Representations of Finite Groups and Related Structures

Robert Boltje (born February 14, 1960) is a mathematician whose research interests include finite groups, their representations, and  applications to number theory. He studied in Munich where he received  his diploma in 1985. He then moved to Augsburg where he obtained his  doctorate under the direction of Jürgen Ritter. The title of his Ph.D. thesis was "Canonical and explicit Brauer induction in the  character ring of a finite group and a generalization for Mackey  functors." He completed his habilitation in Augsburg in 1995, with a  thesis on "Mackey functors in representation theory and number  theory." He was a postdoctoral fellow from 1990 to 1992 and a  Heisenberg fellow from 1997 to 1998, supported by grants from the  Deutsche Forschungsgemeinschaft. In 1999 he moved to the University of California at Santa Cruz where he is now a full professor.

Robert Boltje became known first through his fundamental work on  induction theorems in representation theory. This circle of ideas was partially motivated by questions in number theory and continued  research of Artin and Brauer. Robert Boltje then realized that his  methods carry over to Mackey and biset functors on finite groups. Thus many of his papers are concerned with these functorial methods in  representation theory which also have applications in number theory.  Burnside rings and generalizations of these play a major role.

More recently, he has worked on open conjectures in representation  theory, formulated by Alperin, Broué, Dade and others. These  conjectures link blocks of representations of finite groups to blocks  of representations of local subgroups. With his coauthors, he  introduced p-permutation equivalences between blocks and studied their properties. This also led him to investigate fusion systems and Picard groups of blocks.

Robert Boltje was awarded a number of prizes, both for his research and his teaching. In Santa Cruz, he led several students to their Ph.D. His coauthors include mathematicians from Germany, Mexico, Turkey,  France, Spain, USA and the UK.