most recent 30 from http://mathoverflow.net 2013-05-21T09:19:09Z http://mathoverflow.net/feeds/user/2311 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/20702/reference-request-moduli-spaces-of-bundles-over-singular-curves/20746#20746 Jack Evans 2010-04-08T15:36:27Z 2010-04-08T15:36:27Z

<p>Carlos Simpson has <a href="http://math.unice.fr/~carlos/" rel="nofollow">written</a> a lot on this. <a href="http://arxiv.org/abs/alg-geom/9504015" rel="nofollow">Nasatyr &amp; Steer</a>. <a href="http://www.math.jussieu.fr/~biquard/" rel="nofollow">Biquard</a> <a href="http://en.scientificcommons.org/918305" rel="nofollow">Konno</a> All on basic constructions. Verlinde, Thaddeus and others on structural considerations. Anything to do with modular or automorphic forms is also related. There is a lot, can you be more specific?</p>

http://mathoverflow.net/questions/20355/book-for-probability/20514#20514 Jack Evans 2010-04-06T15:35:12Z 2010-04-06T15:35:12Z

<p>HPS is much cheaper from amazon.co.uk</p>

http://mathoverflow.net/questions/9006/representations-of-surface-groups-via-holomorphic-connections/9030#9030 Jack Evans 2009-12-15T19:21:14Z 2009-12-15T19:21:14Z

<p>Have you compared this to Hitchin's 1987 paper "The Self Duality Equations on a Riemann Surface"? It's like the $SU(2)$ version of your $SL(2,\mathbb{R})$ one.</p>

http://mathoverflow.net/questions/6233/order-statistics-for-components-of-a-random-unit-vector/7801#7801 Jack Evans 2009-12-04T19:12:55Z 2009-12-04T19:12:55Z

<p>The distribution should be obtainable by integrating over the section of the simplex segment of the surface of the hypersphere bounded by the points (1,0,0,0,...), (1,1,0,0,0...)/sqrt(2), (1,1,1,0,0...)/sqrt(3) etc. along the ith axis.</p> <p>All the distributions (n,m) have support contained within the unit interval, are piecewise smooth and share the same set of non-smooth points at the reciprocals of the square roots of the natural numbers. </p>

http://mathoverflow.net/questions/20702/reference-request-moduli-spaces-of-bundles-over-singular-curves/20746#20746 Jack Evans 2010-04-08T17:39:50Z 2010-04-08T17:39:50Z

The modular curve is a well studied singular curve. Most likely you are looking at a bunch of curves that either have the same kind of singularities as the modular curve or which are smooth but glued together. Another example is to consider the spectral curves in the Hitchin moduli space construction and look at what happens to the Prym variety or bundles over an elliptic fibration and consider what happens over singular fibres.

http://mathoverflow.net/questions/20702/reference-request-moduli-spaces-of-bundles-over-singular-curves/20746#20746 Jack Evans 2010-04-08T17:22:23Z 2010-04-08T17:22:23Z

The best understood singularities of curves look like intersections of curves or punctures. The punctures can in the best cases be smoothly completed with a point. It's often convenient to put the point back in and use it as a yardstick for controlling the behaviour of the bundle at the incompleteness which is necessary to form a sensible space. Much of the discussion is therefore about gluing data, either for the extra point or the two points of self intersection. So although much of the analysis is carried out over a smooth curve it is aimed at solving problems over controlled singularities.

http://mathoverflow.net/questions/9006/representations-of-surface-groups-via-holomorphic-connections/9030#9030 Jack Evans 2009-12-17T10:43:40Z 2009-12-17T10:43:40Z

Hitchin fixes a curve or equivalently representation of $\Gamma$ in $PSL(2,\mathbb{R})$ and uses it to identify the cotangent bundle of the space of $SU(2)$ representations with the space of $SL(2,\mathbb{C})$ representations of $\Gamma$. Joel's construction fixes a local system or equivalently a representation of $Gamma$ in $SU(2)$ and uses it to map the cotangent bundle of the space of $PSL(2,\mathbb{R})$ representations to the space of $SL(2,\mathbb{C}) representations. This is a clearer statement of what I was guessing at yesterday and explains the coincidence of dimensions.