Research

Geometry and topology

I study Riemannian manifolds, geometric structures and their invariants. My work includes positive sectional curvature, special holonomy, characteristic classes of foliations and diffeomorphism pseudogroups, and discrete affine geometry.

I constructed the 13-dimensional positively curved manifolds known as Bazaikin spaces. In joint work on foliations, we study Losik classes and their ability to distinguish geometric structures beyond classical invariants. Other recent work concerns affine invariants of piecewise linear curves.

Selected papers: Bazaikin spaces (1996) · Losik classes of pseudogroups (2025) · Discrete affine invariants (2025)

Transport and evolving materials

I develop mathematical models of heat and mass transfer and of changes in porous materials. My methods include analytical solutions of transport equations, phase-field descriptions, and geometric models of surface evolution and sintering.

Recent work gives analytical descriptions of transfer near reactive walls and a phase-field interpretation of mercury porosimetry hysteresis. In the latter, pore constrictions and connectivity-controlled trapping play distinct roles. A continuing question is how changes in pore geometry affect accessibility, storage and release.

Selected papers: Phase-field porosimetry (2026) · Finite heat/mass sink (2026) · Reactive wall segments (2026)

Computational topology and digital structures

I use connectivity, homology and persistence to describe complex structures represented by three-dimensional images. This work connects topological methods with questions about the geometry and evolution of pore space.

With collaborators, I have developed topological analyses of changes caused by chemical dissolution and methods for reducing digital images while tracking their topological information. These studies address a practical mathematical question: which features of a structure must a computational representation preserve?

Selected papers: Topology of pore-space evolution (2020) · Digital image reduction (2021)

Across disciplines

In my applied collaborations, mathematical models connect geometric structure with physical observables such as transferred heat or mass, retained fluid and accessible pore volume. This work involves researchers in mathematics, physics, chemistry and engineering. Computational topology provides one connection between the study of geometric structure and the analysis of real materials.