We’ll do it live!

GIT down with yo bad self!

Geometric Invariant Theory is where the party’s at!

Here is an introduction from René Birkner in Germany.  And then, once again, Nick Proudfoot’s got the hookup, providing us with a note on Geometric Invariant Theory and projective toric varieties.


orbifolds & music theory

this is pretty cool


Tymoczko models musical chords consisting of n notes, not necessarily distinct, as points in the orbifold Tn / Sn – the space of n unordered points (not necessarily distinct) in the circle, realized as the quotient of the n-torus Tn(the space of n ordered points on the circle) by the symmetric group Sn (corresponding from moving from an ordered set to an unordered set).

For dyads (two notes), this yields the closed Möbius strip; for triads (three notes), this yields an orbifold that can be described as a triangular prism with the top and bottom triangular faces identified with a 120° twist (a ⅓ twist) – equivalently, as a solid torus in 3 dimensions with a cross-section an equilateral triangle and such a twist.

The sculpture Topological III, by American artist and physicist Robert R. Wilson, at the entrance to the Harvard Science Center building, Harvard University, Cambridge, Massachusetts.

Algebraic Geometry Northeastern Series: Amherst 2010

This looks pretty great, I want to apply.  Even if I can’t get funding, there is air fare to boston for only $164!

There are some pretty exciting people there; maybe even a chance to hunt down George Shapiro.



i feel like i should be able to understand this after knowing what I know about toric geometry.  understanding this paper is a good goal to work towards! also Dave Anderson seems like an interesting fellow.

Graduate Student Topology Conference

Looks fun, maybe I will attend!

There will be two keynote lectures by:

Douglas Ravenel (University of Rochester)
Alan Reid (University of Texas, Austin)

New this year, there will be three open problem sessions led by:

Moon Duchin (University of Michigan, Ann Arbor) - Geometric Group Theory
Tom Fiore (University of Michigan, Dearborn) - Homotopy Theory
Benjamin Schmidt (Michigan State University) - Differential Geometry

Most importantly, there will be 24 short talks given by graduate students. Talks may be original or expository and can be given by graduate students of any level. We encourage you to apply!


What a week! They feel so different, these 2010s! So fresh, and new!



I am going to resume posting to this blog!

This brings up many issues. I am not an expert, but I think we need a symbolic standard to make computer manipulations easier to document and verify. And with all due respect to the free market, perhaps we should not be dependent on commercial software here. An open-source project could, perhaps, find better answers to the obvious problems such as availability, bugs, backward compatibility, platform independence, standard libraries, etc. One can learn from the success of TEX and more specialized software like Macaulay2. I do hope that funding agencies are looking into this.
— 2006 Fields Medalist Andrei Okounkov mentions Macaulay 2 in an interview.  I found this quote on the Macaulay 2 page. “Macaulay 2 is a software system devoted to supporting research in algebraic geometry and commutative algebra”