Previous Special Year Seminar

In this talk, we will discuss the local geometry of the closure of orbit space that parametrising smooth Fano manifolds inside certain Chow/Hilbert scheme. In particular, we will discuss the separatedness of the moduli of smoothable $K$-polystable $...

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

In 1984 Hirzebruch constructed the first examples of smooth toroidal compactifications of ball quotients with non-nef canonical divisor. In this talk, I will show that if the dimension is greater or equal than three then such examples cannot exist...

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...