Gorenstein Homological Dimension of Groups Through Flat-Cotorsion Modules by Ali Hajizamani

“…Moreover‎, ‎we show that the inequality $\GF (\rga)\leqslant \GF (R)+{\cd_{R}\ga}$ holds for the group ring $\rga$‎, ‎where $\GF (R)$ denotes the supremum of Gorenstein flat-cotorsion dimensions of all $R$-modules and $\cd_{R}\ga$ is the cohomological dimension of $\ga$‎ over $R$‎.…”
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Probing M-theory with tetrahedron instantons by Elli Pomoni, Wenbin Yan, Xinyu Zhang

“…The dimensional reduction of the system allows us to express the cohomological tetrahedron instanton partition function in terms of the MacMahon function, generalizing the correspondence between Gromov-Witten invariants and Donaldson-Thomas invariants for Calabi-Yau threefolds.…”
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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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A proof of Tsygan's formality conjecture for an arbitrary smooth manifold by Dolgushev, Vasiliy A

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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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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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Topological orders, braiding statistics, and mixture of two types of twisted BF theories in five dimensions by Zhi-Feng Zhang, Peng Ye

“…Among all TQFTs, some are not in Dijkgraaf-Witten cohomological classification. To characterize topological orders, we concretely construct all braiding processes among topological excitations, which leads to very exotic links formed by closed spacetime trajectories of particles, loops, and membranes. …”
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A Coherent Categorification of the Asymptotic Affine Hecke Algebra by Propp, Oron Yehonatan

“…In particular, we obtain that the coherent Springer sheaf lies in cohomological degree 0 (i.e., is a sheaf rather than a complex), resolving a conjecture of Ben-Zvi–Chen–Helm–Nadler and Zhu. …”
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Topological phases of matter, symmetries, and K-theory by Thiang, G

“…From the fundamental work of Wigner, we know that topology resides not only in the group of symmetries, but also in the cohomological data of projective unitary-antiunitary representations. …”

A Lagrangian Neighbourhood Theorem for shifted symplectic derived schemes by Joyce, D, Safronov, P

“…We expect our results will have future applications to $k$-shifted Poisson geometry (see arXiv:1506.03699), to defining 'Fukaya categories' of complex or algebraic symplectic manifolds, and to categorifying Donaldson-Thomas theory of Calabi-Yau 3-folds and 'Cohomological Hall algebras'.…”

On induction of class functions by Lusztig, G

“…We show that for large <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="q"> <mml:semantics> <mml:mi>q</mml:mi> <mml:annotation encoding="application/x-tex">q</mml:annotation> </mml:semantics> </mml:math> </inline-formula> this map coincides with the known cohomological induction (whose definition involves a choice of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper P"> <mml:semantics> <mml:mi>P</mml:mi> <mml:annotation encoding="application/x-tex">P</mml:annotation> </mml:semantics> </mml:math> </inline-formula>).…”
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On induction of class functions by Lusztig, George

“…We show that for large <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="q"> <mml:semantics> <mml:mi>q</mml:mi> <mml:annotation encoding="application/x-tex">q</mml:annotation> </mml:semantics> </mml:math> </inline-formula> this map coincides with the known cohomological induction (whose definition involves a choice of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper P"> <mml:semantics> <mml:mi>P</mml:mi> <mml:annotation encoding="application/x-tex">P</mml:annotation> </mml:semantics> </mml:math> </inline-formula>).…”
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Tautological relations via ����-spin structures by Pandharipande, R, Pixton, A, Zvonkine, D

“…The Givental-Teleman classification of CohFT (cohomological field theory) is used at two special semisimple points of the associated Frobenius manifold. …”
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