Abstract: This talk explores Gröbner bases as the nonlinear analog of Gaussian elimination and row echelon form in linear algebra. By comparing polynomial ideals to linear subspaces, we’ll see how Gröbner bases enable systematic solutions to systems of polynomial equations. Using intuitive examples and analogies, we demystify the core principles of Gröbner basis theory.

Abstract: The Adams spectral sequence of the sphere is a cornerstone of stable homotopy theory, yet explicit computations remain notoriously difficult due to prohibitive computational complexity. In this talk, we focus on the case of odd primes, which exhibits distinct structural features compared to the p=2 setting.