Equivariant structures in mirror symmetry

James Pascaleff
University of Illinois at Urbana-Champaign
October 17, 2014
When a variety \(X\) is equipped with the action of an algebraic group \(G\), it is natural to study the \(G\)-equivariant vector bundles or coherent sheaves on \(X\). When \(X\) furthermore has a mirror partner \(Y\), one can ask for the corresponding notion of equivariance in the symplectic geometry of \(Y\). The infinitesimal notion (equivariance for a single vector field) was introduced by Seidel and Solomon (GAFA 22 no. 2), and it involves identifying a vector field with a particular element in symplectic cohomology.

Mastery in Japanese Food Work: The Case of Coffee

Merry White
Professor of Anthropology Boston University
October 17, 2014
Coffee is the most widely consumed social beverage in Japan. Looking at coffee as a Japanese "food" allows us some observations on culinary work in Japan in more general terms, and some approaches to ideas of domestic, artisanal and industrial food preparation, in what some have called "the most principled cuisine in the world." Japanese food, seen from the perspective of its work, is more local, more idiosyncratic, and more personal than the idea of "principled" might imply.

Act globally, compute locally: group actions, fixed points and localization

Tara Holm
Cornell University; von Neumann Fellow, School of Mathematics
October 20, 2014
Localization is a topological technique that allows us to make global equivariant computations in terms of local data at the fixed points. For example, we may compute a global integral by summing integrals at each of the fixed points. Or, if we know that the global integral is zero, we conclude that the sum of the local integrals is zero. This often turns topological questions into combinatorial ones and vice versa. I will give an overview of how this technique arises in symplectic geometry.

Positive cones of higher (co)dimensional numerical cycle classes

Mihai Fulger
Princeton University
October 21, 2014
It is classical to study the geometry of projective varieties over algebraically closed fields through the properties of various positive cones of divisors or curves. Several counterexamples have shifted attention from the higher (co)dimensional case. They show that the analogous definitions do not lead to analogous positivity properties. To correct the negative outlook, we look at stronger positivity conditions on numerical classes. A sample result is that the pseudoeffective cone, the closure of the cone of effective \(k\)-dimensional cycle classes is pointed.