1 citations · 1 across the 8 of their papers we have counts for
9 papers
Lifting curved Kakeya sets to linear Kakeya sets
Arian Nadjimzadah
We prove that many curved Kakeya problems, originally motivated by Hörmander's oscillatory integral problem, lift to the classical Kakeya problem in higher dimensions. As a consequ…
Curved Kakeya problems and the projective geometry of paths
Shaoming Guo, Larry Guth, Arian Nadjimzadah +2
We introduce a general framework for curved Kakeya problems in , encompassing those arising from Hörmander-type oscillatory integrals. Every family of curves determin…
Bourgain's condition, sticky Kakeya, and new examples
Arian Nadjimzadah
We prove that in all dimensions at least 3 and for any Hörmander-type phase function satisfying Bourgain's condition, the sticky case of the corresponding curved Kakeya conjecture…
New curved Kakeya estimates
Arian Nadjimzadah
We prove that for an open class of translation-invariant Hörmander-type phase functions, the corresponding curved Kakeya sets in have Hausdorff dimension at least $(1…
A Study Guide for "A Restriction Estimate using Polynomial Partitioning"
John Green, Terry Harris, Kaiyi Huang +1
This manuscript is intended as an accompaniment to Guth's "A restriction estimate using polynomial partitioning". We begin by summarizing the core ideas of the proof, elaborating t…
Trees of Dot Products in Thin Subsets of
Arian Nadjimzadah
A. Iosevich and K. Taylor showed that compact subsets of with Hausdorff dimension greater than contain trees with gaps in an open interval. Under the same d…
Notions of Tensor Rank
Mandar Juvekar, Arian Nadjimzadah
Tensors, or multi-linear forms, are important objects in a variety of areas from analytics, to combinatorics, to computational complexity theory. Notions of tensor rank aim to quan…
Gaps, Ambiguity, and Establishing Complexity-Class Containments via Iterative Constant-Setting
Lane A. Hemaspaandra, Mandar Juvekar, Arian Nadjimzadah +1
Cai and Hemachandra used iterative constant-setting to prove that Few P (and thus that FewP P). In this paper, we note that there is a tensi…
On Salum's Algorithm for
Arian Nadjimzadah, David E. Narváez
This is a commentary on, and critique of, Latif Salum's paper titled "Tractability of One-in-three : ." Salum purports to give a polynomial…