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A discussion of homotopy limits of (1-)stacks, with an emphasis on fixed point stacks., Comment: Exposition streamlined. Minor errors corrected. Discussion of derived functors added

This note records that in the setting of complex varieties, the cohomological consequence of Ehresmann's fibration theorem holds without the smooth assumption on the base or the total space.

This note records that the Langlands parameter spaces, associated by Adams- Barbasch-Vogan to a real group, may be described as homotopy fixed points (fixed point stacks) of the spaces associated to the corresponding complex group., Comment: Minor grammatical fixes

A construction of braid group actions on coherent sheaves using mixed Hodge modules and some well known constructions from geometric representation theory is given., Comment: 6 pages

The degenerate affine and affine BMW algebras arise naturally in the context of Schur--Weyl duality for orthogonal and symplectic Lie algebras and quantum groups, respectively. Cyclotomic BMW algebras, affine Hecke algebras, cyclotomic Hecke algebras, and their degenerate versions are quotients. In this paper the theory is unified by treating the orthogonal and symplectic cases simultaneously; we make an exact parallel between the degenerate affine and affine cases via a new algebra which takes the role of the affine braid group for the degenerate setting. A main result of this paper is an identification of the centers of the affine and degenerate affine BMW algebras in terms of rings of symmetric functions which satisfy a ``cancellation property'' or ``wheel condition'' (in the degenerate case, a reformulation of a result of Nazarov). Miraculously, these same rings also arise in Schubert calculus, as the cohomology and K-theory of isotropic Grassmannians and symplectic loop Grassmannians. We also establish new intertwiner-like identities which, when projected to the center, produce the recursions for central elements given previously by Nazarov for degenerate affine BMW algebras, and by Beliakova--Blanchet for affine BMW algebras.

An action of the $\mathfrak{sl}_2$-crystal category on graded/mixed (integral) category $\mathcal{O}$ `lifting' the usual tensor product is defined., minor typos fixed

An observation on Hall-Littlewood polynomials.

We give a construction of sl2-categorifications for Uq(gln), for generic q and for q a root of unity.

Background The tall cell variant of papillary thyroid carcinoma is an aggressive subtype that generally present as large tumors in advanced stage. However, little is known about the tall cell variant of microcarcinoma (tumors measuring