has important consequences for how these regions interact with the surrounding liquid and solid regions.  Through linear stability analyses and numerical calculations of mathematical models, convective instabilities that occur in solidifying ternary alloys will be explored.  Novel fluid dynamical phenomena that are predicted for these systems will be discussed.