Cryobiology is the study of life anddeath at low temperatures and provides a fascinating setting for applied mathematics. The interdisciplinary nature of cryobiology mirrors the diversity of applications ranging from animal ...

significance. On the other hand, it was recently shown that the Brunn-Minkowski inequality, specialized to convex sets, follows from a local stochastic dominance for naturally associated random polytopes. In addition, a number of other geometric inequalities...

The thesis is devoted to the study of various problems arising from Convex Geometry and Geometric Functional Analysis using tools of Fourier Analysis. In chapters two through four we consider the Busemann-Petty problem and ...

The purpose of this thesis is to find effective algorithms to numerically solve certain systems of differential equations that arise from standard Newtonian mechanics. Numerical models of elastica has already been well ...

The purpose of this thesis is to advance the study and application of the field of persistent homology through both categorical and quiver theoretic viewpoints. While persistent homology has its roots in these topics, there ...