Minerva group - Spectral Hypergraph Theory

**Head: **

Raffaella Mulas (Email)

**Phone:**

+49 (0) 341 - 9959 - 547

**Fax:**

+49 (0) 341 - 9959 - 658

**Address:**

Inselstr. 22

04103 Leipzig

# Spectral Hypergraph Theory

Spectral hypergraph theory studies the qualitative properties of a hypergraph that can be inferred from the eigenvalues and the eigenvectors of either square matrices or tensors associated with it. It generalizes the spectral theory of graphs, which has a long history and is widely used in applications.

Research topics in this area include, but are not limited to:

- Spectra of given hypergraphs
- Relations between the spectra of hypergraphs and their structural properties
- Eigenvalue bounds
- Spectral classes
- Algorithmic aspects
- Applications to dynamical systems and applications to data analysis of empirical networks (e.g. biological and chemical networks)

## Selected publications

## Events

- Speaker at the 1st East German Tensor Day

(September 1, 2021 | Max-Planck-Institute for Dynamics of Complex Technical Systems, Magdeburg)

## Group Members

Surname, first name | Phone | Office | Homepage | ||

Ph.D. Students | |||||
---|---|---|---|---|---|

Zucal, Giulio | Giulio.Zucal | 525 | A3 11 |

### Raffaella Mulas

I obtained my Master's degree at the University of Bonn (2017), where I worked on mathematical neurosciences and combinatorial stochastic processes under the supervision of Ngoc Mai Tran. I then received my PhD (2020) at the Max Planck Institute for Mathematics in the Sciences under the supervision of Jürgen Jost, with a thesis on the spectral theory of graphs and hypergraphs. From 2020 to 2021, I did a postdoc between the Alan Turing Institute of London and the University of Southampton, where I worked in the group of Ben MacArthur, and was a Visiting Researcher at the London Institute for Mathematical Sciences. During this postdoc, I had the chance to deepen the mathematical foundations of spectral hypergraph theory, as well as to apply this theory to problems arising in physics and biology. In 2020, I was also awarded the Prize "Donna di Scienza - Giovani" (Woman of Science - Young) from my home island of Sardinia. In 2021, I was awarded a Minerva Fast Track Fellowship from the Max Planck Society and chose to become a Minerva Group Leader at the Max Planck Institute for Mathematics in the Sciences. In the same year, I was elected Member of the Elisabeth-Schiemann-Kolleg.

Besides research, I am active in science communication, and enjoy drawing, traveling, reading, swimming, and swing dancing.

### Karel Devriendt

I am a postdoc in the Spectral Hypergraph Theory group of Raffaella Mulas. My research interests lie at the intersection between graph theory, linear algebra and geometry, and I am interested both in developing mathematical theory as well as applying it to various real-world problems. Some specific topics of interest are: Laplacian matrices, the effective resistance, dynamics on graphs, network science and discrete curvature. I am always happy to chat, so please get in touch if you want to share some ideas or discuss any of these topics!

I obtained a B.Sc. in Electrical Engineering from KU Leuven in Belgium (2014), spent an exchange year at KTH in Stockholm, and then obtained an M. Sc. in Electrical Engineering from TU Delft in the Netherlands (2017). After a year as a research assistant working with Piet Van Mieghem at TU Delft, I went to the University of Oxford to obtain Ph.D. in Applied Mathematics (2022) with the thesis “Graph Geometry from Effective Resistances”, under the supervision of Renaud Lambiotte.

Apart from mathematics, I love reading, swimming, drawing, music and more generally, arts.

### Giulio Zucal

I am currently a PhD student at the Max Planck Institute for Mathematics in the Sciences under the supervision of Raffaella Mulas. I obtained my master’s degree in mathematics at the Technical University of Munich, Germany, where I worked on stochastic partial differential equations and stochastic dynamics under the supervision of Christian Kuehn. Previously, I studied at the University of Trento in Italy, where I wrote my thesis with Sonia Mazzucchi. I also spent one exchange semester at the University of Groningen in the Netherlands. My main mathematical interests are currently in combinatorics, analysis, and probability theory. During my PhD, I would like to apply analytic, probabilistic, and geometric techniques to study the limits of growing combinatorial objects such as random graphs and hypergraphs, and the operators that arise in this context. In addition, I am also interested in the applications of graphs and hypergraphs to analyze natural and social sciences phenomena with a particular focus on dynamics on networks. Apart from Mathematics, I love hiking and doing sport. You can easily spark my interest with every type of outdoor activity, especially orienteering which is my childhood passion.