I am interested in complex analytic spaces, perverse sheaves, and the microlocal theory of sheaves. The main focus of my work has been the investigation of singularities of (germs of) analytic spaces via the perverse sheaves of nearby and vanishing cycles, and the general machinery of the derived category of (bounded, constructible complexes of) sheaves. Nowadays I’m spending most of my time exploring the new, wild world of irregular perverse sheaves on complex manifolds, and their interactions with subnanalytic geometry and mathematical physics.
Overall, I’ve got a real soft spot for the different manners in which abstract category theory manifests in concrete geometric problems. In particular, using (various derived categories of) sheaves to study the topology of singular subsets of (real or complex analytic) manifolds.
[6 (preprint, submitted for publication)] Hepler, B. and Hohl, A. Moderate Growth and Rapid Decay Nearby Cycles via Enhanced Ind-Sheaves. .pdf arXiv
[5 (preprint, submitted for publication)] Hepler, B. The Weight Filtration on the constant sheaf on a Parameterized Space. .pdf arXiv
 Hepler, B., Deformation Formulas for Parametrizable Hypersurfaces. (accepted for publication, Annales de l’institut Fourier) .pdf arXiv
 Hepler, B. Rational Homology Manifolds and Hypersurface Normalizations, in Proc. Amer. Math. Soc. 147 (2019), 1605-1613 .pdf arXiv
 Hepler, B. and Massey, D. Perverse Results on Milnor Fibers inside Parameterized Hypersurfaces, in Publ. RIMS Kyoto Univ. 52 (2016), pp. 413-433. .pdf arXiv journal
 Hepler, B. and Massey, D. Some Special Cases of Bobadilla’s Conjecture, in Top. and Appl. 217 (2017), pp. 56-69. .pdf arXiv journal
Hepler, B. Hypersurface Normalizations and Numerical Invariants. .pdf
Notes on the Intermediate Extension of Perverse Sheaves (with examples) pdf