Paul Frank Baum

Najbardziej istotne osiągnięcia naukowe

• Representation theory of reductive p-adic groups: Proved that Bernstein components in the principal series are complex affine varieties (ABP conjecture), implying the local Langlands conjecture in this case.
• Index formula for non-elliptic operators: Established a topological index formula for a natural class of non-elliptic differential operators.
• K-theory for group C-algebras*: Co-formulated the Baum–Connes conjecture linking geometric and analytic K-theory, verified for many major classes of groups.
• K-homology: Proved the equivalence of analytic and topological K-homology, providing a framework extending index theory beyond elliptic operators.
• Riemann–Roch: Extended the Riemann–Roch theorem to singular varieties.
• Foliations: proved a formula equating locally defined numbers at foliation singularities to global invariants.
• Lie group topology: Extended Cartan’s theorem on the cohomology of homogeneous spaces to finite-field coefficients