Ever since the 1970’s, holomorphic twistor spaces have been used to study the geometry and analysis of their base manifolds.
If A is a Banach algebra, there are two products on the second dual A∗∗ which extend the product on A, called the Arens products.
Let $X$ be a smooth algebraic variety, and let $p \in X$. Let $\pi : \tilde{X} \to X$ denote the blow-up of $X$ at $p$ with exceptional divisor $E$. Given an effective divisor $L$ on $X$, we define $\gamma_p(L) = \sup \{ t \geq 0 : \pi^*L - tE \text{ is effective} \}$. In this thesis, we develop the theory of this number.
Given a convergent infinite series of positive terms an, the set of all possible subsums forms a perfect and compact set.
The study of algorithmic randomness, in particular of lowness properties in randomness has led to many exciting recent developments in the area.
I will introduce factors of automorphy as a tool for constructing vector bundles over manifolds. I will then discuss some of the research I have been doing this term with regards to vector bundles over Hopf and Inoue Surfaces.
Just as the moduli space of semistable n-gons in complex projective space can be realized as the representation space of a certain shape of quiver, their hyperkaehler analogues (moduli spaces of hyper-n-gons) are quiver varieties for the same quiver, doubl
Tree Feynman rules are maps from the Connes-Kreimer Hopf algebra of rooted trees to a polynomial ring which satisfy certain algebraic properties. It’s not too hard to show what the most general possible tree Feynman rules are; the answer is rather combinatorial.
This talk will outline the essential ingredients involved in the functorial correspondence between irreducible singular G-monopoles on S1 ×
In this talk I will explain why the ancestor GW correlation functions for an elliptic orbifold are quasi-modular forms.