Related papers: The Geometry of L^k-Canonization I: Rosiness from …
In this paper we study structural properties of residuated lattices that are idempotent as monoids. We provide descriptions of the totally ordered members of this class and obtain counting theorems for the number of finite algebras in…
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
In this paper we investigate using the methodology of algebraic logic, deep algebraic results to prove three new omitting types theorems for finite variable fragments of first order logic. As a sample, we show that it T is an L_n theory and…
We use axioms of abstract ternary relations to define the notion of a free amalgamation theory. These form a subclass of first-order theories, without the strict order property, encompassing many prominent examples of countable structures…
Previous work of the author [39] showed that the Homomorphism Preservation Theorem of classical model theory remains valid when its statement is restricted to finite structures. In this paper, we give a new proof of this result via a…
We introduce and study a genuine equivariant refinement of the Tate construction associated to an extension $\widehat{G}$ of a finite group $G$ by a compact Lie group $K$, which we call the parametrized Tate construction $(-)^{t_G K}$. Our…
Quantization, at least in some formulations, involves replacing some algebra of observables by a (more non-commutative) deformed algebra. In view of the fundamental role played by K-theory in non-commutative geometry and topology, it is of…
We study the $K$-theory and Swan theory of the group ring $R[G]$, when $G$ is a finite group and $R$ is any ring or ring spectrum. In this setting, the well-known assembly map for $K(R[G])$ has a companion called the coassembly map. We…
We establish two consequences of the Kawamata--Morrison--Totaro cone conjecture, and prove them unconditionally in all dimensions. First, for a K-trivial variety, the natural action of its automorphism group on the set of ample divisor…
Using cyclotomic specializations of the equivariant $K$-theory with respect to a torus action we derive congruences for discrete invariants of exceptional objects in derived categories of coherent sheaves on a class of varieties that…
In this thesis we study toric degenerations of projective varieties. We compare different constructions to understand how and why they are related as s first step towards developing a global framework. In focus are toric degenerations…
We provide a universal characterization of the construction taking a scheme $X$ to its stable $\infty$-category $\text{Mot}(X)$ of noncommutative motives, patterned after the universal characterization of algebraic K-theory due to…
Using generalized enriched categories, in this paper we show that Rosick\'{y}'s proof of cartesian closedness of the exact completion of the category of topological spaces can be extended to a wide range of topological categories over…
We give a characterisation of fragmentable, compact linearly order spaces. In particular, we show that if $K$ is a compact, fragmentable, linearly ordered space then $K$ is a Radon-Nikod\'{y}m compact. In addition, we obtain some…
We obtained some sufficient and necessary conditions of existence of faithful irreducible representations of a soluble group $G$ of finite rank over a field $k$. It was shown that the existence of such representations strongly depends on…
In this paper, we introduce a novel Extra-Gradient method with anchor term governed by general parameters. Our method is derived from an explicit discretization of a Tikhonov-regularized monotone flow in Hilbert space, which provides a…
Kac-Moody groups over finite fields are finitely generated groups. Most of them can naturally be viewed as irreducible lattices in products of two closed automorphism groups of non-positively curved twinned buildings: those are the most…
This article surveys results regarding the Tukey theory of ultrafilters on countable base sets. The driving forces for this investigation are Isbell's Problem and the question of how closely related the Rudin-Keisler and Tukey…
We show how to build models of Synthetic Algebraic Geometry over rings k such that finitely presented k-algebra have a decidable equality. The construction is done in a constructive and weak (same proof theoretic strength as dependent type…
Let K and F be complete discrete valuation fields of residue characteristic p>0. Let m be a positive integer no more than their absolute ramification indices. Let s and t be their uniformizers. Let L/K and E/F be finite extensions such that…