Scientific Series

Chern-Simons theory is a topological quantum field theory which leads to link invariants, such as the Jones polynomial, through the expectation values of Wilson loops. The same link invariants also appear in a mathematical construction of Reshetikhin and Turaev which uses a trace on Yang-Baxter operators. Several algebraic structures are involved in these frameworks for computing link invariants, including the braid group, quantum algebras and centralizer algebras (such as the Temperley-Lieb algebra). In this talk, I will explain how the Askey-Wilson algebra, originally introduced in the context of orthogonal polynomials, can also be understood within the Chern-Simons theory and the Reshetikhin-Turaev link invariant construction.

Carl Sagan’s iconic question, "Who speaks for Earth?" from Cosmos invites us to reflect on whose voices are heard as we contemplate humanity's place in the universe. I will explore this question from the perspective of a queer mathematician, intertwining my personal journey with the broader experiences of LGBTQ+ scientists. Our diverse identities contribute to the richness of the scientific narrative, and by embracing our queerness, we ensure that the full spectrum of experiences is represented in the pursuit of knowledge. Drawing on Sagan’s legacy, I will argue that our voices, and our kindness to each other, are not just necessary but essential in shaping the future of science and our collective understanding of the world.

Thin enough black strings are unstable to rippling along their length, and the instability threshold indicates that static inhomogeneous black strings exist. These have indeed been constructed with increasing inhomogeneity until a high-curvature singular pinch appears. We study the string-scale version of this phenomenon: “string-ball strings”, which are linearly extended, self-gravitating configurations of string balls obtained within the Horowitz- Polchinski (HP) approach to near-Hagedorn string states. We construct inhomogeneous HP strings in spatial dimension d ≤ 6, and show that, as the inhomogeneity increases, they approach localized HP balls when d ≤ 5 or cease to exist when d = 6. We then discuss how string theory can smooth out the naked singularities that appear in the Kaluza-Klein black hole/black string transition, and we propose scenarios for the final stage of the evolution of the black string instability after string theory takes over.

The thorium-229 nucleus has a unique, low-lying isometric state allowing for laser spectroscopic investigations that are otherwise only accessible in electronic transitions. Here, we report on the first resonant laser excitation of the Th-229 nucleus. The fluorescence signal is observed from two Th-229 doped CaF2 crystals that enable us to determine the center frequency of 2020.409(7) THz corresponding to 148.3821(5) nm of the nuclear transition. The fluorescence lifetime in the crystal is 630(15) s, corresponding to an isomer half-life of 1740(50) s for a nucleus isolated in vacuum. These results pave the way towards high-resolution nuclear laser spectroscopy of Th-229 and an optical nuclear clock with high sensitivity in fundamental tests. This is work done in a cooperation of PTB and TU Wien: J. Tiedau et al., Phys. Rev. Lett. 132, 182501 (2024)

We are entering the golden age of multi-wavelength astronomical surveys. In the 2020s, a plethora of surveys (such as Euclid, eROSITA, Rubin-LSST, Simons Observatory, and CMB-S4) are underway or planned to provide unprecedented insights into cosmology and astrophysics. In this talk, I will discuss the significant scientific opportunities and challenges that arise in the era of big data, highlighting recent advances in computational modeling and the roles of artificial intelligence and machine learning.

As part of PI’s ongoing initiative aimed at enhancing the skills of our graduate students and post docs, we're introducing a training program designed to equip them with practical insights for delivering compelling non-technical presentations. The sessions will be facilitated by PI's training and outreach personnel.

The operator algebraic approach to quantum field theory is called algebraic quantum field theory. In this setting, we consider a family of operator algebras generated by observables in spacetime regions. This has been particularly successful in 2-dimensional conformal field theory. We present roles of tensor categories, modular invariance, classification theory, induction machinery and connections to vertex operator algebras.

After reviewing the motivation and challenges connected with the dRGT theory of ghost-free massive gravity, we discuss our recent progress in understanding non-linear dynamics of this model. In spherical symmetry, numerical studies suggest the formation of naked singularities during gravitational collapse of matter. Analytically, the same can be seen in the limit where the graviton mass is much smaller than the scales of the matter present. Both of these results underline the need to move beyond spherical symmetry to try and obtain realistic predictions. To that end, we present a new ‘harmonic-inspired’ formulation of the minimal model and argue that it is well-posed, opening the door to full 3+1 numerical simulations. 

I will review some recent progress in derived differential geometry, in particular pertaining to moduli stacks of solutions of elliptic partial differential equations on manifolds (with boundaries, and also with `logarithmic' boundaries, which include, for instance, manifolds with asymptotically cylindrical ends). In particular, this framework allows one to work efficiently with the compactified moduli spaces of symplectic topology and gauge theory. In another direction, I will explain some work in progress on the derived geometry of jet spaces, which can be used to endow moduli stacks of solutions of EOMs of a classical field theory with shifted symplectic structures.