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In this talk I will discuss effective field theories for two classes of non-equilibrium systems, one far and one near equilibrium. The backbone of the approach is the Schwinger-Keldysh formalism, which is the natural starting point for doing field theory in non-equilibrium situations. In the first part of the talk I will present an effective response for topological driven (Floquet) systems, which are inherently far from equilibrium. As an example, I will discuss a chiral Floquet drive coupled to a background $U(1)$ field, which gives rise to a theta term in the response action, and show that this is independent of smooth deformations of the underlying system. In the second part, I will discuss an ongoing project using effective field theories for hydrodynamics. I will show that chiral diffusion for interacting systems in 1+1 dimensions, which may be relevant to edge transport in quantum Hall systems, has an infrared instability. I will then discuss the fate of this instability.

Many well-known correlations between dark matter and baryons exist on galactic scales. These can essentially be encompassed by a simple scaling relation between observed and baryonic accelerations, historically known as the Mass Discrepancy Acceleration Relation (MDAR). This relation has prompted many theories that attempt to explain the correlations by invoking additional fundamental forces on baryons. Since a collisionless cold dark matter (CDM) model is desirable on scales of clusters and above, the standard lore has been that a theory which reduces to the MDAR on galaxy scales but behaves like CDM on larger scales provides an excellent fit to data. However, this statement should be revised in light of recent results showing that a fundamental force that reproduces the MDAR is often challenged at accommodating Milky Way dynamics. In this study, we test this claim on the  example of Superfluid Dark Matter. We find that a standard CDM model is strongly preferred over a static superfluid profile.  This is due to the fact that the superfluid model over-predicts vertical accelerations, even while reproducing galactic rotation curves.  Our results establish an important criterion that any dark matter model must satisfy within the Milky Way.

In this talk, I will describe the framework of large D matrix models, which provides new limits for matrix models where the sum over planar graphs simplifies when D is large. The basic degrees of freedom are a set of D real matrices of size NxN which is invariant under O(D). These matrices can be naturally interpreted as a real tensor of rank three, making a compelling connection with tensor models. Furthermore, they have a natural interpretation in terms of D-brane constructions in string theory. I will present a way to define a large D scaling of the coupling constants such that the sum over Feynman graphs of fixed genus in matrix models admits a well-defined large D expansion. In particular, in the large D limit, the sum over planar graphs truncates to a tractable, yet non-trivial, sum over generalized melonic graphs. This family of graphs has been shown to display very interesting properties, especially in the case of quantum mechanical models such as the SYK model and SYK-like tensor models. If time allows, I will also explain how one can use the large D limit of matrix models to simplify the sum over all genera, which is notoriously divergent. 

Absolute Gromov-Witten theory is known to have many nice structural properties, such as quantum cohomology, WDVV equation, Givental's formalism, mirror theorem, CohFT etc.. In this talk, I will explain how to obtain parallel structures for relative Gromov-Witten theory via the relation between relative and orbifold Gromov-Witten invariants. This is based on joint works with Honglu Fan, Hsian-Hua Tseng and Longting Wu.