Jeffrey S. Cambria

Global Regularity for the Three-Dimensional Incompressible Navier–Stokes Equations on the Torus

The global regularity problem for the three-dimensional incompressible Navier–Stokes equations — one of the seven Millennium Prize Problems of the Clay Mathematics Institute — asks whether smooth initial data always evolve into smooth solutions for all time. We resolve the spatia...

The Modular Character χ

Every region of a quantum system carries a hidden mathematical mirror—the modular conjugation of Tomita–Takesaki theory. This paper studies the number obtained by composing two regions’ mirrors and taking a trace: the modular character χ. The main theorem is that, for separated r...