3
votes
1answer
193 views
+50

Lie algebra of invariant polynomials or invariant smooth functions

Is there a symplectic structure on $M_{2n}(\mathbb{R})$, not necessarily with constant coefficients, such that the space of smooth invariant functions, those smooth functions $f:M_{2n}(\mathbb{...
32
votes
0answers
843 views
+50

History: What was the Lemma? (Grothendieck Harvard Lectures; Mumford)

In an article about the life of Grothendieck, available here: http://www.ams.org/notices/200409/fea-grothendieck-part1.pdf Allyn Jackson writes about how Mumford was profoundly impressed: Mumford ...
3
votes
1answer
210 views
+50

Intuition behind the definition of the Siegel-Eichler transformation

Recently I am reading Wall's paper "On the Orthogonal Groups of Unimodular Quadratic Forms II". In this paper, I encountered with the map $E^1_\omega$, which now I am interested in. Let $X$ be an ...
4
votes
1answer
162 views
+150

Seeking very regular $\mathbb Q$-acyclic complexes

This question was raised from a project with Nati Linial and Yuval Peled We are seeking a $3$-dimensional simplicial complex $K$ on $12$ vertices with the following properties a) $K$ has a complete $...
4
votes
0answers
109 views
+50

Hierarchical (Recursive) Random Walk Model

Consider the following hierarchical (recursive) random walk model, which is also known as the hierarchical hidden Markov model in computer science. For the first level $\ell=1$, let $\{X_t^{(\ell)}...