Announcements
New Book on Spectral Theory of Discrete Structures
Published May 15, 2026
Our emeritus director Jürgen Jost, together with our former PhD student and Minerva Group Leader Raffaella Mulas (now Assistant Professor at VU Amsterdam), and former postdoctoral researcher Dong Zhang (now Assistant Professor at Peking University), has co-authored the new book Spectra of Discrete Structures, published by Cambridge University Press as part of the Cambridge Studies in Advanced Mathematics series. The book develops a comprehensive spectral theory for discrete structures, including graphs, simplicial complexes, and hypergraphs.
While hypergraphs were long underexplored in mathematical research, recent advances—particularly the development of Laplace operators capable of probing their structure—have brought them to the forefront of interdisciplinary study. Today, they play an important role in applications ranging from chemical reaction networks to models of social interaction.
Combining rigorous mathematical foundations with intuitive and often visually accessible examples, the authors present a unified framework for understanding the spectra of discrete structures. Particular emphasis is placed on recent developments such as Cheeger-type inequalities, which establish connections between spectral properties and the geometry—or more precisely, the cohesion—of the underlying structures.
The book is intended for graduate students and researchers in mathematics, especially those working in spectral theory and its applications to discrete systems.
An open-access version of the book is available online, where printed copies can also be ordered.
Spectra of Discrete Structures
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open-access online version
Jürgen Jost, Max Planck Institute for Mathematics in the Sciences, Leipzig
Raffaella Mulas, Vrije Universiteit Amsterdam
Dong Zhang, Peking UniversityCambridge University Press
Cambridge Studies in Advanced Mathematics (221)
Scientific Contact
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Raffaella Mulas Raffaella Mulas
Vrije Universiteit Amsterdam
Department of Mathematics
Editorial Contact
Staff
Jana Gregor
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Announcements
15.05.26
New Book on Spectral Theory of Discrete Structures New Book on Spectral Theory of Discrete Structures
A new book project by Jürgen Jost and former group members Raffaella Mulas and Dong Zhang explores the spectra of graphs, simplicial complexes, and hypergraphs—bridging mathematical theory and interdisciplinary applications.
Announcements
09.01.26
Mathematics Meets Morality: The Trolley Problem discussed in a Podcast Mathematics Meets Morality: The Trolley Problem discussed in a Podcast
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Announcements
08.10.25
Connecting Modern Research with Riemann’s Vision Connecting Modern Research with Riemann’s Vision
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Announcements
06.02.25
ϴ-Positivity: A Unifying Framework for Lie Groups ϴ-Positivity: A Unifying Framework for Lie Groups
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Announcements
09.07.24
New Proof to Solve a Class of Stochastic Partial Differential Equations New Proof to Solve a Class of Stochastic Partial Differential Equations
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Announcements
21.06.24
Congratulations to Daniel Kráľ on the Humboldt Professorship Congratulations to Daniel Kráľ on the Humboldt Professorship
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Announcements
26.04.24
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Announcements
22.04.24
Supporting Young Mathematicians in Europe Supporting Young Mathematicians in Europe
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Announcements
14.03.24
Representing the Interests of Doctoral Researchers Representing the Interests of Doctoral Researchers
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Announcements
05.03.24
New Mathematical Tools for Studying Particle Collisions New Mathematical Tools for Studying Particle Collisions
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Announcements
07.02.24
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Accolades
21.11.23
Anna Wienhard Appointed to Leopoldina Anna Wienhard Appointed to Leopoldina
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Press Releases
26.10.23
Positive Geometry – Millions in Funding for UNIVERSE+ Project Positive Geometry – Millions in Funding for UNIVERSE+ Project
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In Conversation
15.09.23
Samantha Fairchild Establishes New Research Group to Cross the Transcendental Divide Samantha Fairchild Establishes New Research Group to Cross the Transcendental Divide
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Future Proof
23.05.23
Wolfram Barfuss Appointed Professor for Sustainable Futures Wolfram Barfuss Appointed Professor for Sustainable Futures
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Press Releases
25.04.23
Social Media for More Democracy – Million-Euro Funding for Project to Study the Impact of Social Media on Society and Politics Social Media for More Democracy – Million-Euro Funding for Project to Study the Impact…
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Announcements
24.03.23
Abel Laureate Luis A. Caffarelli to Speak at “Shocking Developments” Conference Abel Laureate Luis A. Caffarelli to Speak at “Shocking Developments” Conference
Congratulations to Luis A. Caffarelli for being honored with the prestigious Abel Prize!
Future Proof
13.02.23
Angkana Rüland Appointed to Hausdorff Chair Angkana Rüland Appointed to Hausdorff Chair
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Future Proof
01.02.23
Future Proof — Raffaella Mulas on the Way to Amsterdam Future Proof — Raffaella Mulas on the Way to Amsterdam
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Future Proof
16.01.23
Describing How Fluids Flow – Tristan Buckmaster Appointed Professor at University of Maryland Describing How Fluids Flow – Tristan Buckmaster Appointed Professor at University of…
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Announcements
01.12.22
Congrats to our new Doctors rer. nat. Congrats to our new Doctors rer. nat.
Once again, we are happy to announce that three of our students took a big career step and successfully defended their PhD theses. Congratulations to Chiara Meroni, Henrik Eisenmann, and Daniel Schliewe!
Press Releases
02.11.22
Fascinated by Symmetries – Anna Wienhard Appointed Director at the Max Planck Institute for Mathematics in the Sciences Fascinated by Symmetries – Anna Wienhard Appointed Director at the Max Planck Institute…
We are delighted to welcome Prof. Anna Wienhard as our new Max Planck director! Her newly established research group focuses on fundamental research in the areas of geometry, group theory, and dynamics.
Press Releases
14.07.22
László Székelyhidi Is Appointed Director at the Max Planck Institute for Mathematics in the Sciences László Székelyhidi Is Appointed Director at the Max Planck Institute for Mathematics in…
The Leipzig mathematician and university professor László Székelyhidi was appointed director at the MPI MiS. Prof. Székelyhidi's research focuses on partial differential equations and the calculus of variations and their application.
Announcements
23.05.22
Center for artificial intelligence approved Center for artificial intelligence approved
We are very proud to be part of the Konrad Zuse School of Embedded Composite AI (SECAI) which will be established under the lead of TU Dresden as one of three centers for artificial intelligence in Germany.
Announcements
20.05.22
Max Planck Partner Group in Brazil Max Planck Partner Group in Brazil
We are happy to announce the launch of a new Max Planck Partner Group in Brazil with focus on geometry and probability in dynamical systems. Led by Christian S. Rodrigues, the group will work in close cooperation with our director Jürgen Jost and his group members.
Announcements
03.05.22
Welcome to the new Alexander von Humboldt Professor Sayan Mukherjee Welcome to the new Alexander von Humboldt Professor Sayan Mukherjee
We are happy and proud to welcome Sayan Mukherjee as an Alexander von Humboldt Professor at the University of Leipzig and as a Max Planck fellow at our institute.
Job Openings
25.02.22
SAXAG Algebraic Geometry initiative starts with Postdoc call SAXAG Algebraic Geometry initiative starts with Postdoc call
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Accolades
15.02.22
Guido Montúfar selected as Sloan Research Fellow in Mathematics Guido Montúfar selected as Sloan Research Fellow in Mathematics
The Alfred P. Sloan Foundation has awarded Guido Montúfar a prestigious two-year $75,000 fellowship for his mathematical machine learning research.
Announcements
12.07.21
Making optimal use of mathematical research data Making optimal use of mathematical research data
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Announcements
02.07.21
New Alexander von Humboldt Professorship for Artificial Intelligence 2022 – Sayan Mukherjee nominated New Alexander von Humboldt Professorship for Artificial Intelligence 2022 – Sayan…
The University of Leipzig, in cooperation with the MPI MiS, has attracted Germany's most valuable research award: Professor Sayan Mukherjee has been nominated for an Alexander von Humboldt Professorship 2022.
Announcements
15.04.21
Nihat Ay is the new Editor-in-Chief of INGE Nihat Ay is the new Editor-in-Chief of INGE
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Events
12.03.21
International Day of Mathematics 2021 International Day of Mathematics 2021
Coming Sunday, March 14, is the International Day of Mathematics – a worldwide celebration of the essential role that mathematics and mathematics education plays in breakthroughs in science and technology, improving the quality of life, empowering women and girls and much more.
Accolades
16.02.21
Paul Breiding Awarded Early Career Prize Paul Breiding Awarded Early Career Prize
The SIAM Activity Group on Algebraic Geometry has awarded Paul Breiding their Early Career Prize for his distinguished contributions to the field.
Women in Science
11.02.21
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Today on February 11 is the International Day of Women and Girls in Science – a perfect day to celebrate the achievements of all ladies working in science related fields. And it is a perfect day for us to announce our institutional membership in the European Women in Mathematics.
Announcements
04.08.20
Daniele Agostini Appointed as Nonlinear Algebra Group Leader This Fall Daniele Agostini Appointed as Nonlinear Algebra Group Leader This Fall
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Miscellaneous
31.07.20
Kickoff for Linear Spaces of Symmetric Matrices Study Group Kickoff for Linear Spaces of Symmetric Matrices Study Group
Scientists at MiS and other institutes around the globe have just established a collaborative project that aspires to advance the understanding of linear spaces of symmetric matrices (LSSM).
Announcements
17.04.20
German-Israeli Foundation Grant for Network Curvature Research German-Israeli Foundation Grant for Network Curvature Research
With a grant from the German-Israeli Foundation for Scientific Research and Development (GIF) our director Jürgen Jost and Emil Saucan from the Braude College Israel will continue their successful scientific collaboration for the next three years.
Press Releases
14.04.20
Dr. Noémie Combe on the Fast Track to Structural Unification Dr. Noémie Combe on the Fast Track to Structural Unification
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Future Proof
18.03.20
Future Proof — Angkana Rüland Future Proof — Angkana Rüland
After more than two years of excellent research at the institute, Angkana Rüland is leaving us to become a professor of applied mathematics at the Ruprecht-Karls-University in Heidelberg. We would like to congratulate Angkana on her position and wish her all the best in Heidelberg.
Announcements
19.02.20
Lukas Geuter Honored With DMV Scholarship to Study the Dynamics of Active Systems Lukas Geuter Honored With DMV Scholarship to Study the Dynamics of Active Systems
We would like to give a warm welcome to Lukas Geuter from TU Berlin. Lukas was awarded a study visit scholarship by the German Mathematical Society (DMV) last year. He is in the first year of his PhD and studies the mathematical properties of active systems.
Press Releases
02.12.19
An Exceptional Enrichment for Mathematical Research in Leipzig An Exceptional Enrichment for Mathematical Research in Leipzig
Prof. Dr. Michael Joswig, Einstein-Professor of discrete mathematics and geometry at the Technical University of Berlin, was appointed Max Planck Fellow by the Max Planck Society.
Announcements
25.07.19
Max Planck Fellowship and New Group for Prof. Michael Joswig Max Planck Fellowship and New Group for Prof. Michael Joswig
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Announcements
03.12.18
Bernd Sturmfels Appointed as Ordinary Member of the Berlin-Brandenburg Academy of Sciences and Humanities Bernd Sturmfels Appointed as Ordinary Member of the Berlin-Brandenburg Academy of…
Professor Bernd Sturmfels, director at the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany, has been appointed as an ordinary member of the Berlin-Brandenburg Academy of Sciences and Humanities on Friday, November 30th 2018.
Press Releases
12.11.18
First Steps Towards a New Mathematical Physics Center in Leipzig First Steps Towards a New Mathematical Physics Center in Leipzig
The interplay between mathematics and theoretical physics is at the center of a new joint initiative of the Faculties of Mathematics and Computer Science, Physics and Geosciences of the University of Leipzig and the Max Planck Institute for Mathematics in the Sciences.
Press Releases
21.08.18
Looking at Data Through the Lens of Algebraic Geometry Looking at Data Through the Lens of Algebraic Geometry
In the recent article “Learning algebraic varieties from samples”, a group of researchers from the Max Planck Institute for Mathematics in the Sciences has presented a novel approach to the analysis of datasets that possess an inherent geometric structure.
Press Releases
19.06.18
Detecting Crises with the Aid of Social Networks – International Conference Connects Scientists in Leipzig Detecting Crises with the Aid of Social Networks – International Conference Connects…
Communication mechanisms in social networks are at the centre of the international conference currently taking place at the Max Planck Institute for Mathematics in the Sciences.
Press Releases
07.06.18
Meaningful Relationships – Mathematical Insights into the Geometry of Complex Networks Meaningful Relationships – Mathematical Insights into the Geometry of Complex Networks
Mathematicians from the MPI MiS, in cooperation with the Santa Fé Institute, USA and scientists from India, China, and Israel, have provided concrete proof of the effectiveness of geometrical tools in describing the variety of relationships in complex networks.
Press Releases
29.09.17
Conference in Memory of the Great Leipzig Mathematician Eberhard Zeidler Conference in Memory of the Great Leipzig Mathematician Eberhard Zeidler
On October 6 at 10 a.m., a conference will be held in honor of the mathematician and founding director of the Max Planck Institute for Mathematics in the Sciences, Prof. Dr. Dr. h.c. Eberhard Zeidler.
Press Releases
05.09.17
2017 Sofja Kovalevskaja Award Winner Conducting Research at MPI 2017 Sofja Kovalevskaja Award Winner Conducting Research at MPI
The 2017 Sofja Kovalevskaja Award winner Dr. Matteo Smerlak will be conducting research on the topic of “Structure of Evolution” at the Max Planck Institute for Mathematics in the Sciences starting in December 2017.
Press Releases
11.05.17
Bernd Sturmfels Appointed New Director Bernd Sturmfels Appointed New Director
Bernd Sturmfels has joined the board of directors of the Max Planck Institute for Mathematics in the Sciences. He will head a new working group on “Nonlinear Algebra” at the institute.
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