Previous Conferences & Workshops

Abstract: : Let $g$:$X \rightarrow S$ be a smooth proper family over algebraic varieties over a number field $K$. Consider the statement $W(g,p)$: the weight-monodromy conjectures hold for all fibres of g defined over a finite extension $L/Q_p$. We...

Abstract: To show that the Gamma function, restricted to the positive real half-axis, generates an o-minimal structure over the real field, we had to show (in collaboration with Lou van den Dries) that the expansion of the real field by all...

Abstract: The Zilber-Pink conjecture is a far reaching and widely open conjecture in the area of "unlikely intersections" generalizing many previous results in the area, such as the recently established André-Oort conjecture. Recently the ``G...

Abstract: The classical Rees construction (of common use in commutative algebra and Hodge theory) interpolates between filtrations, viewed as $G_m$-equivariant vector bundles on the affine line, and their associated gradings. Various non-abelian...

Abstract: From the outset, topology has played an important role in the study of o-minimal structures. The central focus has been on developing the theory of o-minimality as a framework for 'tame topology', built upon the natural and well-behaved...

Abstract: Abstract: Let $C$ be a curve defined over a finite field, and let $X/C$ be a non-isotrivial family of K3 surfaces. In joint work with Maulik-Tang, under a compactness assumption (an assumption removed in later work by Tayou), we prove that...

Abstract: A classical theorem due to Borel states that every holomorphic map from a poly-punctured disk into a Shimura variety (with torsion-free level structure) extends holomorphically across the punctures to the minimal compactification. As a...

Abstract: I will talk about mod p versions of the Mumford—Tate and André—Oort conjectures. Via a notion of formal linearity, the two conjectures, together with a third one ($mod p $Ax—Lindemann), are closely entangled with each other — much closer...

Abstract: I will discuss work in progress with M. Orr (Manchester) and G. Papas (Weizmann) on the Zilber-Pink conjecture for $Y(1)^3$. This is known for so-called asymmetric curves by the 2012 work of Habegger-Pila. More recently, an approach known...