Variant A — Fraunces only (single family, opsz axis)
Display: Fraunces opsz=144, SOFT=80, wght=400
Body: Fraunces opsz=14, SOFT=30, wght=400
Exploring mathematics, computational science, and engineering.
I write about mathematics, scientific computing, finance and pretty much anything quantitative—exploring ideas at the intersection of theory and practice. Outside of that, I enjoy diving into philosophical and theological texts and thinking about the big questions of human life.
The standard convergence proof assumes the initial guess lies within a neighborhood where the Jacobian remains nonsingular. This essay examines what happens when that assumption breaks down — and why the Kantorovich theorem gives us tighter guarantees than most undergraduate texts let on.
Föllmer's pathwise approach to stochastic integration shows that Itô's formula is, in a precise sense, a deterministic statement about quadratic variation rather than a probabilistic one. The implications for finance are subtle but real.
Variant B — Fraunces display + Source Serif 4 body (matched pair)
Display: Fraunces opsz=144, SOFT=80, wght=400
Body: Source Serif 4 opsz=14, wght=400
Exploring mathematics, computational science, and engineering.
I write about mathematics, scientific computing, finance and pretty much anything quantitative—exploring ideas at the intersection of theory and practice. Outside of that, I enjoy diving into philosophical and theological texts and thinking about the big questions of human life.
The standard convergence proof assumes the initial guess lies within a neighborhood where the Jacobian remains nonsingular. This essay examines what happens when that assumption breaks down — and why the Kantorovich theorem gives us tighter guarantees than most undergraduate texts let on.
Föllmer's pathwise approach to stochastic integration shows that Itô's formula is, in a precise sense, a deterministic statement about quadratic variation rather than a probabilistic one. The implications for finance are subtle but real.