orcid.org/0000-0002-9769-893X
- Women in automorphic forms, Bielefeld University, Sept 2021
- Quantum Gravity and Modularity, TCD, May 2021
- Mathematical Picture Language Seminar, Harvard University, August 2020
- Conference on Automorphic forms and integrable systems, Mathematical Center of Sirius University, Sochi, Feb 2020
- IMS Meeting, Galway, September 2019
- Research Seminar, SUSTech, Shenzhen, April 2019
Hi, thanks for stopping by. I am a mathematician working on the interface of physics and mathematics. I graduated in mathematics (Leipzig) and hold a PhD in both disciplines.
I just finished a Postdoctoral Fellowship at Trinity College Dublin. Currently I am a visitor to TCD. I am also an Adjunct Fellow with DIAS, while I'm relocating to Germany for family reasons.
My research is dedicated to an improved mathematical understanding of quantum field theory, more specifically rational CFTs.
My work makes a new start by exploring an alternative to the VOA formalism. The objects I deal with are automorphic forms on compact Riemann surfaces, with emphasis on equal treatment of genus one and higher genus (at least for the hyperelliptic case). The basic object is the partition function Z, which is a map from the Riemannian metrics to the real numbers. According to Hilbert (based on work by Einstein) and to Weinberg, the Virasoro N-point function is the Nth functional derivative of Z w.r.t. the metric at N points. One of the simplest yet most beautiful theories is the (2,5) minimal model (also known as Yang-Lee model). For genus one, the partition function for this model is given by the pair of Rogers-Ramanujan functions. The equation is equivalent to a 2nd order hypergeometric differential equation in the algebraic coordinates, with the complex variational parameter being a ramification point of the double covering. The corresponding automorphic forms in genus two solve a fifth order ODE [arXiv:1705.07627]. Alternatively, following the approach by Graeme Segal, the values of the partition function Z on higher genus Riemann surfaces can be constructed successively from data on lower genus Riemann surfaces by sewing along circles. Once the theory of modular forms and more generally automorphic forms is taken into account, Segal's ideas provide an efficient way to compute partition functions for higher genus. In genus two, we obtain Z as power series in the sewing parameter [arXiv:1801.08387]. In addition to the four solutions obtained from all possible pairings of the Rogers-Ramanujan functions on either torus, there is a fifth solution related to a real field of weight (-1/5,-1/5), which satisfies a separate third order ODE. Both approaches continue to work for higher genus, with the respective number of ODEs running through the Fibonacci numbers.
More recently I investigated algebraic and convolution properties of quasi-elliptic functions [arXiv:1908.11815]. This topic arose in the computation of genus one Virasoro correlation functions but turned out to be potentially useful for calculating elliptic Feynman integrals.
My project Higher Genus Automorphic Forms in Conformal Field Theory (CFT) was funded by a competitive Government of Ireland Fellowship from the Irish Research Council from 2018-2020 with a Covid-related funded extension from the HEA until May 2021.