Recent Detections of a Rare Native Lady Beetle, \u3ci\u3eCoccinella Novemnotata\u3c/i\u3e (Coleoptera: Coccinellidae), in Minnesota

Coccinella novemnotata Herbst (Coleoptera: Coccinellidae) was once widespread and commonly collected in North America; however, its abundance and distribution decreased over the 1970s and 1980s. It has not been collected by recent surveys in some areas and in other areas is only rarely collected. Museum records were examined and a survey of Minnesota soybean fields was conducted via sweep-net sampling in July and August 2011. Results suggest that C. novemnotata is absent from or below the detection threshold in the majority of the state of Minnesota. However, there appears to be an area in east central Minnesota with at least sustained low, but detectable populations of C. novemnotata and it is active in agricultural crops

Geometric ergodicity for some space-time max-stable Markov chains

Max-stable processes are central models for spatial extremes. In this paper, we focus on some space-time max-stable models introduced in Embrechts et al. (2016). The processes considered induce discrete-time Markov chains taking values in the space of continuous functions from the unit sphere of $\mathbb{R}^3$ to $(0, \infty)$. We show that these Markov chains are geometrically ergodic. An interesting feature lies in the fact that the state space is not locally compact, making the classical methodology inapplicable. Instead, we use the fact that the state space is Polish and apply results presented in Hairer (2010)

From Gauss Graphs to Giants

We identify the operators in ${\cal N}=4$ super Yang-Mills theory that correspond to ${1\over 8}$-BPS giant gravitons in AdS$_5\times$S$^5$. Our evidence for the identification comes from (1) counting these operators and showing agreement with independent counts of the number of giant graviton states, and (2) by demonstrating a correspondence between correlation functions of the super Yang-Mills operators and overlaps of the giant graviton wave functions.Comment: 16 pages; v2: matches published versio

CFT4 as SO(4,2)-invariant TFT2

We show that correlators of local operators in four dimensional free scalar field theory can be expressed in terms of amplitudes in a two dimensional topological field theory (TFT2). We describe the state space of the TFT2, which has $SO(4,2)$ as a global symmetry, and includes both positive and negative energy representations. Invariant amplitudes in the TFT2 correspond to surfaces interpolating from multiple circles to the vacuum. They are constructed from SO(4,2) invariant linear maps from the tensor product of the state spaces to complex numbers. When appropriate states labeled by 4D-spacetime coordinates are inserted at the circles, the TFT2 amplitudes become correlators of the four-dimensional CFT4. The TFT2 structure includes an associative algebra, related to crossing in the 4D-CFT, with a non-degenerate pairing related to the CFT inner product in the CFT4. In the free-field case, the TFT2/CFT4 correspondence can largely be understood as realization of free quantum field theory as a categorified form of classical invariant theory for appropriate SO(4,2) representations. We discuss the prospects of going beyond free fields in this framework.Comment: 54 pages, 7 figures; version 2: Published version - extended discussion of CFT4/TFT2 in terms of emergent space-time; refs added; typos correcte