Algebraic geometry ... formulation of idele class groups with modulus have integrated techniques from higher-dimensional class field theory, expanding the scope of Bloch’s formula and thus ...

The study of algebraic structures and differential geometry has evolved into a ... surfaces, and their higher-dimensional analogues through calculus. Lie Algebroid: A vector bundle generalising ...

What began with a focus on weather forecasting has evolved toward addressing errors in scientific modeling. In the collaborative environment of the Penn State Institute for Computational and Data ...

Check details in the table below. Quantitative Skills: This section tests mathematical aptitude across Arithmetic, Algebra, Geometry, Modern Math, and Data Interpretation. Key topics include ...