Noncommutative Plurisubharmonic Polynomials Part II: Local Assumptions

We say that a symmetric noncommutative polynomial in the noncommutative free variables (x_1, x_2, ..., x_g) is noncommutative plurisubharmonic on a noncommutative open set if it has a noncommutative complex hessian that is positive semidefinite when evaluated on open sets of matrix tuples of sufficiently large size. In this paper, we show that if a noncommutative polynomial is noncommutative plurisubharmonic on a noncommutative open set, then the polynomial is actually noncommutative plurisubharmonic everywhere and has the form p = \sum f_j^T f_j + \sum k_j k_j^T + F + F^T where the sums are finite and f_j, k_j, F are all noncommutative analytic. In the paper by Greene, Helton, and Vinnikov, it is shown that if p is noncommutative plurisubharmonic everywhere, then p has the form above. In other words, the paper by Greene, Helton, and Vinnikov makes a global assumption while the current paper makes a local assumption, but both reach the same conclusion. This paper uses a Gram-like matrix representation of noncommutative polynomials. A careful analysis of this Gram matrix plus the main theorem in the paper by Greene, Helton, and Vinnikov ultimately force the form in the equation above.Comment: 26 page

Brazil’s Deferred Highway: Mobility, Development, and Anticipating the State in Amazonia

Four decades ago, Brazilian officials plotted designs for colonization and resource extraction in Amazonia; subsequently the region has become a test-lab for successive development regimes. Along the Santarém-Cuiabá Highway (Br-163) in the state of Pará, residents have engaged in a range of licit and illicit activities as official development policy has shifted throughout the years. Despite assertions that living along the unpaved road is tantamount to “being stuck” in place and time, residents move widely throughout the region, using the road, trails, streams, and rivers as thoroughfares. I argue that “being stuck” functions as a discursive label for illegible mobilities and the speculative economies they support as agrarian reform clients, ranchers, and others compete for position in anticipation of the road’s paving. Novel forms of resource speculation result from the labor of moving and maintaining anticipatory structures along the road, a process that remains obscure from state development projects

Are inflation expectations rising from the ashes?

Inflation (Finance) ; Rational expectations (Economic theory)