314 research outputs found
Protein folding disorders: Toward a basic biological paradigm
Mechanistic 'physics' models of protein folding fail to account for the observed spectrum of protein folding and aggregation disorders, suggesting that a more appropriately biological paradigm will be needed for understanding the etiology, prevention, and treatment of these diseases
Some Examples of Minimal Groupoids on a Finite Set (Algebraic System, Logic, Language and Related Areas in Computer Science)
A minimal clone is an atom in the lattice of clones. The classification of minimal clones on a finite set still remains unsolved. A minimal groupoid is a minimal clone generated by a binary idempotent function. In this paper we report some examples of minimal groupoids generated by binary functions which resemble projections
HOMFLYPT Skein Theory, String Topology and 2-Categories
We show that relations in Homflypt type skein theory of an oriented
-manifold are induced from a -groupoid defined from the fundamental
-groupoid of a space of singular links in . The module relations are
defined by homomorphisms related to string topology. They appear from a
representation of the groupoid into free modules on a set of model objects. The
construction on the fundamental -groupoid is defined by the singularity
stratification and relates Vassiliev and skein theory. Several explicit
properties are discussed, and some implications for skein modules are derived.Comment: 55 pages, 1 figur
Endomorphisms of Koszul complexes: formality and application to deformation theory
We study the differential graded Lie algebra of endomorphisms of the Koszul resolution of a regular sequence on a unitary commutative K-algebra R and we prove that it is homotopy abelian over K but not over R (except trivial cases). We apply this result to prove an annihilation theorem for obstructions of (derived) deformations of locally complete intersection ideal sheaves on projective schemes
An introduction to moduli stacks, with a view towards Higgs bundles on algebraic curves
This article is based in part on lecture notes prepared for the summer school
"The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles" at the
Institute for Mathematical Sciences at the National University of Singapore in
July of 2014. The aim is to provide a brief introduction to algebraic stacks,
and then to give several constructions of the moduli stack of Higgs bundles on
algebraic curves. The first construction is via a "bootstrap" method from the
algebraic stack of vector bundles on an algebraic curve. This construction is
motivated in part by Nitsure's GIT construction of a projective moduli space of
semi-stable Higgs bundles, and we describe the relationship between Nitsure's
moduli space and the algebraic stacks constructed here. The third approach is
via deformation theory, where we directly construct the stack of Higgs bundles
using Artin's criterion.Comment: 145 pages, AMS LaTeX, to appear in the NUS IMS Lecture Note Series on
The Geometry, Topology, and Physics of Moduli Spaces of Higgs Bundle
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