During August 19 - 23, 2013 conference

Differential Geometry and its Applications, Brno, Cech Republic

Organized by J.M. Landsberg

contact: jml@math.tamu.edu

Confirmed speakers:

A. Abdesselam (U. Virginia)

E. Briand (U. Sevilla)

P. Burgisser (U. Paderborn)

C. Ikenmeyer (TAMU)

S. Kumar (UNC Chapel Hill)*

J.M. Landsberg (TAMU)

*Kumar will also be a plenary speaker at the conference

Titles and abstracts:

Abdesselam: On the Foulkes-Howe conjecture and why it mattered to 19th century mathematicians

We will discuss the Foulkes-Howe conjecture and its straightforward "cabled" generalization

regarding the injectivity or surjectivity of a map from the p-th symmetric power of

a qr-th symmetric power into the analogous object with p and q exchanged.

We will explain this problem from the point of view of classical invariant and elimination theory,

in relation to the work of Hermite, Gordan, Hadamard and many others in their quest for a good

understanding of multidimensional resultants.

Briand: Recent progress on Kronecker coefficients.

I will present some recent results about Kronecker coefficients, in particular about the sequences of Kronecker coefficients indexed by three partitions with variable first part. These sequences are eventually constant and their limit (the "stable Kronecker coefficients") are interesting objects by themselves.

Besides I will examine closely the explicit formulas known for the Kronecker coefficients indexed by three partitions of lengths 2, 2 and 4, and what this example may tell us about the general case.

Ikenmeyer: Explicit Lower Bounds via Geometric Complexity TheoryKumar: Some geometric and representation theoretic aspects of the orbit closures of determinant and permanent

We prove the lower bound R(M_m) \geq 3/2 m^{^2}- 2 on the border rank of m

x m matrix multiplication by exhibiting explicit representation

theoretic (occurence) obstructions in the sense of the geometric

complexity theory (GCT) program. While this bound is weaker than the one

recently obtained by Landsberg and Ottaviani, these are the first

significant lower bounds obtained within the GCT program. Behind the

proof is the new combinatorial concept of obstruction designs, which

encode highest weight vectors in Sym^d\otimes^{^3}(C^n)^* and provide new

insights into Kronecker coefficients.

Landsberg: New open questions in GCT

Recent advances in the study of shallow circuits

implies that the standard conjectures in algebraic complexity

theory (e.g. VP\neq VNP) can be phrased in terms of

secant varieties of Chow varieties and other natural

G-varieties. I will explain the advances and the new problems.