Previous Special Year Seminar

Let \(Y\) be a smooth rational surface and let \(D\) be an effective divisor linearly equivalent to \(-K_Y\), such that \(D\) is a cycle of smooth rational curves. Such pairs \((Y,D)\) arise in many contexts, for example in the study of...

We will discuss the boundedness of log general type pairs, with the aim on proving the moduli of KSBA stable varieties is bounded.

We discuss the universal triviality of the \(\mathrm{CH}_0\)-group of cubic hypersurfaces, or equivalently the existence of a Chow-theoretic decomposition of their diagonal. The motivation is the study of stable irrationality for these varieties...

Tate's conjecture for divisors on algebraic varieties can be rephrased as a finiteness statement for certain families of polarized varieties with unbounded degrees. In the case of abelian varieties, the geometric part of these finiteness statements...

I will try to explain some intuitions and some history about (mixed) Hodge theory. Warning: the experts will not learn anything new.

Consider a smooth complex projective variety \(M\). To understand the group of birational transformations (resp. regular automorphisms) of \(M\), one can use tools from Hodge theory, dynamical systems, and geometric group theory. I shall try to...

For an odd integer \(n > 3\) the data of generic n-dimensional subspace of the space of skew bilinear forms on an n-dimensional vector space define two different Calabi-Yau varieties of dimension \(n-4\). Specifically, one is a complete intersection...

Being the natural generalization of K3 surfaces, hyperkaehler varieties, also known as irreducible holomorphic symplectic varieties, are one of the building blocks of smooth projective varieties with trivial canonical bundle. One of the guiding...

Consider a smooth complex projective variety \(M\). To understand the group of birational transformations (resp. regular automorphisms) of \(M\), one can use tools from Hodge theory, dynamical systems, and geometric group theory. I shall try to...

A cusp singularity is an isolated surface singularity whose minimal resolution is a cycle of smooth rational curves meeting transversely. Cusp singularities come in naturally dual pairs. In the 1980's Looijenga conjectured that a cusp singularity is...