This proceedings volume explores the interplay between topology and physics in the selforganization and emergent properties of condensed matter and materials, a topic that has gained major prominence in recent years. Across a wide range of systems, including entangled polymers with circular, linked, or knotted structures, liquid crystals and colloids, as well as topological insulators and Majorana fermions, topology plays a decisive role in generating novel physical phenomena and distinctive macroscopic material properties.
Despite its central importance in contemporary condensed matter physics, topology is traditionally given limited attention in standard graduate curricula. The International School of Physics Enrico Fermi was conceived to address this gap by providing participants with a coherent and accessible introduction to both the essential mathematical concepts and the physical principles underlying current research at the interface of topology, hard matter, soft matter, and materials science.
Based on lectures delivered by leading experts, this book offers authoritative and carefully structured lecture notes that bridge abstract topological ideas and concrete physical applications. Complemented by a critical summary from the editors, the volume presents a unified perspective on how topological concepts inform modern approaches to condensed matter and materials research.
It is intended as a valuable resource for graduate students, researchers, and scientists seeking a deeper understanding of how topology shapes the behavior of complex physical systems.
Spectroscopy of Band Topology and Quantum Geometry From Concepts to
Materials.- Molecular Knots: From Modelling and Experiments to Design.-
Finding Hidden Structure: Modern Methods to Identify Local Structure in
Colloidal System.- Knots in Proteins: What, Where, How and Why?.- Rheological
Signatures of Topology.- Topological Quantum Chemistry From Water to
Colloidal Water... Topological Nature of the Liquid-Liquid Transition.-
Greens Function Zeros in Mott Insulators.- Spatiotemporal Organization of
Bacterial Suspensions Under Confinement.- Active Polymers in Relation to
Topology.- Topology in Soft and Hard Matter.
Christos Likos graduated from the National Technical University of Athens with a Diploma in Electrical Engineering in 1988 and subsequently pursued graduate studies in Physics at Cornell, where he obtained his Ph.D. in 1993 under the supervision of Neil Ashcroft and Chris Henley. Afterward, he held postdoctoral positions as an Alexander von Humboldt fellow at the University of Munich, as an EU-fellow in Trieste, and as a research fellow at the Jülich Research Center in Germany. In 2001, he obtained a Heisenberg fellowship from the German Research Foundation, which he spent in part at the University of Cambridge. In 2003, he obtained simultaneous offers for an Associate Professorship at the Foundation of Research and Technology-Hellas in Crete and at the University of Düsseldorf, spending seven years at the latter until 2010, at which point he was elected as a full professor of Physics at the University of Vienna. His research interests lie in computational and theoretical soft matter physics and in the last few years he focuses on topological polymers. Prof. Likos has co-authored about 300 papers in high-impact journals, including Nature, Physical Review Letters, Nature Materials, Nature Communications, ACS Nano, Physical Review X, Angewandte Chemie, Reviews of Modern Physics and Physics Reports. In 2025 he was awarded the UNIVIE Teaching Award and the Teaching Star Prize of the University of Vienna. He has served as Associate Editor of Soft Matter (2011 2020) and he is a Fellow of the Royal Society of Chemistry.
Christoph Dellago is a full professor of Computational Physics at the University of Vienna. After obtaining his Ph.D. in physics in 1996, he worked as a postdoctoral researcher at the University of California at Berkeley. In 1999, he started as an assistant professor at the University of Rochester before returning to the University of Vienna in 2003. His research interests range from simulation methods for rare events and machine learning to fluctuations in non-equilibrium processes, soft matter, and nano-materials. Prof. Dellago has co-authored over 200 papers in many journals including Science, Nature Nanotechnology, the Proceedings of the National Academy of Science of the USA, Physical Review Letters, and Nano Letters. In 2005, he received the Raymond and Beverly Sackler Prize in the Physical Sciences awarded by Tel Aviv University and in 2015 the UNIVIE Teaching Award of the University of Vienna. Prof. Dellago has served as the dean of the Faculty of Physics of the University of Vienna (20082012) and as director of the Erwin Schrödinger Institute for Mathematics and Physics (2017-2026).
Domenico Di Sante is an associate professor at the University of Bologna. He earned a B.S. in physics at the University of LAquila in 2011 and a Ph.D. in physics in 2015. He subsequently was a postdoctoral fellow and young group leader at the Physics Department of the University of Würzburg (20162020), and a Marie Curie research fellow at the Center for Computational Quantum Physics of the Flatiron Institute in New York (20212023). His research is focused on the numerical quantum simulations of the electronic properties of interacting material systems, with an emphasis on topology and spin-orbit driven phenomena. He was the principal investigator of an individual Marie Curie fellowship that aimed at using machine learning applications in condensed matter problems. Prof. Di Sante has co-authored about 100 papers in many journals including Reviews of Modern Physics, Science, Nature Physics, Nature Communications, Physical Review Letters, Advanced Materials and Nano Letters.
Cesare Franchini is a full professor of Computational and Theoretical Condensed Matter Physics at both the University of Vienna and the University of Bologna. He graduated in 1999 from the University of Cagliari (Italy) and earned his Ph.D. in 2002 at the Technical University of Vienna. Following postdoctoral positions in Cagliari and Vienna, he began a tenure-track position at the University of Vienna in 2012. Franchinis research focuses on the theoretical understanding and computational modeling of complex materials using DFT, Quantum Monte Carlo, and Machine Learning approaches. His prolific scientific contributions include about 200 published articles in journals such as Science, Nature Review Materials, Physical Review Letters, Physical Review X, PNAS, and Nature Communications. In addition to his research, Professor Franchini has served on the Scientific Council of the Institute of Advanced Studies at Alma Mater Studiorum Bologna and has contributed to several doctoral schools.
Sofia Kantorovich obtained her degree in Mathematics from Ural State University, where she also pursued her Ph.D. in Physics of Magnetism, completing it in 2004. Following her doctoral studies, she held postdoctoral positions at Max Plank Institute for Polymer Research, the University of Stuttgart, and the University of Rome La Sapienza, where she worked extensively on theoretical and computational approaches in magnetic soft matter physics. In 2012, she was awarded the Start Prize of the Austrian Science Fund, allowing her to establish an independent research group in Vienna, where she moved in 2013. Since 2017, she has been an associate professor, and since 2022a full professor at the University of Vienna, leading a research team focusing on ferrofluids, magnetic soft matter, and self-assembly phenomena in complex fluids. Prof. Kantorovich has published over 100 research articles in high-impact journals, including Physical Review Letters, ACS Nano, Nano Letters, Macromolecules, and Nanoscale.
