Related papers: Models of Lubin-Tate spectra via Real bordism theo…

Lurie's theorem states that there exists a sheaf of ring spectra on the site of formally \'etale Deligne--Mumford stacks over the moduli stack of $p$-divisible groups of height $n$, which agrees with the classical Landweber exact functor…

We give very flexible, concrete constructions of discrete and faithful epresentations of right-angled Artin groups into higher-rank Lie groups. Using the geometry of the associated symmetric spaces and the combinatorics of the groups, we…

Suppose a residually finite group $G$ acts cocompactly on a contractible complex with strict fundamental domain $Q$, where the stabilizers are either trivial or have normal $\mathbb{Z}$-subgroups. Let $\partial Q$ be the subcomplex of $Q$…

We propose a toy model for symmetry-breaking or bubbling, in terms of cobordism of manifolds with circle actions free on a possible boundary. The Swan-Tate cohomology $t_\T E$ of a complex-oriented $E_\infty$ ring-spectrum $E$ is the…

We study the asymptotic behaviour of the cohomology of subgroups $\Gamma$ of an algebraic group $G$ with coefficients in the various irreducible rational representations of $G$ and raise a conjecture about it. Namely, we expect that the…

We define notions of higher order spectra of a complex quasi-projective manifold with an action of a finite group $G$ and with a $G$-equivariant automorphism of finite order, some of their refinements and give Macdonald type equations for…

We give details of models for rational torus equivariant homotopy theory based on (a) all subgroups, connected subgroups or dimensions of subgroups and (b) on pairs or general flags. We provide comparison functors and show the models are…

For $G$ a finite group acting linearly on $\mathbb{A}^2$, the equivariant Hilbert scheme $\operatorname{Hilb}^r[\mathbb{A}^2/G]$ is a natural resolution of singularities of $\operatorname{Sym}^r(\mathbb{A}^2/G)$. In this paper we study the…

This is an extended write-up of a talk given in April, 1993 in honor of Raoul Bott's 70th birthday. We first illustrate how some traditional topological and geometric invariants obey ``gluing laws'' inspired by those in classical and…

We define and study stacks which parametrize Lubin--Tate $(\varphi,\Gamma)$-modules. By working at a perfectoid level, we compare these with the Emerton--Gee stacks of cyclotomic $(\varphi,\Gamma)$-modules. As a consequence, we deduce…

We discuss the role of formal deformation theory in quantum field theories and present various ``higher operations'' which control their deformations, (generalized) OPEs, and anomalies. Particular attention is paid to…

We use localization method to understand the rational equivariant cohomology rings of real Grassmannians and oriented Grassmannians, then relate this to the Leray-Borel description which says the ring generators are equivariant Pontryagin…

We prove an arithmetic Hilbert-Samuel type theorem for semi-positive singular hermitian line bundles of finite height. In particular, the theorem applies to the log-singular metrics of Burgos-Kramer-K\"uhn. Our theorem is thus suitable for…

We define a regularized theta lift from SL_2 to orthogonal groups over totally real fields. It takes harmonic `Whittaker forms' to automorphic Green functions and weakly holomorphic Whittaker forms to meromorphic modular forms on orthogonal…

Previous work constructed a generalized truncated Brown-Peterson spectrum of chromatic height 2 at the prime 2 as an E_infinity-ring spectrum, based on the study of elliptic curves with level-3 structure. We show that the natural map…

Consider the diagonal action of the special orthogonal group on the direct sum of a finite number of copies of the standard representation--the underlying field is assumed to be algebraically closed and of characteristic not equal to two.…

We show how to use equidimensional algebraic correspondences between complex algebraic varieties to construct pull-backs and transforms of certain classes of geometric currents. Using this construction we produce explicit formulas at the…

We show that the 2-local splitting of spin$^c$ bordism by Anderson--Brown--Peterson and Stong refines to a $C_2$-equivariant map in the category of spectra with $C_2$-action from Real spin bordism to a sum of (higher) connective covers of…

We compute the equivariant (stable) complex cobordism ring $(MU_G)_*$ for finite abelian groups $G$.

We introduce a notion of ellipticity of complexes of linear pseudodifferential operators acting on sections of $A$-Hilbert bundles over smooth manifolds, $A$ being a $C^*$-algebra. We prove that the cohomology groups of an $A$-elliptic…