Austria – Uganda workshop on geometry and representation theory

22-23 July 2025

Location: BZ 9 (9th floor), Faculty of Mathematics, University of Vienna, Oskar-Morgenstein-Platz 1

Organised by Balazs Szendroi. If you are interested in participating, please email balazs[dot]szendroi[at]univie[dot]ac[dot]at

Schedule

• Tuesday 22 July
  • 11.30am Nebojsa Pavic (University of Graz, Austria), Derived categories, categorical absorptions and crepant resolutions
  • 2.30pm Caroline Namanya (Makerere University, Uganda), Derived autoequivalences on algebraic flops
  • 4pm Michael Wemyss (University of Glasgow, UK), Namikawa–Weyl groups for cDV singularities
• Wednesday 23 July
  • 10am Martin Kalck (University of Graz, Austria), Paths into transcendence
  • 11.30am Brian Makonzi (Muni University, Uganda), Deformation of surfaces via reconstruction algebras of type A
  • 2pm David Ssevviiri (Makerere University, Uganda), Versatility of locally reduced modules

Abstracts

• Brian Makonzi (Muni University, Uganda), Deformation of surfaces via reconstruction algebras of type A
  • I will discuss how to use noncommutative resolutions of non-Gorenstein singularities to construct classical deformation spaces, by computing the Artin component of the deformation space of a cyclic surface singularity using only the quiver of the corresponding reconstruction algebra. This extends work of Brieskorn, Kronheimer and Cassens–Slodowy to the setting of quotients of the affine plane by groups G ≤ GL(2, C), and also gives a prediction for what is true more generally.
• Martin Kalck (University of Graz, Austria), Paths into transcendence
  • Algebraic numbers are complex numbers that are roots of polynomials with rational coefficients. All other complex numbers are called transcendental. It is typically a hard question to decide whether a given complex number is transcendental. A more general, classical question in ‘transcendental number theory’ (cf. e.g. works of Lindemann and Weierstraß, Gelfond and Schneider, Baker, Wüstholz) is the following: determine the dimension of the vectorspace generated by a (finite) set of complex numbers over the algebraic numbers. For example, the vectorspace generated by 1 and π is two-dimensional since π is transcendental by Lindemann’s Theorem. For certain complex numbers called periods, we will try to explain how this transcendence question can (sometimes) be translated into determining dimensions of certain finite dimensional algebras – in other words, into counting (equivalence classes of) paths in ‘modulated’ quivers (with ‘multiplicities’). The dimension formulas obtained in this way improve and clarify earlier results of Huber & Wüstholz and recover a dimension estimate of Deligne & Goncharov. This is based on joint work with Annette Huber (Freiburg).
• Caroline Namanya (Makerere University, Uganda), Derived autoequivalences on algebraic flops
  • In this talk, I will give a construction of derived autoequivalences associated to an algebraic flopping contraction X -> X_con, where X  is quasi-projective with only mild singularities. These functors are constructed naturally using bimodule cones.
• Nebojsa Pavic (University of Graz, Austria), Derived categories, categorical absorptions and crepant resolutions
  • We study semiorthogonal decompositions of projective varieties with isolated Gorenstein singularities and which admit a crepant desingularization. We give sufficient conditions
     for when derived categories of such varieties admit a semiorthogonal decomposition into two components; a component containing the information of the singularity and a component encoding its smooth information – we call this a categorical absorption of singulairites. We give examples satisfying our condition and, if time permits, we also give criteria which do not allow such decompositions. This contains joint work in progress with M. Kalck.
• Michael Wemyss (University of Glasgow, UK), Namikawa–Weyl groups for cDV singularities
  • I will explain how to produce two reflection groups from the data of a minimal model of a cDV singularity, one finite and one “affine”.  These act on associated hyperplane arrangements, and have various geometric applications.  This is work in progress with Travis Schedler.
    
    

Supported by the Africa-Uninet project Uganda-Austria Collaboration in Algebra and Geometry, and the University of Vienna