We prove that a smooth, complex plane curve of odd degree can be defined by a polynomial with real coefficients if and only if it is isomorphic to its complex conjugate; there are counterexamples in e...
Vertex algebras formalise the properties of what physicists would call operator product expansions (OPEs) in chiral conformal field theories (CFTs). One way to motivate the axioms of vertex algebras i...
The Hodge conjecture is a central problem in modern algebraic geometry. It is notoriously difficult to attack, and we still lack general evidence towards its validity. In my talk I will present a proo...
In the 80's Kudla and Millson introduced a theta function in two variables, nowadays known as the Kudla--Millson theta function. This behaves as a Siegel modular form with respect to one variable, and...
We will investigate the arithmetic properties of the j-invariant of a rank two Drinfeld module having CM by an order of an << imaginary quadratic function field. This talk is based on a joint wo...
An abelian differential is a smooth projective curve endowed with an algebraic one-form. I will discuss the uniformization of the moduli of abelian differentials provided by their periods, its arithme...
Let (X, D) be a projective kit pair, where KX+D is ample and D has standard coefficients. Guenancia and Taji have shown that a suitable version of the famous Miyaoka--Yau inequality holds in this sett...
Positively multiplicative graphs are graphs whose adjacency matrix can be embedded in a matrix algebra admitting a distinguished basis labelled by its vertices with nonnegative structure constants. It...
I discuss how to practically put a log structure on a toroidal crossing space, and hopefully sketch applications to smoothing toric Fano varieties and log birational geometry. This is work in progress...
Motivated by physics, in the late 1990s Sen discussed a construction of complete hyperkähler metrics in (real) dimension 4 and so-called ALF (asymptotically locally flat) asymptotics as a "superpositi...
