Christoph A. Keller

Associate Professor
Email: cakeller (at)
Office: MATH 516
Mail: Mathematics Dept, Univ. of Arizona
617 N. Santa Rita Ave.
P.O. Box 210089
Tucson, AZ 85721-0089
Research Interests: I am interested in the mathematical structure of physics. On the mathematics side, I work on algebra and group theory. I am particularly interested in modular forms and vertex operator algebras (VOA). On the physics side, I work on quantum field theory, string theory and holography. I am particularly interested in conformal field theories (CFT) in two dimensions and their applications in describing black holes.

Some of my current and recent projects are:
  • Constructing new VOAs with good `holographic' properties, with a particular interest in the large central charge limit. This involves investigating the connection to lattices and finite groups, especially permutation groups.
  • Investigating Fourier coefficients of modular and more general automorphic forms, especially their asymptotic behavior in various limits. In this spirit I am also interested in moonshine, both old and new. Recently I have become interested in non-holomorphic modular forms.
  • Conformal perturbation theory for 2d CFTs and its application to holography. This is motivated by my interest in moduli spaces of CFTs and irrational CFTs.
Publications: My publications on arXiv and inSPIRE.
Brief CV: I did my Ph.D. with Matthias Gaberdiel at ETH Zürich from 2006 through 2008. After that I spent a year as a postdoc at Harvard, three years as a McCone fellow at Caltech, and three years as a postdoctoral researcher at Rutgers University. In 2015 I became Assistant Professor in Mathematical Physics at ETH Zürich. In 2018 I moved to the University of Arizona. A more detailed CV can be found here.
Teaching: At Arizona:
  • Fall 2022: Theory of Probability (MATH 464)
  • Spring 2022: Introduction to Abstract Algebra (MATH 415B)
  • Fall 2021: Introduction to Abstract Algebra (MATH 415A)
  • Spring 2021: Mathematical Analysis for Engineers (MATH 322)
  • Fall 2020: Mathematical Analysis for Engineers (MATH 322)
  • Spring 2020: Introduction to Cryptography (MATH 445)
  • Fall 2019: Introduction to Mathematical Physics (MATH 541)
  • Spring 2019: Linear Algebra (MATH 413/513)
  • Fall 2018: Mathematical Analysis for Engineers (MATH 322)
  • Spring 2018: Calculus II (MATH 129)
At ETH Zürich:
  • Summer 2018: Monstrous and Other Moonshine
  • Fall 2017: Introduction to Vertex Operator Algebras (lecture notes)
  • Spring 2017: Introduction to String Theory
  • Fall 2016: Mathematical Methods of Physics I
  • Spring 2016: Introduction to String Theory (lecture notes)
  • Fall 2015: Monstrous Moonshine