My research is focused on advancing our comprehension of analysis and topology within infinite-dimensional spaces, and exploring how this knowledge manifests across diverse mathematical disciplines. These include vector bundle theory, partial differential equations (PDEs), and quantum field theory. 

Although my study is split into two seemingly distinct fields, they share significant intersections that enrich the overall research.

Nonlinear Functional Analysis: 

• Topological Degree Theory 

• Bifurcation Theory on Banach spaces

• Nonlinear Spectral Theory and Applications to topological K-Theory

• Nonlinear Elliptic & Parabolic Partial Differential Equations

Real and Harmonic Analysis:

• Measures on Infinite Dimensional Spaces

• Projective Limits of Probability Measures

• Wiener Measure on Riemannian Manifolds

• Path Integrals and Constructive Quantum Field Theory