Forcing with Adequate Sets of Models as Side Conditions

We present a general framework for forcing on $\omega_2$ with finite conditions using countable models as side conditions. This framework is based on a method of comparing countable models as being membership related up to a large initial segment. We give several examples of this type of forcing, including adding a function on $\omega_2$, adding a nonreflecting stationary subset of $\omega_2 \cap \textrm{cof}(\omega)$, and adding an $\omega_1$-Kurepa tree

Localization for random operators with non-monotone potentials with exponentially decaying correlations

I consider random Schr\"odinger operators with exponentially decaying single site potential, which is allowed to change sign. For this model, I prove Anderson localization both in the sense of exponentially decaying eigenfunctions and dynamical localization. Furthermore, the results imply a Wegner-type estimate strong enough to use in classical forms of multi-scale analysis

Musical Worlds and the Extended Mind

“4E” approaches in cognitive science see mind as embodied, embedded, enacted, and extended. They observe that we routinely “offload” part of our thinking onto body and world. Recently, 4E theorists have turned to music cognition: from work on music perception and musical emotions, to improvisation and music education. I continue this trend. I argue that music — like other tools and technologies — is a beyond-the-head resource that affords offloading. And via this offloading, music can (at least potentially) scaffold various forms of thought, experience, and behavior. To develop this idea, I consider the “material” and “worldmaking” character of music, and I apply these considerations to two cases studies: music as a tool for religious worship, and music as a weapon for torture