Algebra Seminar Speaker: David Treumann (Boston College) Title: Profinite tensor powers Abstract: I'll discuss the problem of defining a tensor product of profinitely many copies of a vector space V, and propose a definition $\bigotimes_X^{mcc} V$ in the special situation that (1) V is finite-dimensional over F_2, and (2) the profinite X indexing the tensor […]
Algebra Seminar Speaker: Linquan Ma (Purdue University) Title: Lech's inequality and stability of local rings Abstract: We explore Lech's inequality relating the colength and multiplicity of m-primary ideals in a Noetherian local ring (R,m). We introduce a natural invariant that measures the sharpness of Lech's inequality and show its connections with singularities of asymptotically semistable varieties […]
Algebra Seminar Speaker: Zhiwei Yun, MIT Title: Character sheaves on the loop Lie algebra and its global implications Abstract: Motivated by Lusztig's definition of character sheaves on a reductive Lie algebra, we propose a definition of character sheaves on the loop Lie algebra. The construction can be viewed as a p-adic analogue of the orbit […]