HSM Early Career Colloquium: Yilong Zhang, Oliver Fürst, Hannah DellHSM Early Career Colloquium

Wednesday Jul 8, 2026, 3:15 PM → 4:30 PM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

Yilong Zhang

Hrushovski construction in ordered fields

The Hrushovski construction is a variant of amalgamation methods invented to construct new strongly minimal theories. The method was later adapted to expansions of fields, including colored fields and powered fields. In this talk, I will present my attempt to apply the Hrushovski construction to ordered fields — constructing expansions of RCF that axiomatize the real field with dense logarithmic spirals and with "power functions" on the unit circle. The construction leads to o-minimal open core, a result on definable open sets in both structures.

Oliver Fürst 

Non-Fredholm Index and Heat Traces of Callias-type Operators

Dirac operators are a central object in global analysis and mathematical physics. The study of their (Fredholm) index is of particular interest, the Atiyah-Singer index theorem treats the case of compact, even dimensional spin manifolds, while the Callias index theorem deals with non-compact, odd dimensional spin manifolds with a potential. In the latter case the perturbed Dirac operator is called a Callias-type operator under certain assumptions on the potential. However, due to the non-compact setting, there are many cases in which Callias-type operators are no longer Fredholm, which already happens for the most basic (even unperturbed) example of $i\partial_{t}$ acting on $L^2(\mathbb{R})$.

The goal of this task is to outline what kind of regularization replaces the Fredholm index of Callias-type operators, and how we may study its rich spectral theory more generally. It will become apparent that a type of heat trace formula will be the central ingredient, which we will discuss in some cases.

Hannah Dell

Inducing hyperkähler automorphisms

How do we produce symmetries of a geometric object? Sometimes we can build new symmetries from known ones. In this talk, we will see an instance of this in algebraic geometry. Our starting point will be a cubic fourfold, i.e. the zero locus of a degree 3 polynomial in 5-dimensional projective space. It's symmetries, called automorphisms, are well understood, partly due to it's explicit description. To any cubic fourfold, we can associate many hyperkähler manifolds, i.e. compact, simply connected complex manifolds with a Kähler form and admitting a unique nowhere degenerate holomorphic 2-form. In this talk we will explain a new way to produce hyperkähler automorphisms using automorphisms of cubic fourfolds. This is joint work with Lucas Li Bassi and Augustinas Jacovskis.