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One of the most important open problems in physics is to reconcile quantum mechanics with our classical intuition. In this talk we look at quantum foundations through the lens of mathematical foundations and uncover a deep connection between the two fields. We show that Cantorian set theory is based on classical concepts incompatible with quantum experiments. Specifically, we prove that Zermelo-Fraenkel axioms of set theory (and the background classical logic) imply a Bell-type inequality. Consequently, quantum experiments violating Bell inequality cannot be described in the framework of classical set theory. This suggests that a non-Cantorian set theory could be a better framework to capture the elusive nature of quantum world. Finally, we discuss several possible options for a future logico-mathematical framework compatible with quantum experiments. 

Direct dark matter (DM) detection experiments almost always focus on Weakly Interacting Massive Particles (WIMPs), which have a mass in the 1--1000 GeV range.  However, what if DM is not a WIMP?  In this talk, new direct detection strategies for DM particles with MeV to GeV mass will be presented.  In this largely unexplored mass range, DM can scatter with electrons, causing ionization of atoms in a detector target material and leading to single- or few-electron events.  I will present the first direct detection limits on DM as light as a few MeV, using XENON10 data.  Theoretically interesting models can already be probed.  Significant improvements in sensitivity should be possible with dedicated experiments, opening up a window to new regions in DM parameter space.  

In this talk I will present evidence that accounting for the presence of hierarchies in string compactifications naturally leads to a UV sensitivity of dark matter in contrast to what is usually assumed. In particular, we will see that the existence of cosmological moduli may lead to a non-thermal history for the early universe and modifications in the primordial production of dark matter. If such a history were realized it would not only require probing new regions in dark matter searches, but also imply that a detection of dark matter would provide a direct probe on the early universe and the UV -- contrary to the thermal WIMP case. Regardless of the history of the early universe I will argue that if current string constructions are representative of more general models then all weak-scale dark matter would indeed be UV sensitive and would be a new prediction of string theory - falsifiable by experiment.