Related papers: Strong convergence in the motivic Adams spectral s…

We show that there is a non-trivial differential $d_4(h_6^3) =h_0^3g_4$ in the mod 2 Adams spectral sequence for spheres. This together with the results in \cite{barratt_differentials_1970,lin_differential_1998,kan_differential_2001}…

We examine bounds on accelerated expansion in asymptotic regions of the moduli space in string theory compactifications to four spacetime dimensions. While there are conjectures that forbid or constrain accelerated expansion in such…

In this paper, we initiate a study of motivic homotopy theory at infinity. We use the six functor formalism to give an intrinsic definition of the stable motivic homotopy type at infinity of an algebraic variety. Our main computational…

Let S be an essentially smooth scheme over a field of characteristic exponent c. Let MGL and HZ denote the algebraic cobordism spectrum and the motivic cohomology spectrum over S, respectively. We show that the canonical map MGL/(a1, a2,…

The motivic Mahowald invariant was introduced in \cite{Qui19a} and \cite{Qui19b} to study periodicity in the $\mathbb{C}$- and $\mathbb{R}$-motivic stable stems. In this paper, we define the motivic Mahowald invariant over any field $F$ of…

We prove the modulo $p$ and modulo $p^2$ cases of Igusa's conjecture on exponential sums. This conjecture predicts specific uniform bounds in the homogeneous polynomial case of exponential sums modulo $p^m$ when $p$ and $m$ vary. We…

We investigate exceptional points of degeneracy (EPDs) in electromagnetic scattering of a sphere dimer from the electroquasistatic limit to the fully retarded regime. In the quasistatic limit, we prove that $\parity\trev$-symmetric…

This paper is mainly concerned with the existence of extremals for the Adams inequality. We first establish an upper bound for the classical Adams functional along of all concentrated sequences in $W^{m,\frac{n}{m}}_{\mathcal{N}}(\Omega)$,…

We prove that for any tree with a vertex of degree at least six, its chromatic symmetric function is not $e$-positive, that is, it cannot be written as a nonnegative linear combination of elementary symmetric functions. This makes…

We analyze the $\mathbb{C}$-motivic (and classical) Adams-Novikov spectral sequence for the $\mathbb{C}$-motivic modular forms spectrum $\mathit{mmf}$ (and for the classical topological modular forms spectrum $\mathit{tmf}$). We primarily…

Let D be a central division algebra over a field F. We study in this note the rigidity of the motivic decompositions of the Severi-Brauer varieties of D, with respect to the ring of coefficients and to the base field. We first show that if…

Selectively excited photoluminescence (SPL) of an array of self-organized In$_{0.5}$Ga$_{0.5}$As quantum dots has been measured in a magnetic field up to 11T. Anomalous magnetic field sensitivity of the SPL spectra has been observed under…

We compute the $\mathbb{C}$-motivic Adams spectral sequence for $\mathit{mmf}/\tau$. Up to reindexing, this spectral sequence is isomorphic to the algebraic Novikov spectral sequence for topological modular forms. We give a full analysis of…

We study the spectra of quantum trees of finite cone type. These are quantum graphs whose geometry has a certain homogeneity, and which carry a finite set of edge lengths, coupling constants and potentials on the edges. We show the spectrum…

We revisit methods of proof of the Adams Conjecture in order to correct and supplement earlier efforts to prove analogous conjectures in the stable homotopy category. We utilize simplicial schemes over an algebraically closed field of…

The AdS/QCD models are believed to interpolate between low and high energy sectors of QCD. This belief is usually based on observations that many phenomenologically reasonable predictions follow from bounds imposed at high energies although…

The $E_2$-term of the Adams spectral sequence for $\mathbf{Y}$ may be described in terms of its cohomology $E^\ast \mathbf{Y}$, together with the action of the primary operations $E^\ast \mathbf{E}$ on it, for ring spectra such as…

The stable mod 2 cohomologies of the spectra for connective real and complex K-theories are well known and easy to work with. However, the known bases are in terms of the anti-automorphism of Milnor basis elements. We offer simple bases in…

We study the orbit behavior of a germ of an analytic vector field of $(C^n,0)$, $n \geq 2$. We prove that if its linear part is semisimple, non--resonant and verifies a Bruno--like condition, then the origin is effectively stable: stable…

Let the base $\beta$ be a complex number, $|\beta|>1$, and let $A \subset \C$ be a finite alphabet of digits. The \emph{$A$-spectrum} of $\beta$ is the set $S_{A}(\beta) = \{\sum_{k=0}^n a_k\beta^k \mid n \in \mathbb{N}, \ a_k \in {A}\}$.…