Mathematikon Entrance

Our Faculty is the academic home of researchers, teachers, and students of Mathematics and Computer Science. Its institutes and facilities are housed in the Mathematikon, pleasantly located on the Campus Neuenheimer Feld of Heidelberg University. Welcome!

Mathematikon Staircase

The Doctorate signifies a proven ability to conduct independent scientific research. Under the auspices of the Combined Faculty of Mathematics, Engineering and Natural Sciences, we confer the academic degree Dr. rer. nat. in the subjects of mathematics and computer science.

Mathematikon Library

Students interested in Mathematics, Computer Science, or an interdisciplinary field, pursuing a B.Sc., M.Sc., or M.Ed., and aiming for a career in research, teaching, or the private sector, will find here in Heidelberg a full range of first-class courses for a challenging and enriching educational experience in an intellectually stimulating environment with historical cachet.

Mathematikon Lobby

We seek to promote the interest in mathematics and computer science by organizing events for schools and for the broader public. Alumns and newcomers join in and contribute to shared knowledge and contacts.

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Heidelberg Schloss und Königsstuhl
Mathematics and Computer Science — Research

Mathematical Physics and Automorphic Forms

Mathematical Physics develops mathematical theories for the description of both elementary and complex physical phenomena, and ensures physical insight through mathematical proofs. The exchange concerns steadily more subfields of pure and applied mathematics.
The theory of Automorphic Forms investigates the incarnation of algebraic structures such as group actions through analytic objects in a far-reaching generalization of classical modular forms. Their unifying role, in particular in the Langlands correspondence, is based on ideas of duality, and has strong ties to Mathematical Physics.

Research in Mathematical Physics in Heidelberg takes place at a variety of interfaces between the two disciplines, ranging from the analysis of functional renormalization and statistical mechanics to applications of ideas from quantum field theory in topology and algebraic geometry. Recent work includes contributions to the -expansion of random tensor theories, renormalization in fermionic and bosonic lattice systems, the geometric description and algebraic properties of open/closed BPS invariants in string theory, and the (super-)geometry of quantum field space. There are close ties to the Institute for Theoretical Physics in the Department of Physics and Astronomy.

The fruitful interaction of mathematics and physics is at the very heart of the cluster of excellence STRUCTURES at Heidelberg University.

Recent work on automorphic forms in Heidelberg has focused on -functions of Siegel modular forms and automorphic representations, bounds and sign changes of their Fourier coefficients, endoscopy for four-dimensional Galois representations, and Drinfeld modular forms.

Historical Perspective


Heidelberg's reputation as an internationally perceived focal point in the field of automorphic forms is based on the long-standing work of Hans Maaß in the postwar period and was later further fueled by researchers such as Eberhard Freitag, Michael Rapoport, Winfried Kohnen, and Rainer Weissauer. Today, the name Maaß is associated first and foremost with the waveforms named after him, which he introduced to establish a link between the theory of modular forms and number theory. But even before Maaß, research in this field had already been carried out in Heidelberg, a prominent example being the investigations of Fuchs groups by Lazarus Fuchs towards the end of the 19th century, which were significant for the theory of modular forms.

Research Groups

If you are interested in the above research directions, we invite you to follow one or more of the intermediate (upper bachelor) course sequences in complex analysis, algebra, theoretical statistical physics, quantum field theory, and general relativity. The knowledge gained in these courses can then be deepened by participation in various seminars and topics courses. Please contact one of the following research group leaders for research opportunities in the framework of final theses in Mathematics and/or theoretical Physics:

Prof. Dr. Gebhard BöckleComputational arithmetic geometry

Mathematical Institute / IWR

Prof. Dr. Gebhard Böckle
Research Interests: Galois representations/deformations, Drinfeld modular forms/varieties
Prof. Dr. Razvan GurauQuantum field theory and random tensors

Institute for Theoretical Physics

Razvan Gurau
My work focuses in particular on random tensor models (higher dimensional generalizations of random matrix models) and tensor field theories. In particular, I discovered that such models support a new 1/N expansion and lead to a new large N limit, the melonic limit. Random tensor models provide a framework for the study of higher dimensional random geometries. Tensor field theories yield a new class of analytically tractable Conformal Field Theories relevant for the AdS/CFT correspondence and condensed matter systems.
Prof. Dr. Manfred SalmhoferMany-body physics

Institute for Theoretical Physics

Manfred Salmhofer
The activities center on many-body theory, quantum field theory and statistical mechanics. A main interest is the mathematical construction of correlated-fermion models by multi-scale methods, with applications in the theory of unconventional superconductivity and other symmetry-broken phases of matter.
Prof. Dr. Johannes WalcherGeometry and string theory

Mathematical Institute

Prof. Dr. Johannes Walcher
The activities derive from the interaction between geometry and high-energy physics that have arisen in string theory since the 1980's. Research builds on supersymmetric and topological field theories, and supergravity. A central topic is mirror symmetry in its various formulations, and the mathematical theory of BPS invariants.
AOR Dr. Hendrik KastenModular Forms, -Functions

Mathematical Institute

Dr. Hendrik Kasten
Last updated on Apr 14, 2023 at 6:48 AM