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We show that a Calabi–Yau structure of dimension d on a smooth dg category CC induces a
symplectic form of degree 2-d 2-d on 'the moduli space of objects' M _ C MC. We show …

We formulate a version of the integral Hodge conjecture for categories, prove the conjecture
for two-dimensional Calabi–Yau categories which are suitably deformation equivalent to the …

Kazhdan and Lusztig identified the affine Hecke algebra ℋ with an equivariant K-group of
the Steinberg variety, and applied this to prove the Deligne-Langlands conjecture, ie, the …

We calculate the dg algebra of global functions on commuting stacks of complex reductive
groups using tools from Betti Geometric Langlands. In particular, we prove that the ring of …

The goal of this paper is to provide a categorical framework that leads to the definition of
shtukas à la Drinfeld and of excursion operators à la V. Lafforgue. We take as the point of …

For a complex reductive group, we construct a semi-orthogonal decomposition of the
cocenter of the universal variant of its affine Hecke category. We use this to calculate the …

We prove a transformation formula for the Goresky-Hingston loop coproduct in string
topology under homotopy equivalences of manifolds. The formula involves the trace of the …

In this paper, we investigate Keller's deformed Calabi–Yau completion of the derived
category of coherent sheaves on a smooth variety. In particular, for an-dimensional smooth …

We develop a theory of generalized characters of local systems in $\infty $-categories, which
extends classical character theory for group representations and, in particular, the induced …