We consider the Cauchy problem for the Einstein equations for cosmological spacetimes, i.e. spacetimes with compact spatial hypersurfaces. Various classes of those dynamical spacetimes have been constructed and analyzed using...
Read more
The gig economy provides workers with the benefits of autonomy and flexibility, but it does so at the expense of work identity and co-worker bonds. Among the many reasons why...
Read more
We present computations of the thermal Hall coefficient of phonons scattering off defects with multiple energy levels. Using a microscopic formulation based on the Kubo formula, we find that the...
Read more
The low dimensional manifold hypothesis posits that the data found in many applications, such as those involving natural images, lie (approximately) on low dimensional manifolds embedded in a high dimensional Euclidean...
Read more
For a smooth projective curve $C/\mathbb{Q}$, how many field extensions of $\mathbb{Q}$ -- of given degree and bounded discriminant --- arise from adjoining a point of $C(\overline{\mathbb{Q}})$? Can we further count the number...
Read more
In 1998, using arguments from M-theory, Gopakumar and Vafa argued that there are integer BPS invariants of symplectic Calabi-Yau 3-folds. Unfortunately, they did not give a direct mathematical definition of...
Read more
We automatically solve, explain, and generate university-level course problems from thirty STEM courses (at MIT, Harvard, and Columbia) for the first time. We curate a new dataset of course questions...
Read more
Motivated by a puzzle arising from recent work on staggered lattice fermions we introduce Kaehler-Dirac fermions and describe their connection both to Dirac fermions and staggered fermions. We show that they...
Read more
The Nishimori line (NL) describes a special one parameter family of disordered spin models which are invariant under a gauge transformation acting jointly on the spins and the disorder. For...
Read more
The random greedy algorithm for finding a maximal independent set in a graph has been studied extensively in various settings in combinatorics, probability, computer science, and chemistry. The algorithm builds...
Read more