Junior Professor at the Institut de Mathématiques de Toulouse
Toulouse, France
Joined November 2019
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New paper out today on "Algebraic metacomplexity and representation theory" together with M. van den Berg, @WeirdlyPranjal, C. Ikenmeyer and V. Lysikov.
arxiv.org/abs/2411.03444
on the computational overhead for restricting the search of lower bounds via representation theory.
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.
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:
arxiv.org/abs/2407.16767
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.
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
fulges.github.io/postdoc_cal…
Deadline is March 8, 2024.
Fulvio Gesmundo retweeted
Hiring a PhD student! vacatures.uva.nl/UvA/job/PhD…
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
arxiv.org/abs/2312.07982
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.
Fulvio Gesmundo retweeted
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!
🎉mis.mpg.de/institute/presse/…
''Quatroids and Rational Plane Cubics'' is our new preprint with Taylor Brysiewicz and Avi Steiner:
arxiv.org/abs/2309.07357
This is a very computationally heavy project, on a very classical problem: How many rational cubic curves pass through 8 points in the plane?
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.
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.
arxiv.org/abs/2308.10957
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.