Abstract:
The survival of an Indic calendar among the Tengger people of the Brama highlands in east Java opens a window on Java’s calendar history. Its hybrid form reflects accommodations between this non-Muslim Javanese group and the increasingly dominant Muslim Javanese culture. Reconstruction is challenging because of this hybridity, because of inconsistencies in practice, and because the historical evidence is sketchy and often difficult to interpret.

Abstract:
The history of calendars is best approached as a technical subject that has cultural and political dimensions. The functions of calendars – to enumerate days, months and years – can be achieved in a variety of ways. In broad terms Muslims expect their calendars to predict the phases of the moon, Christians expect their calendars to match the seasons of the year, and Hindus and Chinese expect their calendars to do both. These expectations can be met by different technical means, so that even among those who subscribe to a common set of expectations, there are invariably differences in the working calendars.

Abstract:
We study the Z/2-equivariant K-theory of the complement of the complexification of a real hyperplane arrangement. We compute the rational K and KO rings, and give two different combinatorial descriptions of the subring of the integral KO ring generated by line bundles.

Abstract:
Let T be an algebraic torus acting on a smooth variety V. We study the relationship between the various GIT quotients of V and the symplectic quotient of the cotangent bundle of V.

Abstract:
This is an expository paper in which we define projective GIT quotients and introduce toric varieties from this perspective. It is intended primarily for readers who are learning either invariant theory or toric geometry for the first time.

Abstract:
Hypertoric varieties are quaternionic analogues of toric varieties, important for their interaction with the combinatorics of matroids as well as for their prominent place in the rapidly expanding field of algebraic symplectic and hyperkahler geometry. The aim of this survey is to give clear definitions and statements of known results, serving both as a reference and as a point of entry to this beautiful subject.

Abstract:
Etingof and Schedler formulated a conjecture about the degree zero Poisson homology of an affine cone that admits a projective symplectic resolution. We strengthen this conjecture in general and prove the strengthened version for hypertoric varieties. We also formulate an analogous conjecture for the degree zero Hochschild homology of a quantization of such a variety.

Abstract:
We give an abstract definition of a hypertoric variety, generalizing the existing constructive definition. We construct a hypertoric variety associated with any zonotopal tiling, and we show that the previously known examples are exactly those varieties associated with regular tilings. In particular, the examples that we construct from irregular tilings have not appeared before. We conjecture that our construction gives a complete classification of hypertoric varieties, analogous to the classification of toric varieties by fans.

Abstract:
Given a real arrangement $A$, the complement $M(A)$ of the complexification of $A$ admits an action of $\mathbb{Z}_2$ by complex conjugation. We define the equivariant Orlik-Solomon algebra of $A$ to be the $\mathbb{Z}_2$-equivariant cohomology ring of $M(A)$ with coefficients in $\mathbb{Z}_2$. We give a combinatorial presentation of this ring, and interpret it as a deformation of the ordinary Orlik-Solomon algebra into the Varchenko-Gel'fand ring of locally constant $\mattbb{Z}_2$-valued functions on the complement $C(A)$ of $A$ in $\mathbb{R}^n$. We also show that the $\mathbb{Z}_2$-equivariant homotopy type of $M(A)$ is determined by the oriented matroid of $A$. As an application, we give two examples of pairs of arrangements $A$ and $A'$ such that $M(A)$ and $M(A')$ have the same nonequivariant homotopy type, but are distinguished by the equivariant Orlik-Solomon algebra.