Research Interest of Charlie Beil

      Publication 1: The noncommutative geometry of square superpotential algebras (URL)
      Publication 2: Geometric aspects of dibaryon operators (URL)
      Publication 3:  (URL)

    URL of Research: 

Statement of Interest:


  My research interests are in noncommutative algebraic geometry and its applications to string theory, and specifically in ways of resolving singularities using matrix-valued functions. My thesis consists of two distinct projects. In my first project I show that a large class of quiver algebras arising from brane tilings in string theory are noncommutative crepant resolutions, and consequently Calabi-Yau algebras. In my second project I introduce a geometric realization of noncommutative singularity resolutions. To do this, I first present a new method of obtaining conventional (minimal) resolutions using noncommutative coordinate rings. Then, using symplectic reduction within these rings, I obtain new, non-conventional resolutions that are hidden if only commutative functions are considered.  Geometrically, these non-conventional resolutions result from shrinking exceptional loci to stack-like points.