## Research interests

### Extended degrees of freedom in QFT

Quantum field theories at strong coupling exhibit a much richer set of degrees of freedom than in the weak coupling limit. A striking example is the existence of two-dimensional, stringlike excitations in large classes of QFTs in 4,5, and 6 dimensions. A main focus of our research is to shed light on the properties of these extended degrees of freedom and use them to understand the non-perturbative behavior of quantum field theories.

**Guglielmo Lockhart and Michele Del Zotto,***The ALE partition functions of M-string orbifolds,*arXiv:2311.00607 [hep-th]**Guglielmo Lockhart and Michele Del Zotto**,*The ALE partition functions of M-strings*, arXiv:2309.00607 [hep-th]**Guglielmo Lockhart and Michele Del Zotto,***Universal Features of BPS Strings in Six-dimensional SCFTs*, arXiv:1804.19694 [hep-th]

### Mathematical physics

Many aspects of quantum field theory and string theory are encoded by rich mathematical structures. Often the interplay with physics leads to a deeper insight into these mathematical structures and their relations among each other. An important aspect of our work is to develop new connections between enumerative and algebraic geometry, representation theory, and various generalizations of modular forms with the aid of string theory techniques.

**Seung-Joo Lee, Wolfgang Lerche, Guglielmo Lockhart and Timo Weigand,***Holomorphic anomalies, fourfolds and fluxes*, JHEP 03 (2022) 072 [arXiv:2012.00766 [hep-th]]**Seung-Joo Lee, Wolfgang Lerche, Guglielmo Lockhart and Timo Weigand**,*Quasi-Jacobi forms, elliptic genera and strings in four dimensions*, JHEP 01 (2021) [arXiv:1005.10837 [hep-th]]

### Formal aspects of string theory

Part of our research is devoted to developing formal aspects of string theory. Two recent developments in this direction are: the discovery of a hidden affine E_{6} symmetry that underlies the pure spinor formulation of superstrings; and understanding the modular transformation properties of conformal blocks in two-dimensional conformal field theory.

**Richard Eager, Guglielmo Lockhart and Eric Sharpe**,*Hidden exceptional symmetry in the pure spinor superstring*, Phys.Rev.D 101 (2020) 2, 026006 [arXiv:1902.09504 [hep-th]]**Miranda Cheng, Terry Gannon and Guglielmo Lockhart**,*Modular Exercises for Four-Point Blocks -- I*, arXiv:2002.11125 [hep-th]