Fulvio Gesmundo

Junior Professor at the Institut de Mathématiques de Toulouse

[Fulvio Gesmundo @ful_ges]

@robinhouston @nechita_ion @GoogleDeepMind My take is that the sentence "first method to find an algorithm [...] with 48 multiplications" is a bit misleading but it is quite fair in the context of matrix multiplication complexity

[Fulvio Gesmundo @ful_ges]

@robinhouston @nechita_ion @GoogleDeepMind Multilinear algorithms for small MaMu scale up and can be performed on big matrices in blocks. So they affect the exponent
Strassen -> omega < log_2(7)
AlphaEvolve -> omega < log_4(48)
and they can in principle be implemented

The MSE one does not scale, at least not obviously

[Fulvio Gesmundo @ful_ges]

The proof is built on beautiful classical representation theory, which is useful and worth learning independently of this application to complexity theory.

[Fulvio Gesmundo @ful_ges]

New paper out today on "Algebraic metacomplexity and representation theory" together with M. van den Berg, @WeirdlyPranjal, C. Ikenmeyer and V. Lysikov.

https://t.co/J5lOquYGEg

on the computational overhead for restricting the search of lower bounds via representation theory.

[Fulvio Gesmundo @ful_ges]

It is common to use representation theory to enhance the search of useful metapolynomials. However, it was unclear how much more expensive the evaluation of metapolynomials with good rep-theoretic properties is compared to arbitrary ones. We prove that this gap is not so large.

[Fulvio Gesmundo @ful_ges]

We characterize the "unexpected preservers" for partition varieties, related to special versions of slice rank. These can be exploited to study equations of these varieties via representation theory. Several natural directions are left open for further investigation.

[Fulvio Gesmundo @ful_ges]

The linear preserver problems aims to determine the maximal subgroup of projective transformations mapping a variety to itself. In our new work, together with Daniel Han and Ben Lovitz, we study "Linear preservers of varieties of tensors".

Check it out:
https://t.co/cNdJi42XSs

[Fulvio Gesmundo @ful_ges]

We prove that the linear preserver is the "expected one" in many cases of secant varieties of Segre varieties, essentially in all nontrivial subspace varieties, and in many other cases. This can be used to characterize preservers in other settings.

[Fulvio Gesmundo @ful_ges]

The focus of the position is on Mathematical Aspects of Complexity Theory: relevant topics include, but are not limited to, tensor decomposition, algebraic complexity theory, quantum many-body physics.

[Fulvio Gesmundo @ful_ges]

We just opened a two years postdoc position in Algebraic Geometry at the Institut de Mathématiques de Toulouse @maths_toulouse .

Check out the call and apply at
https://t.co/SkEHKddde3

Deadline is March 8, 2024.

[Jeroen Zuiddam @jzuiddam]

Hiring a PhD student! https://t.co/09Ts8sYT2s

[Fulvio Gesmundo @ful_ges]

We propose to study these collineation varieties to distinguish tensors up to change of coordinates. For instance, in dimension 3, these varieties recognize tensors of minimal border rank and tensors of maximal border subrank.

[Fulvio Gesmundo @ful_ges]

Distinguishing tensors up to change of coordinates is a fundamental problem in many areas of mathematics.

We propose a "new" way to do this in our preprint "Collineation varieties of tensors" with Hanieh Kenenshlou

https://t.co/v5M8WB8AYj

[Fulvio Gesmundo @ful_ges]

A third order tensor can be identified with a matrix of linear forms. The k-th collineation variety of the tensor is parameterized by size k minors of this matrix.

This is a classical construction, appearing in intersection theory and in the study of certain Hilbert schemes.

[MPI for Mathematics in the Sciences @mpiMathSci]

The @ERC_Research has granted a €10 million Synergy Grant to the UNIVERSE+ project which aims to develop a new math. language to describe physical phenomena at all scales, from particles to the universe's structure. Congrats to the project team!

🎉https://t.co/rx4DJELrz0

[Fulvio Gesmundo @ful_ges]

We compute a stratification of the set of configuration into many many many (779777) strata, and for each stratum we compute the number of rational cubics, and a number of other invariants.

Have fun reading the paper and enjoy the pictures!

[Fulvio Gesmundo @ful_ges]

''Quatroids and Rational Plane Cubics'' is our new preprint with Taylor Brysiewicz and Avi Steiner:

https://t.co/2tR6FJW2eJ

This is a very computationally heavy project, on a very classical problem: How many rational cubic curves pass through 8 points in the plane?

[Fulvio Gesmundo @ful_ges]

If the points are 'generic' the answer is 12, which has been known for more than a century. But what about non-generic configurations of points? To study these, we introduce quatroids, a combinatorial object that generalize matroids.

[Fulvio Gesmundo @ful_ges]

We touch on topics in projective geometry, classical invariant theory and intersection theory. An interesting and fun project with a lot of open directions ready to be explored.

[Fulvio Gesmundo @ful_ges]

Do you know about eigenvalues of tensors? They generalize, of course!, eigenvalues of matrices.

Learn more in "Characteristic polynomials and eigenvalues of tensors" with Francesco Galuppi, Ettore Turatti and Lorenzo Venturello.

https://t.co/mGf0sker3M

[Fulvio Gesmundo @ful_ges]

We learn in linear algebra that infinitely many symmetric matrices share the same eigenvalues. We expect this not to be the case for tensors: we prove that, in the case of binary forms and ternary cubics, any fixed set of eigenvalues is shared by only finitely many tensors.