Research
Research
Research
Research
129+ open-access research outputs.
We construct multiplicative norms on equivariant nonconnective algebraic $K$-theory for finite groups $G$. We also construct a genuine equivariant version of THH equipped with a Dennis trace map from …
We construct a comparison functor from the dual category of motivic homotopy category $\mathcal{SH}$ to the category of $\mathbb{A}^1$-invariant localizing motives $\operatorname{Mot}_{\operatorname{l…
In this short remark, we explain that two examples of invariance under duality for a localizing invariant $F$ hold purely formally when $F$ is $K$-theory, whereas the general statement for arbitrary l…
We investigate whether it is typical for a sparse graph to be uniquely characterized by its adjacency spectrum up to isomorphism. Our first result shows that the giant component of an Erd\H{o}s-R\'eny…
Let $f$ be a meromorphic univalent function on the open unit disk having a simple pole at $p\in (0,1)$ that extends continuously to the left half $\IT^{-}$ of the unit circle. In this article, we prov…
In this paper we study the category of localizing motives $\operatorname{Mot}^{\operatorname{loc}}$ -- the target of the universal finitary localizing invariant of idempotent-complete stable categorie…
Haemers conjectures that almost all graphs are determined by their spectra. Suppose $G \sim \mathcal{G}(n, p)$ is a random graph with each edge chosen independently with probability $p$ with $0 < p < …
We prove that the natural map from the derived Brauer group of a qcqs scheme $X$ to the Picard group of $X$-linear motives is injective, extending results of Tabuada and Tabuada-Van den Bergh.…
In this work, we show that given a finite p-group G, a number field K having a trivial p-class group Cl K , and a finite set of primes S of K, there exists a finite extension F/K such that the S-split…
Complement-reducible graphs (or cographs) are the graphs formed from the single-vertex graph by the operations of complement and disjoint union. By combining the Johnson-Newman theorem on generalized …
We elaborate on a connection between the $SU(2)$-valued nonlinear Fourier series and sequences of left and right orthogonal polynomials for complex measures on the unit circle. We show a convergence r…
Let $D$ be an oriented graph with skew adjacency matrix $S(D)$. Two oriented graphs $D$ and $C$ are said to share the same generalized skew spectrum if $S(D)$ and $S(C)$ have the same eigenvalues, and…
We prove the uniqueness of general Bessel models for $\mathrm{GSpin}$ groups over a local field of characteristic zero. The proof is to reduce it to the spherical case, which has been proved by Emory …
We define a class of motivic equivalences of small stable $\infty$-categories $W_{\mathrm{mot}}$ and show that the Dwyer--Kan localization functor $\mathrm{Cat}^{\mathrm{perf}}_\infty \to \mathrm{Cat}…
Given a compact Lie group $G$ acting on a space $X$, the classical Atiyah-Segal completion theorem identifies topological $K$-theory of the homotopy quotient $X/G$ with an explicit completion of $G$-e…
This paper introduces a spectral Monte Carlo iterative method (SMC) for solving linear Poisson and parabolic equations driven by $\alpha$-stable L\'evy process with $\alpha\in (0,2)$, which was initia…
We show that a "mate'' $B$ of a set $A$ in a near-factorization $(A,B)$ of a finite group $G$ is unique. Further, we describe how to compute the mate $B$ very efficiently using an explicit formula for…
To every non-extreme point $b$ of the unit ball of $\hil^\infty$ of the unit disk there corresponds a Pythagorean mate, a bounded outer function $a$ satisfying the equation $|a|^2 + |b|^2 = 1$ on the …
In this paper, we study the de Branges-Rovnyak spaces $\mathcal{H}(B)$ generated by row Schur functions $B$ with mate $a$. We prove that the polynomials are dense in $\mathcal{H}(B)$, and characterize…
The set of perfect matchings of a connected bipartite plane graph $G$ has the structure of a distributive lattice, as shown by Propp, where the partial order is induced by the height of a matching. In…
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