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SUMMARY:HSM Early Career Colloquium: Yilong Zhang\, Oliver Fürst\, Hannah
  Dell [HSM Early Career Colloquium]
DTSTART:20260708T131500Z
DTEND:20260708T143000Z
DTSTAMP:20260716T203700Z
UID:indico-event-1350@math-events.uni-bonn.de
DESCRIPTION:Yilong Zhang\nHrushovski construction in ordered fields\nThe H
 rushovski construction is a variant of amalgamation methods invented to co
 nstruct new strongly minimal theories. The method was later adapted to exp
 ansions of fields\, including colored fields and powered fields. In this t
 alk\, I will present my attempt to apply the Hrushovski construction to or
 dered fields — constructing expansions of RCF that axiomatize the real f
 ield with dense logarithmic spirals and with "power functions" on the unit
  circle. The construction leads to o-minimal open core\, a result on defin
 able open sets in both structures.\nOliver Fürst \nNon-Fredholm Index an
 d Heat Traces of Callias-type Operators\nDirac operators are a central obj
 ect in global analysis and mathematical physics. The study of their (Fredh
 olm) index is of particular interest\, the Atiyah-Singer index theorem tre
 ats the case of compact\, even dimensional spin manifolds\, while the Call
 ias index theorem deals with non-compact\, odd dimensional spin manifolds 
 with a potential. In the latter case the perturbed Dirac operator is calle
 d a Callias-type operator under certain assumptions on the potential. Howe
 ver\, due to the non-compact setting\, there are many cases in which Calli
 as-type operators are no longer Fredholm\, which already happens for the m
 ost basic (even unperturbed) example of $i\\partial_{t}$ acting on $L^2(\\
 mathbb{R})$.\nThe goal of this task is to outline what kind of regularizat
 ion replaces the Fredholm index of Callias-type operators\, and how we may
  study its rich spectral theory more generally. It will become apparent th
 at a type of heat trace formula will be the central ingredient\, which we 
 will discuss in some cases.\nHannah Dell\nInducing hyperkähler automorphi
 sms\nHow do we produce symmetries of a geometric object? Sometimes we can 
 build new symmetries from known ones. In this talk\, we will see an instan
 ce of this in algebraic geometry. Our starting point will be a cubic fourf
 old\, i.e. the zero locus of a degree 3 polynomial in 5-dimensional projec
 tive space. It's symmetries\, called automorphisms\, are well understood\,
  partly due to it's explicit description. To any cubic fourfold\, we can a
 ssociate many hyperkähler manifolds\, i.e. compact\, simply connected com
 plex manifolds with a Kähler form and admitting a unique nowhere degenera
 te holomorphic 2-form. In this talk we will explain a new way to produce h
 yperkähler automorphisms using automorphisms of cubic fourfolds. This is 
 joint work with Lucas Li Bassi and Augustinas Jacovskis.\n\nhttps://math-e
 vents.uni-bonn.de/event/1350/
LOCATION:Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/1350/
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