arXiv subjects

Brian Weber

Publications and source records attributed to Brian Weber.

28 records · Page 2Linked to original sources

arXiv2018

The SFS Summer Research Study at UMBC: Project-Based Learning Inspires Cybersecurity Students

May 30-June 2, 2017, Scholarship for Service (SFS) scholars at the University of Maryland, Baltimore County (UMBC) analyzed the security of a targeted aspect of the UMBC computer systems. During this hands-on study, with complete access to source code, students identified vulnerabilities, devised and implemented exploits, and suggested mitigations. As part of a pioneering program at UMBC to extend SFS scholarships to community colleges, the study helped initiate six students from two nearby community colleges, who transferred to UMBC in fall 2017 to complete their four-year degrees in computer science and information systems. The study examined the security of a set of "NetAdmin" custom scripts that enable UMBC faculty and staff to open the UMBC firewall to allow external access to machines they control for research purposes. Students discovered vulnerabilities stemming from weak architectural design, record overflow, and failure to sanitize inputs properly. For example, they implemented a record-overflow and code-injection exploit that exfiltrated the vital API key of the UMBC firewall. This report summarizes student activities and findings, and reflects on lessons learned for students, educators, and system administrators. Our students found the collaborative experience inspirational, students and educators appreciated the authentic case study, and IT administrators gained access to future employees and received free recommendations for improving the security of their systems. We hope that other universities can benefit from our motivational and educational strategy of teaming educators and system administrators to engage students in active project-based learning centering on focused questions about their university computer systems.

cs.CR↗

arXiv2018

Topology of Kähler manifolds with weakly pseudoconvex boundary

We study Kahler manifolds-with-boundary, not necessarily compact, with weakly pseudoconvex boundary, each component of which is compact. If such a manifold $K$ has $l\ge2$ boundary components (possibly $l=\infty$), then it has first betti number at least $l-1$, and the Levi form of any boundary component is zero. If $K$ has $l\ge1$ pseudoconvex boundary components and at least one non-parabolic end, the first betti number of $K$ is at least $l$. In either case, any boundary component has non-vanishing first betti number. If $K$ has one pseudoconvex boundary component with vanishing first betti number, the first betti number of $K$ is also zero. Especially significant are applications to Kahler ALE manifolds, and to Kahler 4-manifolds. This significantly extends prior results in this direction (eg. Kohn-Rossi), and uses substantially simpler methods.

math.DG↗

arXiv2018

Energy and Asymptotics of Ricci-Flat 4-Manifolds with a Killing Field

Given a complete, Ricci-flat 4-manifold with a Killing field, we give an estimate on the manifold's energy in terms of a certain asymptotic quantity of the Killing field. If the Killing field has no zeros and satisfies a certain asymptotic condition, the manifold is flat.

math.DG↗

arXiv2015

Classification of polytope metrics and complete scalar-flat Kähler 4-Manifolds with two symmetries

We study unbounded 2-dimensional metric polytopes such as those arising as Kähler quotients of complete Kähler 4-manifolds with two commuting symmetries and zero scalar curvature. Under a mild closedness condition, we obtain a complete classification of metrics on such polytopes, and as a result classify all possible metrics on on the corresponding Kähler 4-manifolds. If the polytope is the plane or half-plane then only flat metrics are possible, and if the polytope has one corner then the 2-parameter family of generalized Taub-NUTs (discovered by Donaldson) are indeed the only possible metrics. Polytopes with $n\ge3$ edges admit an $(n+2)$-dimensional family of possible metrics.

math.DG↗

arXiv2013

Harnack Inequalities for Critical 4-manifolds with a Ricci Curvature Bound

We study critical Riemannian 4-manifolds with a lower bound on Ricci curvature, but no a priori analytic constraints such as on Sobolev constants. We derive elliptic-type estimates for the local curvature radius, which itself controls sectional curvature. The primary method is construction of blow-ups of degenerating metrics, followed by a geometric/topological triviality result from a previous work.

math.DG↗

arXiv2013

Curvature Estimates for Critical 4-Manifolds with a Lower Ricci Curvature Bound

We draw elliptic regularity results for 4-manifolds with an elliptic system, without Sobolev constant control. Direct use of analysis is circumvented; the results come mainly through geometric and topological arguments. In contrast to our previous paper, which worked predominantly on the scale of the curvature radius, the results here provide curvature controls on a fixed scale.

math.DG↗

arXiv2011

Regularity and convergence of 4-dimensional extremal Kahler metrics

We establish a regularity result for the metric on any 4-dimensional extremal Kähler manifold, and a weak compactness theorem on the space of such metrics. Specifically, the sectional curvature at a point is bounded when the quantity $L^2(|\Riem|)$ in a surrounding ball is sufficiently small compared to the pointwise norm of its scalar curvature. Consequently sequences of 4-dimensional extremal Kähler metrics with uniformly bounded Calabi energies and scalar curvature have convergent subsequences in the Gromov-Hausdorff topology. Gromov-Hausdorff limits are length spaces with the structure of Riemannian orbifolds away from finitely many point-like singularities of unknown structure.

math.DG↗

arXiv2008

Convergence of compact Ricci solitons

We show that sequences of compact gradient Ricci solitons converge to complete orbifold gradient solitons, assuming constraints on volume, the $L^{n/2}$-norm of curvature, and the auxiliary constant $C_1$. The strongest results are in dimension 4, where $L^2$ curvature bounds are equivalent to upper bounds on the Euler number. We obtain necessary and sufficient conditions for limits to be compact.

math.DG↗

arXiv2007

On Conformally Kaehler, Einstein Manifolds

We prove that any compact complex surface with positive first Chern class admits an Einstein metric which is conformally related to a Kaehler metric. The key new ingredient is the existence of such a metric on the blow-up of the complex projective plane at two distinct points.

math.DG↗

arXiv2007

Moduli spaces of critical Riemannian metrics with L^{n/2} norm curvature bounds

We consider the moduli space of the extremal Kähler metrics on compact manifolds. We show that under the conditions of two-sided total volume bounds, $L^{n\over2}$-norm bounds on $\Riem$, and Sobolev constant bounds, this Moduli space can be compactified by including (reduced) orbifolds with finitely many singularities. Most of our results go through for certain other classes of critical Riemannian metrics.

math.DG↗