Hot Research on Social Media
Operational Research: Methods and Applications
Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts.
Optimization and Control
Harder-Narasimhan Filtrations of Persistence Modules
We introduce the skyscraper invariant, which amalgamates the HN types along central charges supported at single vertices, and generalise the rank invariant from multiparameter persistence modules to arbitrary quiver representations.
Representation Theory Algebraic Geometry Algebraic Topology 16G20, 55N30, 55N31
The fiber of persistent homology for trees
Consider the space of continuous functions on a geometric tree $X$ whose persistent homology gives rise to a finite generic barcode $D$.
Algebraic Topology
Classification of Self-Dual Vertex Operator Superalgebras of Central Charge at Most 24
We classify the self-dual (or holomorphic) vertex operator superalgebras of central charge 24, or in physics parlance the two-dimensional (possibly fermionic) conformal field theories with just one primary field.
Quantum Algebra High Energy Physics - Theory Representation Theory 17B69
The embedding theorem in Hurwitz-Brill-Noether Theory
More precisely, in classical Brill-Noether theory, the embedding theorem states that a general linear series of degree d and rank r on a general curve of genus g is an embedding if r is at least 3.
Algebraic Geometry 14H51
On the failure of the bootstrap for Chatterjee's rank correlation
While researchers commonly use the bootstrap for statistical inference, many of us have realized that the standard bootstrap, in general, does not work for Chatterjee's rank correlation.
Statistics Theory Econometrics Statistics Theory
The Subspace Flatness Conjecture and Faster Integer Programming
Kannan and Lov\'asz proved that $\mu(\Lambda, K) \leq n \cdot \mu_{KL}(\Lambda, K)$ and the Subspace Flatness Conjecture by Dadush (2012) claims a $O(\log n)$ factor suffices, which would match the lower bound from the work of Kannan and Lov\'asz.
Optimization and Control Computational Complexity Discrete Mathematics Data Structures and Algorithms Combinatorics 15A, 52A, 52C, 68Q, 68R, 68W, 90B, 90C F.2.2; G.1.6
Balancing Communication and Computation in Gradient Tracking Algorithms for Decentralized Optimization
In this paper, we present a framework that unifies gradient tracking methods and is endowed with flexibility with respect to the number of communication and computation steps.
Optimization and Control
Optimal Supersaturated Designs for Lasso Sign Recovery
Supersaturated designs, in which the number of factors exceeds the number of runs, are often constructed under a heuristic criterion that measures a design's proximity to an unattainable orthogonal design.
Statistics Theory Statistics Theory
The true story of the Quantum Ergodic Theorem
The story on the early days of the Quantum Ergodic Theorem.
History and Overview 2020: 35Q60, 01A65
