This paper unconditionally proves the Orthogonal Vectors and Monotone Orthogonal Vectors conjectures in concrete computational models, and provides stronger lower bounds for Boolean formulas and branc…

The polynomial-time low-degree conjecture, which predicts that low-degree indistinguishability, a uniform null distribution, permutation invariance, and independent resampling imply polynomial-time ha…

This paper improves the known bounds on the ratio between domination number and packing number in unit disk graphs and bridgeless claw-free cubic graphs.

The paper refutes Steurer's conjecture regarding the existence of large constant-separated sets within families of unit-norm vectors with low average correlation, using high-dimensional expanders to s…

This paper provides bounds on the difference between the annihilation number and independence number of a finite simple graph, and proves these bounds for various types of graphs.

The paper proves that the proximity gaps conjecture fails for a specific family of Reed-Solomon codes near their capacity rate, specifically at radii $O(1/ ext{log } n)$ below capacity.

This paper provides bounds on the neighborhood complexity of graphs with bounded treewidth and pathwidth, and constructs reaching these bounds.

This paper proves that a majority of filled-in Sudoku grids require a logarithmic fraction of cells to be filled by clues, and constructs grids requiring 18 and 80 clues for 9x9 and 16x16 Sudoku, resp…

This paper proves lower bounds for the size of multiplicative graph spanners in the $f$-degree fault tolerant model, matching previous conditional lower bounds and current upper bounds.

This paper settles the complexity of three sketching problems in graphs and distributions.

The paper proves a stochastic comparison for Gaussian maxima, resolving the Weak Simplex Conjecture and proving the Simplex Mean Width Conjecture.

The authors improve the bound on the chromatic number of t-perfect graphs from 199053 to 186 by refining the proof of Chudnovsky et al.

This paper provides a bound on the hat guessing number of a graph based on its order and maximum degree.

This paper disproves a conjecture about the longest-path lengths of MaxSTN and MinSTN algorithms for producing $st$-orientations of biconnected graphs.

This paper studies the maximum size of an independent set in the discrete simplex graph and provides new bounds using translated smaller graphs and finite rational linear systems.