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Articles 1 - 7 of 7
Full-Text Articles in Physical Sciences and Mathematics
Regularity Of Mean Curvature Flow Of Graphs On Lie Groups Free Up To Step 2, Luca Capogna, Giovanna Citti, Maria Manfredini
Regularity Of Mean Curvature Flow Of Graphs On Lie Groups Free Up To Step 2, Luca Capogna, Giovanna Citti, Maria Manfredini
Mathematics Sciences: Faculty Publications
We consider (smooth) solutions of the mean curvature flow of graphs over bounded domains in a Lie group free up to step two (and not necessarily nilpotent), endowed with a one parameter family of Riemannian metrics σ ε collapsing to a subRiemannian metric σ0 as ε → 0. We establish Ckα estimates for this flow, that are uniform as ε → 0 and as a consequence prove long time existence for the subRiemannian mean curvature flow of the graph. Our proof extend to the setting of every step two Carnot group (not necessarily free) and can be adapted following …
Quantum Mechanical Derivation Of The Wallis Formula For Π, Tamar Friedmann, C. R. Hagen
Quantum Mechanical Derivation Of The Wallis Formula For Π, Tamar Friedmann, C. R. Hagen
Mathematics Sciences: Faculty Publications
A famous pre-Newtonian formula for π is obtained directly from the variational approach to the spectrum of the hydrogen atom in spaces of arbitrary dimensions greater than one, including the physical three dimensions.
The Robinson-Schensted Correspondence And A2-Web Bases, Matthew Housley, Heather M. Russell, Julianna Tymoczko
The Robinson-Schensted Correspondence And A2-Web Bases, Matthew Housley, Heather M. Russell, Julianna Tymoczko
Mathematics Sciences: Faculty Publications
We study natural bases for two constructions of the irreducible representation of the symmetric group corresponding to [n, n, n]: the reduced web basis associated to Kuperberg’s combinatorial description of the spider category; and the left cell basis for the left cell construction of Kazhdan and Lusztig. In the case of [n, n], the spider category is the Temperley-Lieb category; reduced webs correspond to planar matchings, which are equivalent to left cell bases. This paper compares the image of these bases under classical maps: the Robinson–Schensted algorithm between permutations and Young tableaux and Khovanov–Kuperberg’s bijection between Young tableaux and reduced …
Modular Classes Of Lie Groupoid Representations Up To Homotopy, Rajan Amit Mehta
Modular Classes Of Lie Groupoid Representations Up To Homotopy, Rajan Amit Mehta
Mathematics Sciences: Faculty Publications
We describe a construction of the modular class associated to a representation up to homotopy of a Lie groupoid. In the case of the adjoint representation up to homotopy, this class is the obstruction to the existence of a volume form, in the sense of Weinstein’s “The volume of a differentiable stack”.
The Atiyah Class Of A Dg-Vector Bundle, Rajan Amit Mehta, Mathieu Stiénon, Ping Xu
The Atiyah Class Of A Dg-Vector Bundle, Rajan Amit Mehta, Mathieu Stiénon, Ping Xu
Mathematics Sciences: Faculty Publications
We introduce the notions of Atiyah class and Todd class of a differential graded vector bundle with respect to a differential graded Lie algebroid. We prove that the space of vector fields X(M) on a dg-manifold M with homological vector field Q admits a structure of L∞[1]-algebra with the Lie derivative LQ as unary bracket λ1, and the Atiyah cocycle AtM corresponding to a torsion-free affine connection as binary bracket λ2.
Vassiliev Invariants Of Virtual Legendrian Knots, Patricia Cahn, Asa Levi
Vassiliev Invariants Of Virtual Legendrian Knots, Patricia Cahn, Asa Levi
Mathematics Sciences: Faculty Publications
We introduce a theory of virtual Legendrian knots. A virtual Legendrian knot is a cooriented wavefront on an oriented surface up to Legendrian isotopy of its lift to the unit cotangent bundle and stabilization and destabilization of the surface away from the wavefront. We show that the groups of Vassiliev invariants of virtual Legendrian knots and of virtual framed knots are isomorphic. In particular, Vassiliev invariants cannot be used to distinguish virtual Legendrian knots that are isotopic as virtual framed knots and have equal virtual Maslov numbers.
Triangle-Free Uniquely 3-Edge Colorable Cubic Graphs, Sarah-Marie Belcastro, Ruth Haas
Triangle-Free Uniquely 3-Edge Colorable Cubic Graphs, Sarah-Marie Belcastro, Ruth Haas
Mathematics Sciences: Faculty Publications
This paper presents infinitely many new examples of triangle-free uniquely 3-edge colorable cubic graphs. The only such graph previously known was given by Tutte in 1976.