I have long enjoyed teaching, and have had a wide variety of teaching jobs over the past dozen years. I’ve worked in many different capacities at summer math programs for nine summers, I taught a sophomore tutorial at Harvard, I’ve given over 30 seminar talks at Berkeley, and I taught four sections of Calculus at U.C. Berkeley. Beyond a general interest in teaching, I have strong particular int...

We introduce the notion of a half-ribbon Hopf algebra, which is a Hopf algebra H along with a distinguished element t ∈ H such that (H, R,C) is a ribbon Hopf algebra, where R = (t ⊗ t)∆(t) and C = t. The element t is closely related to the topological ‘half-twist’, which twists a ribbon by 180 degrees. We construct a functor from a topological category of ribbons with half-twists to the categor...

Subfactors of the hyperfinite II1 factor of index less than or equal to 4 were classified in the late 80s and early 90s through work of Jones, Ocneanu, Popa, and many others. There is an ADE classification, and all of the examples are closely related to quantum or classical SU(2). When the index is larger than 4, there is one family of A∞ subfactors related to quantum SU(2) which are difficult ...

!e world’s demand for energy is causing a dramatic escalation of social and political unrest. Likewise, the environmental impact of global climate change due to the combustion of fossil fuels is becoming increasingly alarming. One way to improve the sustainability of our electricity base is through the scavenging of waste heat with thermoelectric generators (Box 1). Home heating, automotive exh...

Snyder-Robinson syndrome

Modern area preserving projections employed by cartographers and geographers have closed forms when transitioning between the sphere and the plane. Inversions from the planar map to the spherical approximation of the Earth are slower, requiring iterative root finding approaches or entirely undetermined. Recent optimizations of the common Inverse Snyder Equal Area Polyhedral projection have been...