Departamento de Matemática
Universidade de Brasília - UnB

Automorphic Forms and Number Theory

This group at the UnB consists of:

• Hemar Godinho
  
• Nigel Pitt
  
• Salahoddin Shokranian
  
• Rui Seimetz
  
• Marcus Soares
  

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Number theory, as Gauss said, is the queen of mathematics. Automorphic forms are a modern part with old roots in which one meets geometry, analysis, algebra and number theory in the study of groups, their representations and their harmonic analysis. There are presently four members of our group, and we hope to grow and solidify. We are neither the first nor the only people working in beautiful Brazil in this direction, but we are presently the largest such group. Our interaction occurs mostly through our weekly seminar, which attracts the interest of students, where we discuss both our own work and recent advances in the field. We hope and expect to have more students and some visitors, thanks to some recent grants offered by the state and the government of Brazil.

Research Topics:

• Classical number theory such as Artin's Conjecture for diagonal forms and Additive Number Theory.
• The Selberg trace formula and its applications in the Fourier coefficient of modular forms for SL(2), analytic number theory along the line developed in the recent years through the works and conjectures of Selberg.
• The trace formulas in its full generality, as developed by Selberg, and Arthur based on the visionary work of Langlands and his Conjectures, the topological trace formula based on the works of Arthur, Goresky-MacPherson which leads to the geometric theory of automorphic forms, symmetric spaces, and zeta functions of cones and their applications.
• Representation theory and automorphic forms along the lines developed by Langlands and his school, particularly the study of Heisenberg groups, Weil representation and Whittaker models for the unitary groups.

All those interested in our M.Sc. and/or Ph.D. program, or in a position in the department, are invited to look through our homepages. There are grants available for both programs.

Links of General Interest: