Speakers

Title: Automorphisms and Hodge isometries of surfaces with K^2 = p_g = 1 

Abstract: By a theorem of Catanese, the canonical model of a minimal surface of general type whose canonical class has self-intersection one and whose geometric genus is one is a complete intersection of two sextics in P(1,2,2,3,3). We describe the automorphism group of these surfaces and prove that its order is at most 72. We also classify the surfaces attaining the bound: two surfaces with singular canonical model and a one-parameter family of smooth surfaces. For this smooth family we compute a basis of the primitive cohomology given by residues of monomials, together with the intersection form. We then show that the Torelli principle for automorphisms fails: the primitive part of the Néron–Severi lattice contains a root system of rank twelve whose reflections are Hodge isometries. As a result, the automorphism group has index at least 55.296 in the group of Hodge isometries of the primitive lattice taken up to sign. This is joint work with Jorge Duque Franco and Alvaro Liendo.  

Title: Equivariant automorphism groups and real forms of complexity-one varieties

Abstract: Let G be a connected reductive algebraic group over a perfect field. I will discuss the representability of equivariant automorphism groups of certain G-varieties. More precisely, for a broad class of G-varieties, called G-varieties of complexity one, I will explain why this group is representable by a group scheme locally of finite type, and even by a linear algebraic group in the almost homogeneous case. Finally, I will show how understanding the equivariant automorphism group, particularly through a description in terms of an exact sequence, allows us to address the question of the finiteness of real forms of G-varieties of complexity one. This is joint work with Giancarlo Lucchini Arteche (arXiv:2507.18475).

Title: TBA

Abstract: TBA.