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This paper discusses the twisted conjugacy classes in loop groups. We restrict to classical groups and give some explicit classifications. [ABSTRACT FROM AUTHOR]

In this paper, we compare the virtual fundamental classes of the stacks of (g, β, μ)-stable ramified maps ,Ug, μ(X, β) and of (g, β, μ)-log stable ramified maps Ulog g,μ(X, β). For that we will see how they are identified via virtual normalization and then apply Costello's push-forward formula. [ABSTRACT FROM AUTHOR]

The intent of this paper is to present a set of axioms that are sufficient for a closure operation to generate a balanced big Cohen-Macaulay module $ B$. Conversely, we show that if such a $ B$, then there exists a closure operation that satisfies the given axioms. [ABSTRACT FROM AUTHOR]

In this short paper we prove that, for $3 le N le 9$, the problem $ -Delta u = e^u$ on the entire Euclidean space $mathbb {R}^N$ does not admit any solution stable outside a compact set of $mathbb {R}^N$. This result is obtained without making any assumption about the boundedness of solutions. Furthermore, as a consequence of our analysis, we also prove the non-existence of finite Morse Index solutions for the considered problem. We then use our results to give some applications to bounded domain problems. [ABSTRACT FROM AUTHOR]

In this paper we describe an algorithm for producing infinitely many examples of set-theoretic complete intersection monomial curves in $mathbb {P}^{n+1}$, starting with a single set-theoretic complete intersection monomial curve in $mathbb {P}^{n}$. Moreover we investigate the numerical criteria to decide when these monomial curves can or cannot be obtained via semigroup gluing. [ABSTRACT FROM AUTHOR]