October 4, 2018—Seoul
Abstract. We obtain novel results concerning the deformation theory of twistor spaces of irreducible holomorphic symplectic (ihs) manifolds. Specifically we show that the local deformations of such twistor spaces are unobstructed. The proof is based upon an extension theorem for families of ihs manifolds which compensates for the fact that, generally, fine moduli spaces of marked ihs manifolds do not exist.
On the local moduli of twistor spaces.
September 13, 2018—Seoul (KIAS)
Abstract. I present and discuss new results concerning the deformation theory of compact complex manifolds that are non-isotrivially fibered in irreducible holomorphic symplectic manifolds. I exemplify these results with twistor spaces.
June 28, 2018—Chemnitz
Abstract. I present some novel results concerning the deformation theory of twistor spaces of hyperkähler type. First and foremost, I show that the (local) deformations of such twistor spaces are unobstructed—a result which is new even in the K3 surface case. Time permitting, I touch upon the (global) structure of the moduli of hyperkähler twistor spaces.
May 16, 2018—Grenoble
Abstract. Based on a joint project with Brecan, Schwald, and Greb I present some new results on twistor spaces of hyperkähler manifolds—with an emphasis on the K3 surface case. In particular, I show that the deformations of such twistor spaces are unobstructed.
Group actions on holomorphic Lagrangian fibrations.
March 9, 2018—Toulouse
Abstract. Let $n$ be a natural number, $G$ be a finite subgroup of the general linear group of degree $n$, and $B$ be an open neighborhood of the origin in $\mathbb C^n$ on which $G$ acts by matrix multiplication. Moreover, let $f \colon (X,\sigma) \to B$ be a holomorphic Lagrangian fibration and assume that we are given a holomorphic symplectic action of $G$ on $(X,\sigma)$ which makes the map $f$ equivariant. In my talk I ask: When the action of $G$ on $X$ is fixed point free, so that we can form the quotient $X/G$ as a complex manifold, what can we say about $G$? If $n=1$, for instance, the group $G$ is necessarily trivial. I will present partial results for $n>1$ and explain how these can be applied to study the singularities of base spaces of fibrations on irreducible holomorphic symplectic manifolds.
January 18, 2018—Nice
Abstract. Twistor spaces of K3 surfaces are, noticeably non-Kähler, compact complex manifolds of dimension $3$ that come equipped with a holomorphic submersion to the complex-projective line. These spaces play a fundamental role in the moduli theory of K3 surfaces. In my talk I will explain this role and review the definition/construction of twistor spaces for general hyperkähler manifolds. Then, based on joint work in progress with Ana-Maria Brecan (Bayreuth), Martin Schwald, and Daniel Greb (both Essen), I present new results concerning the deformations of twistor spaces of K3 surfaces. Moreover, I will touch upon open problems and possible research directions.
October 25, 2017—Torino
October 12, 2017—Rauischholzhausen
March 30, 2017—Marburg
January 27, 2017—Essen
Abstract. I will report on a joint project with Patrick Graf (Bayreuth). Using Graf's results about the algebraic approximation of Kähler threefolds of Kodaira dimension zero, we show that a three-dimensional compact, connected Kähler space $X$ with canonical singularities is the finite quotient of a complex torus if and only if the first and second Chern classes of $X$ vanish, in an appropriate sense. This brings together an old theorem of Yau (where $X$ is smooth) and a theorem of Shepherd-Barron and Wilson (where $X$ is projective).
July 19, 2016—Mainz
Abstract. I will report on a current project with Patrick Graf (Bayreuth). Using Graf's recent results about the algebraic approximation of Kähler threefolds of Kodaira dimension zero, we show that a three-dimensional compact, connected Kähler space $X$ with isolated canonical singularities is the finite quotient of a complex torus if and only if the first and second Chern classes of $X$ vanish. This brings together an old theorem of Yau (where $X$ is smooth) and a theorem of Shepherd-Barron and Wilson (where $X$ is projective).
Extendability of parallel sections in vector bundles.
January 15, 2015—Essen
Singular irreducible symplectic spaces.
July 12, 2013—Bielefeld
On singular symplectic complex spaces.
April 26, 2013—Bochum
Period mappings for families of manifolds.
March 15, 2013—Freiburg
The local Torelli theorem for irreducible symplectic spaces.
September 5, 2012—Oberwolfach
June 30, 2016—Essen
March 19, 2016—Bayreuth