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Articles 1 - 12 of 12
Full-Text Articles in Other Mathematics
General Covariance With Stacks And The Batalin-Vilkovisky Formalism, Filip Dul
General Covariance With Stacks And The Batalin-Vilkovisky Formalism, Filip Dul
Doctoral Dissertations
In this thesis we develop a formulation of general covariance, an essential property for many field theories on curved spacetimes, using the language of stacks and the Batalin-Vilkovisky formalism. We survey the theory of stacks, both from a global and formal perspective, and consider the key example in our work: the moduli stack of metrics modulo diffeomorphism. This is then coupled to the Batalin-Vilkovisky formalism–a formulation of field theory motivated by developments in derived geometry–to describe the associated equivariant observables of a theory and to recover and generalize results regarding current conservation.
Evolutionary Dynamics Of Bertrand Duopoly, Julian Killingback, Timothy Killingback
Evolutionary Dynamics Of Bertrand Duopoly, Julian Killingback, Timothy Killingback
Computer Science Department Faculty Publication Series
Duopolies are one of the simplest economic situations where interactions between firms determine market behavior. The standard model of a price-setting duopoly is the Bertrand model, which has the unique solution that both firms set their prices equal to their costs-a paradoxical result where both firms obtain zero profit, which is generally not observed in real market duopolies. Here we propose a new game theory model for a price-setting duopoly, which we show resolves the paradoxical behavior of the Bertrand model and provides a consistent general model for duopolies.
Real-Time Dengue Forecasting In Thailand: A Comparison Of Penalized Regression Approaches Using Internet Search Data, Caroline Kusiak
Real-Time Dengue Forecasting In Thailand: A Comparison Of Penalized Regression Approaches Using Internet Search Data, Caroline Kusiak
Masters Theses
Dengue fever affects over 390 million people annually worldwide and is of particu- lar concern in Southeast Asia where it is one of the leading causes of hospitalization. Modeling trends in dengue occurrence can provide valuable information to Public Health officials, however many challenges arise depending on the data available. In Thailand, reporting of dengue cases is often delayed by more than 6 weeks, and a small fraction of cases may not be reported until over 11 months after they occurred. This study shows that incorporating data on Google Search trends can improve dis- ease predictions in settings with severely …
Kazhdan-Lusztig Cells In Planar Hyperbolic Coxeter Groups And Automata, Mikhail V. Belolipetsky, Paul E. Gunnells, Richard A. Scott
Kazhdan-Lusztig Cells In Planar Hyperbolic Coxeter Groups And Automata, Mikhail V. Belolipetsky, Paul E. Gunnells, Richard A. Scott
Paul Gunnells
Let C be a one- or two-sided Kazhdan–Lusztig cell in a Coxeter group (W, S), and let Red(C) be the set of reduced expressions of all w ∈ C, regarded as a language over the alphabet S. Casselman has conjectured that Red(C) is regular. In this paper, we give a conjectural description of the cells when W is the group corresponding to a hyperbolic polygon, and show that our conjectures imply Casselman's.
Generalised Burnside Rings, G-Categories And Module Categories, Paul E. Gunnells, Andrew Rose, Dmitriy Rumynin
Generalised Burnside Rings, G-Categories And Module Categories, Paul E. Gunnells, Andrew Rose, Dmitriy Rumynin
Paul Gunnells
This note describes an application of the theory of generalised Burnside rings to algebraic representation theory. Tables of marks are given explicitly for the groups S4 and S5 which are of particular interest in the context of reductive algebraic groups. As an application, the base sets for the nilpotent element F4(a3) are computed.
Resolutions Of The Steinberg Module For Gl(N), Avner Ash, Paul E. Gunnells, Mark Mcconnell
Resolutions Of The Steinberg Module For Gl(N), Avner Ash, Paul E. Gunnells, Mark Mcconnell
Paul Gunnells
We give several resolutions of the Steinberg representation St_n for the general linear group over a principal ideal domain, in particular over Z. We compare them, and use these results to prove that the computations in [AGM4] are definitive. In particular, in [AGM4] we use two complexes to compute certain cohomology groups of congruence subgroups of SL(4,Z). One complex is based on Voronoi's polyhedral decomposition of the symmetric space for SL(n,R), whereas the other is a larger complex that has an action of the Hecke operators. We prove that both complexes allow us to compute the relevant cohomology groups, and …
Torsion In The Cohomology Of Congruence Subgroups Of Sl (4. Z) And Galois Representations, Avner Ash, Paul E. Gunnells, Mark Mcconnell
Torsion In The Cohomology Of Congruence Subgroups Of Sl (4. Z) And Galois Representations, Avner Ash, Paul E. Gunnells, Mark Mcconnell
Paul Gunnells
We report on the computation of torsion in certain homology theories of congruence subgroups of SL(4,Z). Among these are the usual group cohomology, the Tate–Farrell cohomology, and the homology of the sharbly complex. All of these theories yield Hecke modules. We conjecture that the Hecke eigenclasses in these theories have attached Galois representations. The interpretation of our computations at the torsion primes 2, 3, 5 is explained. We provide evidence for our conjecture in the 15 cases of odd torsion that we found in levels ⩽31.
On The Nondegeneracy Of Constant Mean Curvature Surfaces, Nick Korevaar, Robert Kusner, Jesse Ratzkin
On The Nondegeneracy Of Constant Mean Curvature Surfaces, Nick Korevaar, Robert Kusner, Jesse Ratzkin
Robert Kusner
We prove that many complete, noncompact, constant mean curvature (CMC) surfaces $f:\Sigma \to \R^3$ are nondegenerate; that is, the Jacobi operator Δf+|Af|2 has no L2 kernel. In fact, if Σ has genus zero and f(Σ) is contained in a half-space, then we find an explicit upper bound for the dimension of the L2 kernel in terms of the number of non-cylindrical ends. Our main tool is a conjugation operation on Jacobi fields which linearizes the conjugate cousin construction. Consequences include partial regularity for CMC moduli space, a larger class of CMC surfaces to use in gluing constructions, and a surprising …
Conformal Structures And Necksizes Of Embedded Constant Mean Curvature Surfaces, Robert Kusner
Conformal Structures And Necksizes Of Embedded Constant Mean Curvature Surfaces, Robert Kusner
Robert Kusner
Let M = M_{g,k} denote the space of properly (Alexandrov) embedded constant mean curvature (CMC) surfaces of genus g with k (labeled) ends, modulo rigid motions, endowed with the real analytic structure described in [kmp]. Let P=Pg,k=rg,k×Rk+ be the space of parabolic structures over Riemann surfaces of genus g with k (marked) punctures, the real analytic structure coming from the 3g-3+k local complex analytic coordinates on the Riemann moduli space r_{g,k}. Then the parabolic classifying map, Phi: M --> P, which assigns to a CMC surface its induced conformal structure and asymptotic necksizes, is a proper, real analytic map. It …
The Topology, Geometry And Conformal Structure Of Properly Embedded Minimal Surfaces, Pascal Collin, Robert Kusner, William H. Meeks, Harold Rosenberg
The Topology, Geometry And Conformal Structure Of Properly Embedded Minimal Surfaces, Pascal Collin, Robert Kusner, William H. Meeks, Harold Rosenberg
Robert Kusner
This paper develops new tools for understanding surfaces with more than one end and infinite topology which are properly minimally embedded in Euclidean three-space. On such a surface, the set of ends forms a totally disconnected compact Hausdorff space, naturally ordered by the relative heights of the ends in space. One of our main results is that the middle ends of the surface have quadratic area growth, and are thus not limit ends. This implies that the surface can have at most two limit ends, which occur at the top and bottom of the ordering, and thus only a countable …
The Second Hull Of A Knotted Curve, Jason Cantarella, Greg Kuperberg, Robert B. Kusner, John M. Sullivan
The Second Hull Of A Knotted Curve, Jason Cantarella, Greg Kuperberg, Robert B. Kusner, John M. Sullivan
Robert Kusner
The convex hull of a set K in space consists of points which are, in a certain sense, "surrounded" by K. When K is a closed curve, we define its higher hulls, consisting of points which are "multiply surrounded" by the curve. Our main theorem shows that if a curve is knotted then it has a nonempty second hull. This provides a new proof of the Fary/Milnor theorem that every knotted curve has total curvature at least 4pi.
The Moduli Space Of Complete Embedded Constant Mean Curvature Surfaces, Robert Kusner, Rafe Mazzeo, Daniel Pollack
The Moduli Space Of Complete Embedded Constant Mean Curvature Surfaces, Robert Kusner, Rafe Mazzeo, Daniel Pollack
Robert Kusner
We examine the space of surfaces in $\RR^{3}$ which are complete, properly embedded and have nonzero constant mean curvature. These surfaces are noncompact provided we exclude the case of the round sphere. We prove that the space $\Mk$ of all such surfaces with k ends (where surfaces are identified if they differ by an isometry of $\RR^{3}$) is locally a real analytic variety. When the linearization of the quasilinear elliptic equation specifying mean curvature equal to one has no L2−nullspace we prove that $\Mk$ is locally the quotient of a real analytic manifold of dimension 3k−6 by a finite group …