Heterotic-F-theory duality with Wilson line symmetry-breaking by Herbert Clemens, Stuart Raby

“…Using Heterotic/F-theory duality we are able to define the cohomologies used to derive the massless spectrum. Our model for the 'correct' F-theory dual of a Heterotic model with Wilson-line symmetry-breaking builds on prior literature but employs the stack-theoretic version of the dictionary between the Heterotic semi-stable Es-bundles with Yang-Mills connection and the dP9-fibrations used to construct the F-theory dual.…”
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K-theoretic Hall algebras for quivers with potential by Pădurariu, Tudor(Tudor Gabriel)

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Analogues of Kähler geometry on Sasakian manifolds by Tievsky, Aaron M

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Curved twistor spaces by Ward, R, Ward, R. S.

“…Chapter 2 is devoted to various preliminaries: a brief outline of twistor theory; an introduction to vector bundles and sheaf cohomology and some of their applications in twistor theory; and a discussion of potentials for electromagnetic fields.…”

On counting special Lagrangian homology 3-spheres by Joyce, D

“…In order for this invariant to be interesting, it should either be unchanged by deformations of the underlying (almost) Calabi-Yau structure, or else transform according to some rigid set of rules as the periods of the almost Calabi-Yau structure pass through some topologically determined hypersurfaces in the cohomology of M. As we deform the underlying almost Calabi-Yau 3-fold, the collection of special Lagrangian homology 3-spheres only change when they become singular. …”

On finite dimensional Nichols algebras of diagonal type by Nicolás Andruskiewitsch, Iván Angiono

“…The knowledge of these algebras is the cornerstone of the classification program of pointed Hopf algebras with finite dimension, or finite Gelfand–Kirillov dimension; and their structure should be indispensable for the understanding of the representation theory, the computation of the various cohomologies, and many other aspects of finite dimensional pointed Hopf algebras. …”
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Codimension-2 defects and higher symmetries in (3+1)D topological phases by Maissam Barkeshli, Yu-An Chen, Sheng-Jie Huang, Ryohei Kobayashi, Nathanan Tantivasadakarn, Guanyu Zhu

“…The intersection between twist strings and Abelian flux loops sources Abelian point charges, which defines an $H^4$ cohomology class that characterizes part of an underlying 3-group symmetry of the topological order. …”
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Grothendieck lines in 3d N $$ \mathcal{N} $$ = 2 SQCD and the quantum K-theory of the Grassmannian by Cyril Closset, Osama Khlaif

“…We also consider the 2d/0d limit of our 3d/1d construction, which gives us local defects in the 2d GLSM, the Schubert defects, that realise equivariant quantum cohomology classes.…”
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The equivariant topology of stable Kneser graphs by Carsten Schultz

“…We establish a close equivariant relationship between the graphs $SG_{n,k}$ and Borsuk graphs of the $k$-sphere and use this together with calculations in the $\mathbb{Z}_2$-cohomology ring of $D_{2m}$ to tell which stable Kneser graphs are test graphs in the sense of Babson and Kozlov. …”
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Exceptional super Yang-Mills in 27 + 3 and worldvolume M-theory by Michael Rios, Alessio Marrani, David Chester

“…Extending previous results of Dijkgraaf, Verlinde and Verlinde, we also put forward the realization of spinors as total cohomologies of (the largest spatially extended) branes which centrally extend the (1,0) superalgebra underlying the corresponding exceptional super Yang-Mills theory. …”
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Distinguishing open symplectic mapping tori via their wrapped Fukaya categories by Kartal, Yusuf Bariș.

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Geometric quantization and dynamical constructions on the space of Kähler metrics by Rubinstein, Yanir Akiva

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Thom-Sebastiani and duality for matrix factorizations, and results on the higher structures of the Hochschild invariants by Preygel, Anatoly

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The affine Yangian of gl₁, and the infinitesimal Cherednik algebras by Tsymbaliuk, Oleksandr

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Rational Cherednik algebras and link invariants by Ghedin, E

“…Smith and Thomas proved that taking the plat closure of the braid, this cohomology does not produce a link invariant but is close to doing so, and they conjectured that, in order to fix the one knot relation that is not satisfied, one has to consider a deformation of the Hilbert scheme.…”

F -zips with additional structure by Pink, R, Wedhorn, T, Ziegler, P

“…The results can be applied to the algebraic de Rham cohomology of smooth projective varieties (or generalizations thereof) and to truncated Barsotti-Tate groups of level 1. …”

On the motivic Galois theory of some families of Feynman integrals by Tapuskovic, M

“…We show that computations in twisted cohomology reflect the expected effect of expanding the space of motivic Feynman integrals by introducing the 'motivic lifts' of dimensionally regularized Feynman integrals.…”

Quantized topological terms in weak-coupling gauge theories with a global symmetry and their connection to symmetry-enriched topological phases by Hung, Ling-Yan, Wen, Xiao-Gang

“…We show that the quantized topological terms are classified by a pair (G,ν[subscript d]), where G is an extension of G[subscript s] by G[subscript g] and ν[subscript d] an element in group cohomology H[superscript d](G,R/Z). When d = 3 and/or when G[subscript g] is finite, the weak-coupling gauge theories with quantized topological terms describe gapped symmetry enriched topological (SET) phases (i.e., gapped long-range-entangled phases with symmetry). …”
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Symmetry-protected topological invariants of symmetry-protected topological phases of interacting bosons and fermions by Wen, Xiao-Gang

“…Recently, it was realized that quantum states of matter can be classified as long-range entangled states (i.e., with nontrivial topological order) and short-range entangled states (i.e., with trivial topological order). We can use group cohomology class H[superscript d](SG,R/Z) to systematically describe the SRE states with a symmetry SG [referred as symmetry-protected trivial (SPT) or symmetry-protected topological (SPT) states] in d-dimensional space-time. …”
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Equivariant k-theory by Segal, G

“…Equivariant K-theory is a generalisation of K-theory, a rather well-known cohomology theory arising from consideration of the vector-bundles on a space. …”