Abstract: Quantum anomalies can arise when regularized determinants and traces of infinite dimensional operators in quantum field theories lose their multiplicative and tracial property. I will explain the basic ideas and methods and if time allows, will go over the celebrated Polyakov conformal anomaly formula and how the anomaly cancellation dictates the critical dimension D=26 for bosonic string theory.

Abstract: The classical Adams spectral sequence can be computed via higher order operations in mod p cohomology. Baues and Jibladze carried out computations of the differential $d_2$ using the algebra of secondary operations. Baues and Blanc described an algebro-combinatorial structure which encodes enough information about $n^{th}$ order operations to compute the differential $d_n$. In joint work with Baues, we specialize that work to the case $n=3$ and describe a more concrete algebraic structure which suffices to compute the differential $d_3$.