Victor Reis

@vetohaze

Senior researcher @MSFTResearch. Previously postdoc @the_IAS, PhD @uwcse

Bellevue, WA

victoreis.github.io

Joined July 2020

142 Following

714 Followers

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Victor Reis
@vetohaze
Oct 22
Can a strongly log-concave probability distribution f be uniform modulo a lattice Λ? The answer is yes, as long as every nonzero sublattice Γ ⊆ Λ* has det Γ ≥ 1. Uniform modulo Λ means that for any x ∈ ℝⁿ, the sum Σ_{λ ∈ Λ} f(x+λ) is the same (equal to 1/det Λ). [1/3]
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Victor Reis
@vetohaze
Oct 6
The Kannan-Lovász-Simonovits conjecture is finally solved. Congratulations to @realZhaoSong and to my MSR office mate Xinzhi Zhang on the huge breakthrough!
arxiv.org
An $O(1)$ Bound for the KLS Constant
The Kannan--Lovász--Simonovits (KLS) conjecture asks whether every isotropic log-concave probability measure on $\mathbb R^n$ has a Cheeger constant bounded below by a universal positive...
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Victor Reis
@vetohaze
Sep 29
In 1985, Spencer showed that given a₁,…,aₙ ∈ {−1,1}ⁿ, there exist signs x ∈ {−1,1}ⁿ with |⟨aᵢ, x⟩| ≤ 6√n for all i. We improve this to 3√n and construct a lower bound so that |⟨aᵢ, x⟩| > 1.0000002√n for all choices of signs. [1/3]
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Victor Reis
@vetohaze
Aug 2
Morell and Skutella conjectured that for any flow x in a single-source DAG, there exists an unsplittable flow y with |x - y| ≤ max demand. The conjecture was proved for planar DAGs [TVZ23], while Dinitz, Garg and Goemans showed a one-sided bound in 1999. I believed it. R.I.P.
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Victor Reis
@vetohaze
Jul 24
Update: we now know there exist ℓ₁ sparsifiers of sparsity O(n/ε²)! Our new argument unveils a connection between sparsification and Bonami’s 1970 hypercontractivity theorem, and also yields spectral sparsifiers. Who would have guessed? arxiv.org/abs/2606.28147
Victor Reis
@vetohaze
Jun 30
In 1990, Michel Talagrand showed that given a₁,…,aₘ ∈ ℝⁿ, there are weights w₁,…,wₘ ≥ 0, only O(n log n) of them nonzero, such that ∑ᵢ wᵢ|⟨aᵢ,x⟩| ≈ ∑ᵢ |⟨aᵢ,x⟩| within 1% for all x ∈ ℝⁿ. 36 years later, that last log is gone: O(n) nonzeros suffice! [1/5]
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Victor Reis

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