We propose an analogue definition of No Independence Property (NIP) for abstract elementary classes (AECs) that coincides with NIP when the class is elementary. We construct a forking-like relation on AECs with NIP, and show that its negation leads to being able to encode subsets.

An NIP-like notion in abstract elementary classes

Tue, Apr. 4 2:30pm (Math 3…

Lie Theory

Aparna Upadhyay (University of Arizona)

X

The core of a finite dimensional kG-module M is obtained by deleting all the summands of M that are projective. Benson and Symonds defined an invariant for M, called the gamma invariant. This invariant is a result of studying the asymptotics of the core of tensor powers of M. In this talk, we will see some interesting properties of this invariant. We will explore the sequence of dimensions of the core of $M}^{\otimes n$, and see that it has algebraic Hilbert series when M is Omega-algebraic. When M is $\Omega}^{+$-algebraic then these dimension sequences are eventually linearly recursive. This partially answers a conjecture by Benson and Symonds.

The asymptotics of the decomposition of tensor powers of modules Sponsored by the Meyer Fund

Tue, Apr. 4 3:30pm (MATH 3…

Topology

Emily Montelius (CU Boulder) Segal's Gamma-Spaces and the Barratt-Priddy-Quillen Theorem