Observation of incompressibility atν=4/11andν=5/13

Incompressibility of Products

We show that the conjectural criterion of p-incompressibility for products of projective homogeneous varieties in terms of the factors, previously known in a few special cases only, holds in general. We identify the properties of projective homogeneous varieties actually needed for the proof to go through. For instance, generically split (nonhomogeneous) varieties also satisfy these properties....

Incompressibility of Orthogonal Grassmannians

We prove the following conjecture due to Bryant Mathews (2008). Let Q be the orthogonal grassmannian of totally isotropic i-planes of a non-degenerate quadratic form q over an arbitrary field (where i is an integer satisfying 1 ≤ i ≤ (dim q)/2). If the degree of each closed point on Q is divisible by 2 and the Witt index of q over the function field of Q is equal to i, then the variety Q is 2-i...

Modeling durational incompressibility

We show how incompressibility, a well-described property of some prosodic timing effects, can be accounted for in an optimization-based model of speech timing. Preliminary results of a corpus study are presented, replicating and generalizing previous findings on incompressibility as a function of increasing speaking rate. We then introduce the architecture of our model and present results of si...

Recurrence and Incompressibility

Incompressibility of Generic Orthogonal Grassmannians

Given a non-degenerate quadratic form over a field such that its maximal orthogonal grassmannian is 2-incompressible (a condition satisfied for generic quadratic forms of arbitrary dimension), we apply the theory of upper motives to show that all other orthogonal grassmannians of this quadratic form are 2-incompressible. This computes the canonical 2-dimension of any projective homogeneous vari...