PROJECT TYPE:

• Institutional Research Project IIP-UNIPU-010159 

PROJECT DURATION:

• Oct 1, 2025 – Sept 30, 2029 

PRINCIPAL INVESTIGATOR AND PROJECT TEAM MEMBERS: 

• Branka Antunović, Juraj Dobrila University of Pula
• Barbara Bošnjak, University of Zagrebu
• Tihana Galinac Grbac, Juraj Dobrila University of Pula
• Neven Grbac, Juraj Dobrila University of Pula, principal investigator
• Lovro Greganić, Juraj Dobrila University of Pula
• Harald Grobner, University of Vienna
• Marcela Hanzer, University of Zagreb
• Ana Kontrec, Research Institute for Mathematical Sciences, Kyoto
• Ivan Matić, Josip Juraj Strossmayer University of Osijek
• Antun Milas, University at Albany – State University of New York
• Alberto Minguez, University of Seville and University of Vienna
• Goran Muić, University of Zagreb
• David Renard, Ecole polytechnique, Paris
• Joachim Schwermer, University of Vienna
• Alexander Stadler, University of Vienna
• Marko Tadić, University of Zagreb 

PROJECT ABSTRACT: 

The Langlandsov program is one of the deepest and most ambitious research areas of contemporary mathematics that interconnects all traditional parts of mathematics (algebra, geometry, mathematical analysis and number theory). Automorphic forms and automorphic representations are cornerstones of the Langlands program. Main goal of the project is to explore the internal structure of spaces of automorphic forms on reductive groups in terms of representation theory, as well as the structure of representations of vertex and Lie algebras. The new findings will be applied to other project goals related to important problems in number theory (analytic properties of automorphic L-functions and Eisenstein series, special values of L-functions), geometry (automorphic cohomology, cohomology of arithmetic groups) and applications in physics and quantum computing (quantum modular forms). Geometric and topological methods used in the project have potential applications in computer science (topological data analysis, explainable artificial intelligence, topological approach to quantum computers, computer assisted mathematics), which are emerging technologies of near future, and it is of special importance for the local industry to catch the wave of these new trends through scientific research early enough in order to become locomotives of development at the international level. And last, but not least, the goal of the project is the creation of a strong research base in the field of mathematics and its applications, as well as dissemination and popularization of research in the local community and educational institutions. 

PROJECT GOALS:

The project goal consists of the following interconnected and intertwined objectives: 

• C1. Explore the internal structure of spaces of automorphic forms, representations of reductive groups over local and global fields, and representations of vertex algebras and Lie algebras 
• C2. Apply the new findings in arithmetic (analytic properties of Eisenstein series, automorphic L-functions), geometry (cohomology of arithmetic groups), physics (quantum modular forms) 
• C3. Explore application of the used methods in computer science (topological data analysis, geometry of artificial intelligence, quantum computers, computer assisted mathematics), including dissemination towards local community 
• C4. Creation of a strong research base and infrastructure in the field of mathematics at the Juraj Dobrila University of Pula with an international team, and dissemination and popularization of research in local community and educational institutions 

PROJECT INSTITUTION: Juraj Dobrila University of Pula