I will explain how complex and real toric varieties and their non-negative parts can easily be defined topologically. This gives in particular canonical cell decompositions of these spaces.

I will also discuss consequences to the ordinary and equivariant integral cohomology of toric varieties. For example, if the ordinary cohomology is concentrated in even degrees, then the equivariant cohomology can be described by piecewise polynomials. If the toric variety is in addition smooth or compact, then its ordinary cohomology is necessarily torsion-free.

Abstract: The aim of this talk is to present the notion of holomorphic structure in noncommutative setting. Focusing on quantum projective line we will see that some of the classical structures have perfect analogues here. Also we shall explain a twisted positive Hochschild cocycle related to this complex structure.

Let X be a hyperbolic Riemann surface and A be a closed subset of X. We study spaces of integrable, square-integrable and bounded holomorphic k-differentials on X-A. Our main results provide a description of the kernel of the Poincare series map. This is joint work with N. Askaripour.

Group theory is the mathematical language of symmetry, and as such has many real world applications, ranging from the study of crystals to fundamental ideas about the workings of the universe. In this talk, we will introduce group theory and see how it is used to create a wonderful algorithm to solve Rubik's cube.

Everyone welcome!

In a seminal 1859 paper, Riemann gave two proofs of the analytic continuation and functional equation of his zeta function. The ideas behind his theta function proof were later developed into a powerful theory of Fourier analysis on number fields, in work of Hecke, Tate and others. In this talk, I will focus instead on the contour integral proof, and based on the ideas therein, will present two infinite families of new proofs of the analytic continuation and functional equation. The proofs are facilitated by geometric data coming from the fact that the polylogarithm generating function is a flat section of the universal unipotent bundle with connection over $\mathbb{P}^{1} \backslash \{0,1,\infty\}$.