Polyhedral Combinatorics in Representation Theory and Algebraic Geometry View Homepage


Ontology type: schema:MonetaryGrant     


Grant Info

YEARS

1999-2002

FUNDING AMOUNT

78000 USD

ABSTRACT

Polyhedral Combinatorics in Representation Theory and Algebraic Geometry The investigator studies the following research topics: tropical calculus approach to parametrizations of canonical bases for quantum groups and their representations; geometry of totally positive varieties and double Bruhat cells; generalized determinantal calculus with applications to canonical bases for semisimple groups, Kac-Moody groups and their quantizations; generalized Schubert cells in multiple flag varieties. The project ties together several mathematical disciplines: algebraic geometry, representation theory, mathematical physics, and polyhedral combinatorics. The main unifying ingredient is tropical calculus which takes its origin in applied mathematics (control theory and combinatorial optimization). This demonstrates the significance of viewing mathematics as a unique subject, and that of bringing together traditionally separated ideas and concepts. More... »

URL

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