@article{22303, abstract = {We present the discovery of AT 2024wpp (‘Whippet’), a fast and luminous 18cow-like transient. At a redshift of z = 0 . 0868 , revealed by Keck Cosmic Web Imager spectroscopy of its faint star-forming host, it is the fourth-nearest example of its class to date. Rapid identification of the source in the Zwicky Transient Facility data stream permitted ultraviolet-through- optical observations to be obtained prior to peak, allowing the first determination of the peak bolometric luminosity ( 2 ×1045 erg s−1 ), maximum photospheric radius ( 1015 cm), and total radiated energy ( 1051 erg) of an 18cow-like object. We present results from a comprehensive multiwavelength observing campaign, including a far-ultraviolet spectrum from the Cosmic Origins Spectrograph on the Hubble Space Telescope and deep imaging extending > 100 d post-explosion from the Very Large Telescope, Hubble Space Telescope , Very Large Array, and Atacama Large Millimetre Array. We interpret the observations under a model in which a rapidly accreting central engine blows a fast ( ∼0.2 c ) wind into the surrounding medium and irradiates it with X-rays. The high Doppler velocities and intense ionization within this wind prevent identifiable spectroscopic features from appearing in the ejecta or in the surrounding circumstellar material. Weak H and He signatures do emerge in the spectra after 35 d in the form of double-peaked narrow lines. Each peak is individually narrow (full width δv ∼3000 km s−1 ) but the two components are separated by v ∼6600 km s−1 , indicating stable structures of denser material, possibly representing streams of tidal ejecta or an ablated companion star.}, author = {Perley, Daniel A and Ho, Anna Y Q and McGrath, Zoë and Camilo, Michael and Sevilla, Cassie and Chen, Ping and Schroeder, Genevieve and Govreen-Segal, Taya and Bochenek, Aleksandra and Qin, Yu-Jing and Gillanders, James H and Amend, Benjamin and Anderson, Joseph P and Andreoni, Igor and Aryan, Amar and Bellm, Eric C and Bloom, Joshua S and de Boer, Thomas and Carney, Jonathan and Caiazzo, Ilaria and Chambers, Ken C and Charalampopoulos, Panos and Chen, Ting-Wan and Chen, Tracy X and Coughlin, Eric R and Coughlin, Michael and Dennefeld, Michel and Dimitriadis, Georgios and Fremling, Christoffer and Frostig, Danielle and Gal-Yam, Avishay and Galbany, Lluís and Gangopadhyay, Anjashay and Ghendrih, Melzie and Graham, Matthew J and Gromadzki, Mariusz and Groom, Steven L and Gutiérrez, Claudia P and Hinds, K -Ryan and Huber, Mark E and Inserra, Cosimo and Kaiser, Benjamin C and Kasliwal, Mansi M and Koivisto, Niilo E and Lin, Chien-Cheng and Liu, Chang and Lowe, Thomas B and Magnier, Eugene and Mahabal, Ashish A and Milligan, Andrew and Minguez, Paloma and Mo, Geoffrey and Müller-Bravo, Tomás E and Nicholl, Matt and Pessi, Priscila J and Pignata, Giuliano and Purdum, Josiah and Rehemtulla, Nabeel and Rich, R Michael and Sahu, Anwesha and Singh, Avinash and Smartt, Stephen J and Smith, Ian A and Sollerman, Jesper and Srinivasaragavan, Gokul and Srivastav, Shubham and Stein, Robert D and Schulze, Steve and Tweddle, Jack W and Wainscoat, Richard and Wise, Jacob L and Yan, Lin and Young, David R}, issn = {1365-2966}, journal = {Monthly Notices of the Royal Astronomical Society}, keywords = {stars: black holes, supernovae: individual: AT2024wpp, radio continuum: transients}, number = {1}, publisher = {Oxford University Press}, title = {{AT 2024wpp: An extremely luminous fast ultraviolet transient powered by accretion onto a black hole}}, doi = {10.1093/mnras/stag678}, volume = {549}, year = {2026}, } @article{20585, abstract = {Motivated by applications in medical sciences, we study finite chromatic sets in Euclidean space from a topological perspective. Based on the persistent homology for images, kernels and cokernels, we design provably stable homological quantifiers that describe the geometric micro- and macro-structure of how the color classes mingle. These can be efficiently computed using chromatic variants of Delaunay and alpha complexes, and code that does these computations is provided.}, author = {Cultrera di Montesano, Sebastiano and Draganov, Ondrej and Edelsbrunner, Herbert and Saghafian, Morteza}, issn = {2639-8001}, journal = {Foundations of Data Science}, keywords = {Topological data analysis, Delaunay mosaic, alpha complex, chromatic sets, persistent homology, kernel/image/cokernel persistent homology, radius function, discrete Morse theory, exact sequences}, pages = {30--62}, publisher = {AIMS}, title = {{Chromatic alpha complexes}}, doi = {10.3934/fods.2025003}, volume = {8}, year = {2026}, } @article{18706, abstract = {We prove discrete-to-continuum convergence for dynamical optimal transport on Zd -periodic graphs with cost functional having linear growth at infinity. This result provides an answer to a problem left open by Gladbach, Kopfer, Maas, and Portinale (Calc Var Partial Differential Equations 62(5), 2023), where the convergence behaviour of discrete boundary-value dynamical transport problems is proved under the stronger assumption of superlinear growth. Our result extends the known literature to some important classes of examples, such as scaling limits of 1 -Wasserstein transport problems. Similarly to what happens in the quadratic case, the geometry of the graph plays a crucial role in the structure of the limit cost function, as we discuss in the final part of this work, which includes some visual representations.}, author = {Portinale, Lorenzo and Quattrocchi, Filippo}, issn = {1469-4425}, journal = {European Journal of Applied Mathematics}, keywords = {optimal transport, discrete-to-continuum, homogenisation, linear growth, gamma-convergence}, number = {3}, pages = {614--642}, publisher = {Cambridge University Press}, title = {{Discrete-to-continuum limits of optimal transport with linear growth on periodic graphs}}, doi = {10.1017/s0956792524000810}, volume = {37}, year = {2026}, } @article{10045, abstract = {Given a fixed finite metric space (V,μ), the {\em minimum 0-extension problem}, denoted as 0-Ext[μ], is equivalent to the following optimization problem: minimize function of the form minx∈Vn∑ifi(xi)+∑ijcijμ(xi,xj) where cij,cvi are given nonnegative costs and fi:V→R are functions given by fi(xi)=∑v∈Vcviμ(xi,v). The computational complexity of 0-Ext[μ] has been recently established by Karzanov and by Hirai: if metric μ is {\em orientable modular} then 0-Ext[μ] can be solved in polynomial time, otherwise 0-Ext[μ] is NP-hard. To prove the tractability part, Hirai developed a theory of discrete convex functions on orientable modular graphs generalizing several known classes of functions in discrete convex analysis, such as L♮-convex functions. We consider a more general version of the problem in which unary functions fi(xi) can additionally have terms of the form cuv;iμ(xi,{u,v}) for {u,v}∈F, where set F⊆(V2) is fixed. We extend the complexity classification above by providing an explicit condition on (μ,F) for the problem to be tractable. In order to prove the tractability part, we generalize Hirai's theory and define a larger class of discrete convex functions. It covers, in particular, another well-known class of functions, namely submodular functions on an integer lattice. Finally, we improve the complexity of Hirai's algorithm for solving 0-Ext on orientable modular graphs. }, author = {Dvorak, Martin and Kolmogorov, Vladimir}, issn = {1436-4646}, journal = {Mathematical Programming}, keywords = {minimum 0-extension problem, metric labeling problem, discrete metric spaces, metric extensions, computational complexity, valued constraint satisfaction problems, discrete convex analysis, L-convex functions}, pages = {279--322}, publisher = {Springer Nature}, title = {{Generalized minimum 0-extension problem and discrete convexity}}, doi = {10.1007/s10107-024-02064-5}, volume = {209}, year = {2025}, } @phdthesis{18979, abstract = {Topological Data Analysis (TDA) is a discipline utilizing the mathematical field of topology to study data, most prominently collections of point sets. This thesis summarizes three projects related to computations in TDA. The first one establishes a variant of TDA for chromatic point sets, where each point is given a color. For example, we are given positions of cells within a tumor microenvironment, and color the cancerous cells red, and the immune cells blue. The aim is then to give a quantitative description of how the two or more sets of points spatially interact. Building on image, kernel and cokernel variants of persistent homology, we suggest six-packs of persistent diagrams as such a descriptor. We describe a construction of a chromatic alpha complex, which enables efficient computation of several variants of the six-packs. We give topological descriptions of natural subcomplexes of the chromatic alpha complex, and show that the radii of the simplices form a discrete Morse function. Finally, we provide an implementation of the presented chromatic TDA pipeline. The second part aims to translate a powerful tool of sheaf theory to elementary terms using labeled matrices. The goal is to enable their use in computational settings. We show that derived categories of sheaves over finite posets have, up to isomorphism, unique objects---minimal injective resolutions---and give a concrete algorithm to compute them. We further describe simple algorithms to compute derived pushforwards and pullbacks for monotonic maps, and their proper variants for inclusions, and demonstrate their tractability by providing an implementation. Finally, we suggest a discrete definition of microsupport and show desirable properties inspired by discrete Morse theory. In the last part, we present a collection of observations about collapses. We give a characterization of collapsibility in terms of unitriangular submatrices of the boundary matrix, a cotree-tree decomposition, and the optimal solution to a variant of the Procrustes problem. We establish relation between dual collapses and relative Morse theory and pose several open questions. Finally, focusing on complexes embedded in the three-dimensional Euclidean space, we describe a relation between the collapsibility and the triviality of a polygonal knot.}, author = {Draganov, Ondrej}, issn = {2663-337X}, keywords = {topological data analysis, chromatic point set, alpha complex, persistent homology, six pack, sheaf, microlocal discrete Morse, injective resolution, collapse, knot, discrete Morse theory}, pages = {140}, publisher = {Institute of Science and Technology Austria}, title = {{Structures and computations in topological data analysis}}, doi = {10.15479/at:ista:18979}, year = {2025}, } @article{12311, abstract = {In this note, we prove a formula for the cancellation exponent kv,n between division polynomials ψn and ϕn associated with a sequence {nP}n∈N of points on an elliptic curve E defined over a discrete valuation field K. The formula greatly generalizes the previously known special cases and treats also the case of non-standard Kodaira types for non-perfect residue fields.}, author = {Naskręcki, Bartosz and Verzobio, Matteo}, issn = {1473-7124}, journal = {Proceedings of the Royal Society of Edinburgh Section A: Mathematics}, keywords = {Elliptic curves, Néron models, division polynomials, height functions, discrete valuation rings}, number = {5}, pages = {1646--1660}, publisher = {Cambridge University Press}, title = {{Common valuations of division polynomials}}, doi = {10.1017/prm.2024.7}, volume = {155}, year = {2025}, } @article{21528, abstract = {We present a framework for the end-to-end optimization of metasurface imaging systems that reconstruct targets using compressed sensing, a technique for solving underdetermined imaging problems when the target object exhibits sparsity (e.g., the object can be described by a small number of nonzero values, but the positions of these values are unknown). We nest an iterative, unapproximated compressed sensing reconstruction algorithm into our end-to-end optimization pipeline, resulting in an interpretable, data-efficient method for maximally leveraging metaoptics to exploit object sparsity. We apply our framework to super-resolution imaging and high-resolution depth imaging with a phase-change material. In both situations, our end-to-end framework effectively optimizes metasurface structures for compressed sensing recovery, automatically balancing a number of complicated design considerations to select an imaging measurement matrix from a complex, physically constrained manifold with millions of dimensions. The optimized metasurface imaging systems are robust to noise, significantly improving over random scattering surfaces and approaching the ideal compressed sensing performance of a Gaussian matrix, showing how a physical metasurface system can demonstrably approach the mathematical limits of compressed sensing.}, author = {Arya, Gaurav and Li, William F. and Roques-Carmes, Charles and Soljačić, Marin and Johnson, Steven G. and Lin, Zin}, issn = {2330-4022}, journal = {ACS Photonics}, keywords = {end-to-end, optimization, metasurface, imaging, compressed sensing}, number = {5}, pages = {2077--2087}, publisher = {American Chemical Society}, title = {{End-to-end optimization of metasurfaces for imaging with compressed sensing}}, doi = {10.1021/acsphotonics.4c00259}, volume = {11}, year = {2024}, } @article{21672, abstract = {We present a framework for the end-to-end optimization of metasurface imaging systems that reconstruct targets using compressed sensing, a technique for solving underdetermined imaging problems when the target object exhibits sparsity (i.e. the object can be described by a small number of non-zero values, but the positions of these values are unknown). We nest an iterative, unapproximated compressed sensing reconstruction algorithm into our end-to-end optimization pipeline, resulting in an interpretable, data-efficient method for maximally leveraging metaoptics to exploit object sparsity. We apply our framework to super-resolution imaging and high-resolution depth imaging with a phase-change material. In both situations, our end-to-end framework computationally discovers optimal metasurface structures for compressed sensing recovery, automatically balancing a number of complicated design considerations to select an imaging measurement matrix from a complex, physically constrained manifold with millions ofdimensions. The optimized metasurface imaging systems are robust to noise, significantly improving over random scattering surfaces and approaching the ideal compressed sensing performance of a Gaussian matrix, showing how a physical metasurface system can demonstrably approach the mathematical limits of compressed sensing.}, author = {Arya, Gaurav and Li, William F. and Roques-Carmes, Charles and Soljačić, Marin and Johnson, Steven G. and Lin, Zin}, issn = {2330-4022}, journal = {ACS Photonics}, keywords = {end-to-end, optimization, metasurface, imaging, compressed sensing}, publisher = {American Chemical Society}, title = {{End-to-end optimization of metasurfaces for imaging with compressed sensing}}, doi = {10.1021/acsphotonics.4c00259}, year = {2024}, } @article{12287, abstract = {We present criteria for establishing a triangulation of a manifold. Given a manifold M, a simplicial complex A, and a map H from the underlying space of A to M, our criteria are presented in local coordinate charts for M, and ensure that H is a homeomorphism. These criteria do not require a differentiable structure, or even an explicit metric on M. No Delaunay property of A is assumed. The result provides a triangulation guarantee for algorithms that construct a simplicial complex by working in local coordinate patches. Because the criteria are easily verified in such a setting, they are expected to be of general use.}, author = {Boissonnat, Jean-Daniel and Dyer, Ramsay and Ghosh, Arijit and Wintraecken, Mathijs}, issn = {1432-0444}, journal = {Discrete & Computational Geometry}, keywords = {Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology, Theoretical Computer Science}, pages = {156--191}, publisher = {Springer Nature}, title = {{Local criteria for triangulating general manifolds}}, doi = {10.1007/s00454-022-00431-7}, volume = {69}, year = {2023}, } @article{14499, abstract = {An n-vertex graph is called C-Ramsey if it has no clique or independent set of size Clog2n (i.e., if it has near-optimal Ramsey behavior). In this paper, we study edge statistics in Ramsey graphs, in particular obtaining very precise control of the distribution of the number of edges in a random vertex subset of a C-Ramsey graph. This brings together two ongoing lines of research: the study of ‘random-like’ properties of Ramsey graphs and the study of small-ball probability for low-degree polynomials of independent random variables. The proof proceeds via an ‘additive structure’ dichotomy on the degree sequence and involves a wide range of different tools from Fourier analysis, random matrix theory, the theory of Boolean functions, probabilistic combinatorics and low-rank approximation. In particular, a key ingredient is a new sharpened version of the quadratic Carbery–Wright theorem on small-ball probability for polynomials of Gaussians, which we believe is of independent interest. One of the consequences of our result is the resolution of an old conjecture of Erdős and McKay, for which Erdős reiterated in several of his open problem collections and for which he offered one of his notorious monetary prizes.}, author = {Kwan, Matthew Alan and Sah, Ashwin and Sauermann, Lisa and Sawhney, Mehtaab}, issn = {2050-5086}, journal = {Forum of Mathematics, Pi}, keywords = {Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics, Statistics and Probability, Algebra and Number Theory, Analysis}, publisher = {Cambridge University Press}, title = {{Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture}}, doi = {10.1017/fmp.2023.17}, volume = {11}, year = {2023}, } @article{22046, abstract = {We show that solutions to the Ablowitz–Ladik system converge to solutions of the cubic nonlinear Schrödinger equation for merely L2 initial data. Furthermore, we consider initial data for this lattice model that excites Fourier modes near both critical points of the discrete dispersion relation and demonstrate convergence to a decoupled system of nonlinear Schrödinger equations.}, author = {Killip, Rowan and Ouyang, Zhimeng and Visan, Monica and Wu, Lei}, issn = {1361-6544}, journal = {Nonlinearity}, keywords = {Ablowitz–Ladik, continuum limit, cubic NLS}, number = {7}, pages = {3751--3775}, publisher = {IOP Publishing}, title = {{Continuum limit for the Ablowitz–Ladik system}}, doi = {10.1088/1361-6544/acd978}, volume = {36}, year = {2023}, } @article{14466, abstract = {The first long-lived turbulent structures observable in planar shear flows take the form of localized stripes, inclined with respect to the mean flow direction. The dynamics of these stripes is central to transition, and recent studies proposed an analogy to directed percolation where the stripes’ proliferation is ultimately responsible for the turbulence becoming sustained. In the present study we focus on the internal stripe dynamics as well as on the eventual stripe expansion, and we compare the underlying mechanisms in pressure- and shear-driven planar flows, respectively, plane-Poiseuille and plane-Couette flow. Despite the similarities of the overall laminar–turbulence patterns, the stripe proliferation processes in the two cases are fundamentally different. Starting from the growth and sustenance of individual stripes, we find that in plane-Couette flow new streaks are created stochastically throughout the stripe whereas in plane-Poiseuille flow streak creation is deterministic and occurs locally at the downstream tip. Because of the up/downstream symmetry, Couette stripes, in contrast to Poiseuille stripes, have two weak and two strong laminar turbulent interfaces. These differences in symmetry as well as in internal growth give rise to two fundamentally different stripe splitting mechanisms. In plane-Poiseuille flow splitting is connected to the elongational growth of the original stripe, and it results from a break-off/shedding of the stripe's tail. In plane-Couette flow splitting follows from a broadening of the original stripe and a division along the stripe into two slimmer stripes.}, author = {Marensi, Elena and Yalniz, Gökhan and Hof, Björn}, issn = {1469-7645}, journal = {Journal of Fluid Mechanics}, keywords = {turbulence, transition to turbulence, patterns}, publisher = {Cambridge University Press}, title = {{Dynamics and proliferation of turbulent stripes in plane-Poiseuille and plane-Couette flows}}, doi = {10.1017/jfm.2023.780}, volume = {974}, year = {2023}, } @article{12129, abstract = {Given a finite point set P in general position in the plane, a full triangulation of P is a maximal straight-line embedded plane graph on P. A partial triangulation of P is a full triangulation of some subset P′ of P containing all extreme points in P. A bistellar flip on a partial triangulation either flips an edge (called edge flip), removes a non-extreme point of degree 3, or adds a point in P∖P′ as vertex of degree 3. The bistellar flip graph has all partial triangulations as vertices, and a pair of partial triangulations is adjacent if they can be obtained from one another by a bistellar flip. The edge flip graph is defined with full triangulations as vertices, and edge flips determining the adjacencies. Lawson showed in the early seventies that these graphs are connected. The goal of this paper is to investigate the structure of these graphs, with emphasis on their vertex connectivity. For sets P of n points in the plane in general position, we show that the edge flip graph is ⌈n/2−2⌉-vertex connected, and the bistellar flip graph is (n−3)-vertex connected; both results are tight. The latter bound matches the situation for the subfamily of regular triangulations (i.e., partial triangulations obtained by lifting the points to 3-space and projecting back the lower convex hull), where (n−3)-vertex connectivity has been known since the late eighties through the secondary polytope due to Gelfand, Kapranov, & Zelevinsky and Balinski’s Theorem. For the edge flip-graph, we additionally show that the vertex connectivity is at least as large as (and hence equal to) the minimum degree (i.e., the minimum number of flippable edges in any full triangulation), provided that n is large enough. Our methods also yield several other results: (i) The edge flip graph can be covered by graphs of polytopes of dimension ⌈n/2−2⌉ (products of associahedra) and the bistellar flip graph can be covered by graphs of polytopes of dimension n−3 (products of secondary polytopes). (ii) A partial triangulation is regular, if it has distance n−3 in the Hasse diagram of the partial order of partial subdivisions from the trivial subdivision. (iii) All partial triangulations of a point set are regular iff the partial order of partial subdivisions has height n−3. (iv) There are arbitrarily large sets P with non-regular partial triangulations and such that every proper subset has only regular triangulations, i.e., there are no small certificates for the existence of non-regular triangulations.}, author = {Wagner, Uli and Welzl, Emo}, issn = {1432-0444}, journal = {Discrete & Computational Geometry}, keywords = {Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology, Theoretical Computer Science}, number = {4}, pages = {1227--1284}, publisher = {Springer Nature}, title = {{Connectivity of triangulation flip graphs in the plane}}, doi = {10.1007/s00454-022-00436-2}, volume = {68}, year = {2022}, } @article{12148, abstract = {We prove a general local law for Wigner matrices that optimally handles observables of arbitrary rank and thus unifies the well-known averaged and isotropic local laws. As an application, we prove a central limit theorem in quantum unique ergodicity (QUE): that is, we show that the quadratic forms of a general deterministic matrix A on the bulk eigenvectors of a Wigner matrix have approximately Gaussian fluctuation. For the bulk spectrum, we thus generalise our previous result [17] as valid for test matrices A of large rank as well as the result of Benigni and Lopatto [7] as valid for specific small-rank observables.}, author = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J}, issn = {2050-5094}, journal = {Forum of Mathematics, Sigma}, keywords = {Computational Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics, Statistics and Probability, Algebra and Number Theory, Theoretical Computer Science, Analysis}, publisher = {Cambridge University Press}, title = {{Rank-uniform local law for Wigner matrices}}, doi = {10.1017/fms.2022.86}, volume = {10}, year = {2022}, } @article{12216, abstract = {Many trace inequalities can be expressed either as concavity/convexity theorems or as monotonicity theorems. A classic example is the joint convexity of the quantum relative entropy which is equivalent to the Data Processing Inequality. The latter says that quantum operations can never increase the relative entropy. The monotonicity versions often have many advantages, and often have direct physical application, as in the example just mentioned. Moreover, the monotonicity results are often valid for a larger class of maps than, say, quantum operations (which are completely positive). In this paper we prove several new monotonicity results, the first of which is a monotonicity theorem that has as a simple corollary a celebrated concavity theorem of Epstein. Our starting points are the monotonicity versions of the Lieb Concavity and the Lieb Convexity Theorems. We also give two new proofs of these in their general forms using interpolation. We then prove our new monotonicity theorems by several duality arguments.}, author = {Carlen, Eric A. and Zhang, Haonan}, issn = {0024-3795}, journal = {Linear Algebra and its Applications}, keywords = {Discrete Mathematics and Combinatorics, Geometry and Topology, Numerical Analysis, Algebra and Number Theory}, pages = {289--310}, publisher = {Elsevier}, title = {{Monotonicity versions of Epstein's concavity theorem and related inequalities}}, doi = {10.1016/j.laa.2022.09.001}, volume = {654}, year = {2022}, } @article{10588, abstract = {We prove the Sobolev-to-Lipschitz property for metric measure spaces satisfying the quasi curvature-dimension condition recently introduced in Milman (Commun Pure Appl Math, to appear). We provide several applications to properties of the corresponding heat semigroup. In particular, under the additional assumption of infinitesimal Hilbertianity, we show the Varadhan short-time asymptotics for the heat semigroup with respect to the distance, and prove the irreducibility of the heat semigroup. These results apply in particular to large classes of (ideal) sub-Riemannian manifolds.}, author = {Dello Schiavo, Lorenzo and Suzuki, Kohei}, issn = {1432-1807}, journal = {Mathematische Annalen}, keywords = {quasi curvature-dimension condition, sub-riemannian geometry, Sobolev-to-Lipschitz property, Varadhan short-time asymptotics}, pages = {1815--1832}, publisher = {Springer Nature}, title = {{Sobolev-to-Lipschitz property on QCD- spaces and applications}}, doi = {10.1007/s00208-021-02331-2}, volume = {384}, year = {2022}, } @article{10643, abstract = {We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding Gelfand–Naimark–Segal Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that a similar adiabatic theorem also holds in the bulk of finite systems up to errors that vanish faster than any inverse power of the system size, although the corresponding finite-volume Hamiltonians need not have a spectral gap. }, author = {Henheik, Sven Joscha and Teufel, Stefan}, issn = {2050-5094}, journal = {Forum of Mathematics, Sigma}, keywords = {computational mathematics, discrete mathematics and combinatorics, geometry and topology, mathematical physics, statistics and probability, algebra and number theory, theoretical computer science, analysis}, publisher = {Cambridge University Press}, title = {{Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk}}, doi = {10.1017/fms.2021.80}, volume = {10}, year = {2022}, } @article{12286, abstract = {Inspired by the study of loose cycles in hypergraphs, we define the loose core in hypergraphs as a structurewhich mirrors the close relationship between cycles and $2$-cores in graphs. We prove that in the $r$-uniform binomial random hypergraph $H^r(n,p)$, the order of the loose core undergoes a phase transition at a certain critical threshold and determine this order, as well as the number of edges, asymptotically in the subcritical and supercritical regimes. Our main tool is an algorithm called CoreConstruct, which enables us to analyse a peeling process for the loose core. By analysing this algorithm we determine the asymptotic degree distribution of vertices in the loose core and in particular how many vertices and edges the loose core contains. As a corollary we obtain an improved upper bound on the length of the longest loose cycle in $H^r(n,p)$.}, author = {Cooley, Oliver and Kang, Mihyun and Zalla, Julian}, issn = {1077-8926}, journal = {The Electronic Journal of Combinatorics}, keywords = {Computational Theory and Mathematics, Geometry and Topology, Theoretical Computer Science, Applied Mathematics, Discrete Mathematics and Combinatorics}, number = {4}, publisher = {Electronic Journal of Combinatorics}, title = {{Loose cores and cycles in random hypergraphs}}, doi = {10.37236/10794}, volume = {29}, year = {2022}, } @article{11135, abstract = {We consider a correlated NxN Hermitian random matrix with a polynomially decaying metric correlation structure. By calculating the trace of the moments of the matrix and using the summable decay of the cumulants, we show that its operator norm is stochastically dominated by one.}, author = {Reker, Jana}, issn = {2010-3271}, journal = {Random Matrices: Theory and Applications}, keywords = {Discrete Mathematics and Combinatorics, Statistics, Probability and Uncertainty, Statistics and Probability, Algebra and Number Theory}, number = {4}, publisher = {World Scientific Publishing}, title = {{On the operator norm of a Hermitian random matrix with correlated entries}}, doi = {10.1142/s2010326322500368}, volume = {11}, year = {2022}, } @article{11446, abstract = {Suppose that n is not a prime power and not twice a prime power. We prove that for any Hausdorff compactum X with a free action of the symmetric group Sn, there exists an Sn-equivariant map X→Rn whose image avoids the diagonal {(x,x,…,x)∈Rn∣x∈R}. Previously, the special cases of this statement for certain X were usually proved using the equivartiant obstruction theory. Such calculations are difficult and may become infeasible past the first (primary) obstruction. We take a different approach which allows us to prove the vanishing of all obstructions simultaneously. The essential step in the proof is classifying the possible degrees of Sn-equivariant maps from the boundary ∂Δn−1 of (n−1)-simplex to itself. Existence of equivariant maps between spaces is important for many questions arising from discrete mathematics and geometry, such as Kneser’s conjecture, the Square Peg conjecture, the Splitting Necklace problem, and the Topological Tverberg conjecture, etc. We demonstrate the utility of our result applying it to one such question, a specific instance of envy-free division problem.}, author = {Avvakumov, Sergey and Kudrya, Sergey}, issn = {1432-0444}, journal = {Discrete & Computational Geometry}, keywords = {Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology, Theoretical Computer Science}, number = {3}, pages = {1202--1216}, publisher = {Springer Nature}, title = {{Vanishing of all equivariant obstructions and the mapping degree}}, doi = {10.1007/s00454-021-00299-z}, volume = {66}, year = {2021}, }