All reports by Author Abhibhav Garg:

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TR23-074
| 14th May 2023
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Abhibhav Garg, Rafael Mendes de Oliveira, Shir Peleg, Akash Sengupta#### Radical Sylvester-Gallai Theorem for Tuples of Quadratics

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TR22-037
| 10th March 2022
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Abhibhav Garg, Rafael Mendes de Oliveira, Akash Sengupta#### Robust Radical Sylvester-Gallai Theorem for Quadratics

Abhibhav Garg, Rafael Mendes de Oliveira, Shir Peleg, Akash Sengupta

We prove a higher codimensional radical Sylvester-Gallai type theorem for quadratic polynomials, simultaneously generalizing [Han65, Shp20]. Hansen's theorem is a high-dimensional version of the classical Sylvester-Gallai theorem in which the incidence condition is given by high-dimensional flats instead of lines. We generalize Hansen's theorem to the setting of quadratic forms ... more >>>

Abhibhav Garg, Rafael Mendes de Oliveira, Akash Sengupta

We prove a robust generalization of a Sylvester-Gallai type theorem for quadratic polynomials, generalizing the result in [S'20].

More precisely, given a parameter $0 < \delta \leq 1$ and a finite collection $\mathcal{F}$ of irreducible and pairwise independent polynomials of degree at most 2, we say that $\mathcal{F}$ is a ...
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