Talks

Kontsevich and Soibelman defined Donaldson-Thomas invariants of a 3d Calabi-Yau category with a stability condition. Any cluster variety gives rise to a family of such categories. Their DT invariants are encapsulated in single formal automorphism of the cluster variety, called the DT-transformation. An oriented surface S with punctures, and a finite number of special points on the boundary give rise to a moduli space, closely related to the moduli space of PGL(m)-local systems on S, which carries a canonical cluster Poisson variety structure. We determine the DT-transformation of this space. This is a joint work with Alexander Goncharov.

Over the past several years, our understanding of topological electronic phases of matter has advanced dramatically.   A paradigm that has emerged is that insulating electronic states with an energy gap fall into distinct topological classes.   Interfaces between different topological phases exhibit gapless conducting states that are protected topologically and are impossible to get rid of.   In this talk we will discuss the application of this idea to the quantum Hall effect, topological insulators,  topological superconductors and the quest for Majorana fermions in condensed matter.   We will then show that similar ideas arise in a completely different class of problems.    Isostatic lattices are arrays of masses and springs that are at the verge of mechanical instability.   They play an important role in our understanding of granular matter, glasses and other 'soft' systems.  Depending on their geometry, they can exhibit zero-frequency 'floppy' modes localized on their boundaries that are insensitive to local perturbations.   The mathematical relation between this classical system and quantum electronic systems reveals an unexpected connection between theories of hard and soft matter.

Quantum non-demolition measurements performed using qubit-based artificial atoms may enable the next generation of higher mass dark matter axion search experiments.  These QND measurements can precisely determine the amplitude of the photon wave sourced by the dark matter axions while placing the back reaction noise into the phase quadrature. By evading the standard quantum limit of phase-preserving amplifiers, the QND photon can potentially reduce readout noise by orders of magnitude.  Combined with the radio frequency quantum buses to extract the signals, the next generation axion dark matter detector may closely resemble or actually be a multi-qubit quantum computer.

The Lambda Cold Dark Matter framework successfully accounts for observational constraints on large (> 1 Mpc) scales, from the clustering of galaxies to the angular dependence of the Cosmic Microwave Background to the structure and matter content of galaxy clusters. On the scale of individual galaxies and, in particular, of dwarf systems much fainter than the Milky Way, a number of apparent conflicts with LCDM expectations have been reported. These have prompted the consideration of a number of radical modifications to LCDM, such as the possibility that dark matter might be "self-interacting", or that it might not be “cold”. I will review the status of these alleged problems and will report on recent work that reevaluates the observational evidence and reexamines the role of systematic uncertainties in the comparison between observation and model predictions. In particular, I will propose a possible resolution to the “cusp vs core” problem that requires no cores; an explanation for the mass discrepancy-acceleration relation that requires no changes to LCDM halos; and a plausible tidal origin for the enigmatic population of galaxies inhabiting “extremely cold” dark matter halos, such as the recently discovered Crater 2 satellite.