Related papers: Spectral morphisms, K-theory, and stable ranks

We develop an algebraic formalism for topological $\mathbb{T}$-duality. More precisely, we show that topological $\mathbb{T}$-duality actually induces an isomorphism between noncommutative motives that in turn implements the well-known…

We cast Kasparov's equivariant KK-theory in the framework of model categories. We obtain a stable model structure on a certain category of locally multiplicative convex $G$-$C^*$-algebras, which naturally contains the stable…

A general method of producing correspondences and spectral categories out of symmetric ring objects in general categories is given. As an application, stable homotopy theory of spectra $SH$ is recovered from modules over a commutative…

We study the Hitchin morphism for higher dimensional varieties and show that, for a certain class of varieties which we call r-small, the set-theoretic image of the Hitchin morphism from the Dolbeault moduli space coincides with the…

This is the integral text of my thesis. The first part is an expanded version of "Riemann-Roch theorems for Deligne-Mumford stacks", where I deal with Artin stacks over general bases. In the second part, I prove some Riemann-Roch statment…

In this note, we investigate fundamental relations between exploration processes in random graphs, and branching processes. We formulate a class of models that we call {\em rank-$k$ random graphs}, and that are special in that their…

Let $S$ be a finite dimensional noetherian scheme. For any proper morphism between smooth $S$-schemes, we prove a Riemann-Roch formula relating higher algebraic $K$-theory and motivic cohomology, thus with no projective hypothesis neither…

This paper extends the relation established for group cohomology by Green, Hunton and Schuster between chromatic phenomena in stable homotopy theory and certain natural subrings of singular cohomology. This exploits the theory due to Henn,…

In this article, we define two equivalent new model structures on $\mathbf{sCat}$ the category of simplicial objects in $\mathbf{Cat}$. Then we construct the corresponding stable model category of spectra $Sp(\mathbf{sCat})$ and make some…

We study the general and connected stable ranks for C*-algebras. We estimate these ranks for pullbacks of C*-algebras, and for tensor products by commutative C*-algebras. Finally, we apply these results to determine these ranks for certain…

Spectral transformation is known to set up a birational morphism between the Hitchin and Beauville-Mukai integrable systems. The corresponding phase spaces are: (a) the cotangent bundle of the moduli space of bundles over a curve C, and (b)…

We study the back stable $K$-theory Schubert calculus of the infinite flag variety. We define back stable (double) Grothendieck polynomials and double $K$-Stanley functions and establish coproduct expansion formulae. Applying work of…

We show that for a coconnective ring spectrum satisfying regularity and flatness assumptions, its algebraic K-theory agrees with that of its $\pi_0$. We prove this as a consequence of a more general devissage result for stable infinity…

In the context of commutative $C^*$-algebras we solve a problem related to a question of M. Rieffel by showing that the all-units rank and the norm-one rank coincide with the topological stable rank. We also introduce the notion of unitary…

We give a more conceptual construction of a comparison algebra morphism from the K-theoretical Hall algebra to a twist of the cohomological Hall algebra associated to a symmetric quiver, and extend the result to quivers with potential.

In this note, we discuss a number of open problems in K-stability theory.

We extend the Killeen-Taylor study in \cite{KT} by investigating in different Banach spaces ($\ell^\alpha(\N), c_0(\N),c_c(\N)$) the point, continuous and residual spectra of stochastic perturbations of the shift operator associated to the…

We prove an explicit combinatorial formula for the structure constants of the Grothendieck ring of a Grassmann variety with respect to its basis of Schubert structure sheaves. We furthermore relate K-theory of Grassmannians to a bialgebra…

In this article, we are interested in endomorphism's impact on the commutativity of a Banach algebra. Our research uses a topological approach, drawing on specific results from functional analysis and algebraic techniques.\;Also, we provide…

For twisted K-theory whose twist is classified by a degree three integral cohomology of infinite order, universal even degree characteristic classes are in one to one correspondence with invariant polynomials of Atiyah and Segal. The…