We introduce $F$-gauges over a prism, construct syntomic cycle classes, and prove the prismatic Poincaré duality for proper smooth schemes. \begin{align*} \mathrm{H ...
Poincare showed that this objection could be met if the nebula were initially highly heterogeneous, with all but gAtj of its mass in the central body. The matter left behind would not form ...
Nestled on a quiet street and centrally located handy to Tanilba Bay's primary amenities, this beautifully maintained and presented home offers a delightful blend of comfort and versatility. With ...
I study partial differential equations that arise in mathematical physics, particularly equations that model vibrating objects. More precisely, I study eigenvalue problems that seek to describe the ...
Recent progress in manipulating quantum states of light and matter brings quantum-enhanced measurements closer to prospective applications. The current challenge is to make quantum metrologic ...
Experts said Mochizuki’s proof is similar in importance to groundbreaking solutions to other protracted math problems, such as Fermat's Last Theorem, which was solved in 1995, and the Poincare ...