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Award ID contains: 1855464

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  1. ; ; (, Journal of Graph Theory)
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  2. ; ; (, Journal of Algebra)
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  3. ; ; ; ; (, SIAM Journal on Discrete Mathematics)
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  4. ; ; (, Journal of Combinatorial Theory, Series B)
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  5. ; ; (, Combinatorics, Probability and Computing)
    Abstract We show that the diameter of a uniformly drawn spanning tree of a simple connected graph on n vertices with minimal degree linear in n is typically of order $$\sqrt{n}$$ . A byproduct of our proof, which is of independent interest, is that on such graphs the Cheeger constant and the spectral gap are comparable. 
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  6. ; ; ; ; (, Discrete & Computational Geometry)
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  7. ; ; ; ; (, Journal of the ACM)
    Let H be a binary-labeled concept class. We prove that H can be PAC learned by an (approximate) differentially private algorithm if and only if it has a finite Littlestone dimension. This implies a qualitative equivalence between online learnability and private PAC learnability. 
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  8. ; ; (, Advances in Applied Mathematics)
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  9. ; (, International Mathematics Research Notices)
    Abstract We establish lower bounds on the rank of matrices in which all but the diagonal entries lie in a multiplicative group of small rank. Applying these bounds we show that the distance sets of finite pointsets in $$\mathbb {R}^d$$ generate high-rank multiplicative groups and that multiplicative groups of small rank cannot contain large sumsets. 
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  10. ; (, Discrete Mathematics)
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