# ResearchBridging Theory and Experiment

5 August 2021

## New professors at the STRUCTURES Cluster of Excellence

The STRUCTURES Cluster of Excellence at Heidelberg University has been joined by three new professors, Prof. Dr Beatrice Pozzetti, Prof. Dr Razvan Gurau and Prof. Dr Lauriane Chomaz. They are leading experts in their respective fields of pure mathematics, mathematical physics, and experimental physics, and are now driving interdisciplinary collaboration forward – not only within STRUCTURES but also at their departments and institutes. In accordance with a key idea of the cluster – that underlying all physical structure is mathematical structure – their work bridges theoretical and experimental approaches in these fields, and will contribute to the cluster’s research across disciplines and scales.

## Identifying structures in geometry and beyond

Beatrice Pozzetti first joined Heidelberg University as a junior mathematics professor in 2017, and accepted a professorial appointment with tenure track as part of the STRUCTURES community in July 2020. With her independent research group, funded in part through the Emmy Noether Programme of the German Research Foundation, Prof. Pozzetti is conducting fundamental research into geometry and its applications in other scientific disciplines – from computer science to theoretical physics. She is a member of the Research Station Geometry and Dynamics at the Mathematical Institute of Ruperto Carola and a project leader on the DFG priority programme SPP 2026 Geometry at Infinity, which seeks to combine and transcend existing approaches in differential geometry, geometric topology, and global analysis.

“I consider myself a pure mathematician. Most of my research is very abstract – and very difficult to explain to those not familiar with its language or concepts,” Prof. Pozzetti notes. “In the broadest sense, however, pure maths is about finding very rigorous structure.” Part of her research is in geometric group theory, which studies the symmetries and dynamic transformations of mathematical objects and the spaces they act on. She says: “Generalising and playing around with these symmetries is one way of uncovering interesting new geometric features. These, in turn, can help us to address challenges in fields such as data science, machine learning or theoretical physics.” As part of the STRUCTURES cluster, Beatrice Pozzetti is applying concepts and theorems from geometric group theory, for instance, to identify new structures in data or to gain a deeper understanding of how neural networks work. She is also confident, she says, that the synergies between mathematics and physics promoted by the cluster will lead to significant progress in the field of string theory: “There is so much opportunity to meet and work with other people across a range of disciplines. This is one of the things I love most about Heidelberg and about STRUCTURES.”

Originally from Bergamo (Italy), Beatrice Pozzetti studied mathematics at the Scuola Normale Superiore in Pisa, where she was accepted as one of 30 successful candidates out of a batch of 300. She went on to earn her PhD from ETH Zurich (Switzerland), followed by postdoctoral research at the Mathematical Sciences Research Institute in Berkeley (California) and at the University of Warwick (UK). During this time, she also spent time at Princeton University and at the Isaac Newton Institute for Mathematical Sciences in Cambridge. In the summer semester of 2019, she held the position of interim professor at the University of Bonn.

## Modelling multi-dimensional spaces with random tensors

Geometry in the widest sense is also what interests Razvan Gurau. A theoretical physicist by education, he is a leading expert in the field of random tensors and their implications for quantum field theory, gravity, and topology. Razvan Gurau was appointed a STRUCTURES professor in mathematical physics in December 2020. Before accepting his current appointment at Heidelberg University – a bridge professorship designed to maximise synergies between maths and physics both within and beyond the STRUCTURES cluster – he was “directeur de recherche” at the Centre National de la Recherche Scientifique (CNRS) in the Center for Theoretical Physics (CPHT) of the École Polytechnique in Palaiseau (France).

“I started looking into random tensors during my postdoc and, using approaches from mathematics and theoretical physics, built a rich line of research around this topic,” Prof. Gurau explains. Tensors belong to the same family of algebraic objects as scalars, vectors, and matrices. While scalars are real numbers that represent a physical quantity such as mass, and vectors represent physical quantities that have both magnitude and direction – such as velocity or acceleration – and can be seen as a string of numbers, tensors can be best described as cubes (or hypercubes) of numbers. Such cubes can be used to organise data in multi-dimensional spaces – in particular three dimensions or more. “Essentially, tensors provide a concise mathematical framework for posing and solving physics problems in a range of areas including random geometry, quantum gravity, conformal field theory and others. Furthermore, they are relevant for the study of artificial intelligence,” the scientist adds.

The original motivation to study random tensor models was quantum gravity, says Prof. Gurau: “One idea to reconcile quantum physics and gravity – besides string theory and various other approaches founded in theoretical physics – is through the study of random geometry. In the beginning, random tensors were thought to be relevant in this context because random matrices – their lower rank version – yield a good working theory of random surfaces. Random tensors model random spaces in higher dimensions.” So far, however, quantum gravity remains elusive. Instead, the study of random tensors has contributed significantly to advancing our knowledge in a range of other disciplines. In quantum field theory, for instance, random tensors have proven an important tool for simplifying what is known as strongly coupled systems – systems so complex that they elude description with the currently available mathematical tools. Tensor models have also been used to study how black holes behave in certain conditions, with implications both for high energy physics and cosmology. And they may provide insights into what is happening in the deep layers of neural networks. As part of the STRUCTURES cluster, Prof. Gurau is looking to expand these and related lines of research into complex systems – across disciplines and scales.

Razvan Gurau started studying physics in his native Romania and completed his undergraduate degree at the École Normale Supérieure de Paris (France). He earned his PhD from the Université Paris Sud 11 in 2008 and his habilitation on the topic of random tensors in 2015. Prior to accepting his appointment at Heidelberg University, Prof. Gurau spent time as a postdoctoral researcher at the Perimeter Institute for Theoretical Physics in Ontario (Canada) and was an honorary lecturer at the University of East Anglia in Norwich (UK). In 2012, he was appointed “chargé de recherche” at the Centre National de la Recherche Scientifique (CNRS) in the Center for Theoretical Physics (CPHT) of the École Polytechnique in Palaiseau, and promoted “directeur de recherche” in 2019, a position he held until his appointment to Heidelberg University. Razvan Gurau was awarded the Hermann Weyl Prize in mathematical physics for discovering and developing the theory of coloured random tensors in 2012, and he received an ERC Consolidator Grant of the European Research Council (ERC) for a project on random tensors and field theory in 2018.

## Discovering new effects from long-range interactions at the quantum level

Lauriane Chomaz joined the STRUCTURES cluster in February 2021 as a tenure track professor in experimental physics. With her research group at the Institute for Physics of Ruperto Carola, she is exploring the behaviour of quantum fluids using ultracold assemblies of atoms, especially dysprosium atoms. As an experimental physicist, much of her work consists in designing and carrying out experiments that generate new insights into how particles behave in a collective and quantum manner. “I am interested in observing novel quantum phenomena whose investigation may help to fill the gaps in our knowledge. In the widest sense, the most interesting aspect of our research is when we encounter effects that we are unable to explain using the current theoretical framework,” says Prof. Chomaz.

A major focus of her research is on the effect of dipole-dipole interactions in ultracold quantum gases. “Most atoms in ultracold gases only interact when they come into direct contact with each other. However, in some atomic species, long-range and anisotropic dipole-dipole interactions can also be important. This is due to the large magnetic dipole moment arising from the specific electronic configurations of some atoms in their ground state. This is the case with dysprosium in particular. Dysprosium atoms thus interact not only by colliding, but also at a distance, like tiny magnets.” These interactions may, in certain conditions, give rise to previously unknown quantum effects. Within the last few years, breakthroughs were made through experiments using dipolar quantum gases, leading to the discovery of liquid-like states stabilised by quantum fluctuations – known as quantum droplets – as well as droplet assemblies, roton excitations, and, most recently, supersolid states. As Prof. Chomaz explains, supersolids are particularly exciting as they form a paradoxical state where both superfluid and solid orders coexist. This means that two continuous symmetries of different nature are simultaneously broken. Such states were envisioned by theorists back in the 1950s but remained elusive for more than sixty years, before being observed in quantum-gas experiments. Lauriane Chomaz participated in these discoveries as a postdoctoral researcher.

Since coming to Heidelberg, Prof. Chomaz has been in the process of building a new-generation experiment based on dysprosium, the most magnetic of the atoms, combining it with special confinements provided by laser light in order to form systems of reduced dimensions. “By playing around with the parameters of our experimental set-up we hope to uncover new quantum phenomena,” the physicist says. These may involve patterns and structures that spontaneously arise from the mere effect of inter-particle interaction. As such, they may also afford new insights into other systems such as electron gas or stars.

Lauriane Chomaz studied mathematics and physics at the École Polytechnique and the École Normale Supérieure in Paris (France), completing her studies with a major in quantum physics in 2010. She earned her PhD from ENS with a dissertation on Bose gases in reduced dimensions, followed by postdoctoral research at the University of Innsbruck (Austria), where she received funding through the Marie Skłodowska-Curie actions of the European Union and through the Elise Richter Programme of the Austrian Science Fund (FWF). In 2018 she received the Early Career Award of the New Journal of Physics, which the Institute of Physics (IOP) awards in collaboration with the German Physical Society (DPG).