Colloquium

Following the tradition of the American Mathematical Society, the seventh colloquium of the Society was held as part of the summer meeting that took place at the University of Wisconsin, in Madison. Two sets of lectures were presented: On Invariants and the Theory of Numbers, by L. E. Dickson, and Functions of Several Complex Variables, by W. F. Osgood. Dickson considers invariants of quadratic forms, with a special emphasis on invariants of forms defined in characteristic $p$, also called modular invariants, which have number-theoretic consequences. He is able to find a fundamental set of invariants for both settings. For binary forms, Dickson introduces semi-invariants in the modular case, and again finds a fundamental set. These studies naturally lead to the important study of invariants of the standard action of the modular group. The lectures conclude with a study of ``modular geometry'', which is now known as geometry over $\mathbf{F}_p$. The lectures by Osgood review the state of the art of several complex variables. At this time, the theory was entirely function-theoretic. Already, though, Osgood can introduce the ideas and theorems that will be fundamental to the subject for the rest of the century: Weierstrass preparation, periodic functions and theta functions, singularities--including Hartogs' phenomenon, the boundary of a domain of holomorphy, and so on.

Proceedings of the VIIth International Colloquium on Amphipoda held in Walpole, Maine, USA, September 14-16, 1990

Since 2001 the Scuola Normale Superiore di Pisa has organized the "Colloquio De Giorgi", a series of colloquium talks named after Ennio De Giorgi. The Colloquio is addressed to a general mathematical audience, and especially meant to attract graduate students and advanced undergraduate students. The lectures are intended to be not too technical, in fields of wide interest. They must provide an overview of the general topic, possibly in a historical perspective, together with a description of more recent progress. The idea of collecting the materials from these lectures and publishing them in annual volumes came out recently, as a recognition of their intrinsic mathematical interest, and also with the aim of preserving memory of these events. ​

This latest BACAP Proceedings covers three key areas in ancient philosophy, ethics, method and physics. Under ethics, there are three papers on Socratic piety, Aristotelian friendship, and Augustinian-Platonic virtue. Under method, Socratic elenchos, Socratic maieutic, and Aristotelian aporematic inquiry. Under physics, life in Plato and Proclus's reconsideration of Aristotelian motion.