We introduce a new quasi-local mass with interesting properties along null flows off of a 2-sphere in space-time or, equivalently, foliations of a null cone. We also show how certain convexity assumptions along a foliation of a null cone give rise to the Penrose inequality. For monotonicity from a MOTS, one requires these convexity assumptions be sharp, so we explore existence within a Weakly Isolated Horizon. Building on a lemma of S. Alexakis, this allows us to show that the Penrose Inequality is stable under small perturbations of the standard Schwarzschild null cone.

A meeting to decide the schedule for the semester and to have brief presentations by a few faculty members of their broad area of research.

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Let K be a global field, f in K[x], and b in K. Let K_n be the splitting field of f^n(x)−b, where f^n denotes n-fold composition. The projective limit of the groups Gal(K_n/K) embeds into the automorphism group of an infinite rooted tree. A major problem in arithmetic dynamics, motivated by Serre's open image theorem, is to determine when the index is finite. I discuss the solution of the problem for quadratic, cubic, and unicritical polynomials by classifying all obstructions to finite index, and the issues that arise in trying to apply the same ideas to polynomials in general.

Join us for the talk by Ole Hjortland & Ben Martin (Bergen, Norway) in the Logic Colloquium!

"Anti-Exceptionalism and Explanations in Logic"

Abstract:

According to logical anti-exceptionalism we come to be justified in believing logical theories by similar means to scientific theories. This is often explained by saying that theory choice in logic proceeds via abductive arguments (Priest, Russell, Williamson, Hjortland). Thus, the success of classical and non-classical theories of validity are compared by their ability to explain the relevant data. However, as of yet there is no agreed upon account of which data logical theories must explain, and subsequently how they prove their mettle. In this paper, we provide a non-causal account of logical explanation, and show how it can accommodate important disputes about logic.

All welcome!

https://logic.uconn.edu/calendar/

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