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

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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

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Consider the space of continuous functions on a geometric tree $X$ whose persistent homology gives rise to a finite generic barcode $D$.

Algebraic Topology

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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

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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

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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

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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

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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

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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

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The story on the early days of the Quantum Ergodic Theorem.

History and Overview 2020: 35Q60, 01A65

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