Title:  Matroids in Algebra and Geometry

Abstract:  Matroids are combinatorial structures that generalize the notion of independence in linear algebra and graph theory.  Rota conjectured that certain invariants of a matroid should always form a log concave sequence.  We will report on recent work of Adripasato, Huh, and Katz, in which they use techniques from algebra and geometry to prove Rota's Conjecture.

Lunch Workshop: 12:00 - 1:30 p.m., 105 Breckinridge Hall. Interested attendees should contact Dr. Marion Rust in advance for a copy of the paper at marion.rust@uky.edu.

Dr. Mahmood Mamdani is a distinguished public intellectual who has made important scholarly contributions to colonial and post-colonial theory, African politics, and a range of critical contemporary issues such as the "war on terror" and the roots of genocide. Dr. Mamdani is Herbert Lehman Professor of Government at the School of International and Public Affairs and Professor of Anthropology, Political Science and African Studies at Columbia University. He maintains his involvement with the intellectualand political life of his native Uganda as Director of the Makerere Institute of Social Research (MISR) at Makerere University, in Kampala. Dr. Mamdani has written a number of important books that address the intersection between culture, identity, power, and politics, including Citizen and Subject: Contemporary Africa and The Legacy of Late Colonialism (1996), When Victims become Killers: Colonialism, Nativism, and the Genocide in Rwanda (2001), Good Muslim, Bad Muslim: America, the Cold War, and the Roots of Terror (2005), and Saviors and Survivors: Darfur, Politics, and the War on Terror (2010).

Title:  Singular Value Computation and Subspace Clustering

Abstract:  In this dissertation we discuss two problems. In the First part, we consider the problem of computing a few extreme singular values of a symmetric defnite generalized eigenvalue problem or a large and sparse matrix C. Most existing numerical methods are based on reformulating the singular value problem as an equivalent symmetric eigenvalue problem. The standard method of choice of computing a few extreme eigenvalues of a large symmetric matrix is the Lanczos or the implicitly restarted Lanczos method. These methods usually employ a shift-and-invert transformation to accelerate the speed of convergence, which is not practical for truly large problems. With this in mind, Golub and Ye proposes an inverse-free preconditioned Krylov subspace method, which uses preconditioning instead of shift-and-invert to accelerate the convergence. The inverse-free Krylov subspace method focuses on the computation of one extreme eigenvalue and a deflation technique is needed to compute additional eigenvalues. The Wielandt deflation has been considered and can be used in a straightforward manner. However, the Wielandt deflation alters the structure of the problem and may cause some difficulties in certain applications such as the singular value computations. So we First propose to consider a deformation by restriction method for the inverse-free Krylov subspace method. We generalize the original convergence theory for the inverse-free preconditioned Krylov subspace method to justify this deflation scheme. We next extend the inverse-free Krylov subspace method with deflation by restriction to the singular value problem. We consider preconditioning based on robust incomplete factorization to accelerate the convergence. Numerical examples are provided to demonstrate effciency and robustness of the new algorithm.

In the second part of this thesis, we consider the so-called subspace clustering problem, which aims for extracting a multi-subspace structure from a collection of points lying in a high-dimensional space. Recently, methods based on Self Expressive Property(SEP) such as Sparse Subspace Clustering(SSC) and Low Rank Representations( LRR) have been shown to enjoy superior performances than other methods. Self Expressive Property means the points can be expressed as linear combinations of themselves. However, methods with SEP may result in representations that are not amenable to clustering through graph partitioning. We propose a method where the points are expressed in terms of an orthonormal basis. The orthonormal basis is optimally chosen in the sense that the representation of all points is sparsest. Nnumerical results are given to illustrate the effectiveness and effciency of this method. 

Title:  Large-Scale Boundary Regularity Estimates in Periodic Homogenization

Abstract:  In this talk I will discuss some of recent progress on boundary regularity at large scale in homogenization of second-order elliptic systems in divergence form with rapidly oscillating periodic coecients. Here we are interested in the estimates, due to homogenization, for operators with bounded measurable coecients. These large-scale estimates, combined with the small-scale estimates obtained by rescaling, lead to the sharp regularity estimates at all scales.  In particular, the cases of the Rellich estimates in Lipschitz domains and the Lipschitz estimates in C1; domains will be presented.

WELCOME BACK CADETS!

Welcome all new cadets and we are happy to see that the Fall Semester 2015 is already moving along. We are excited to see all the new faces, and definitely all the old faces and hope everyone is adjusting well back to campus and with their courses. The AFROTC Cadre are here to help you succeed and answer any and all questions you may have. 

Please stop by and say hello, and we will see you all on Thursday. 

Enjoy your week everyone!!!

"Tell me again about Europe and her pains, 

  Who's tortured by the drought, who by the rains.

  Glut me with floods where only the swine can row" -- William Empson

Europe is in crisis, deep economic and political crisis. With many member-state economies now tottering on zero-growth meltdown, professional politicians and economists persist with austerity drives and devise ideological covers for the continued plundering of public resources. Frack capitalism power-drills into the public realm, extorting value from erstwhile common property. A para-state of technocrats and Euro-bureaucrats, meanwhile, governs, "sending us rain and sunshine from above" (Marx). One big problem such professional representation poses for ordinary Europeans -- for people I shall call amateur shadow citizens -- is PARTICIPATION. Shadow citizens are disenfranchised Euro-citizens who express a citizenship waiting in the wings, a potential solidarity haunting the mainstream, floating across frontiers and through designated checkpoints. This lecture investigates the dialectic between professional austerians and shadow citizens, doing so while attempting to put a fresh spin on Henri Lefebvre's "late" ideal that the right to the city is "nothing less than a new conception of revolutionary citizenship."

Andy Merrifield, Supernumerary Fellow in Human Geography, Murray Edwards College, University of Cambridge

Andy Merrifield is a writer, social theorist, and urban geographer. He has taught human geography at the University of Southampton, King's College, London, and Clark University in Massachusetts, and has been a visiting scholar at Johns Hopkins University, Baltimore, the University of California, Los Angeles (UCLA), the University of Sao Paulo, Brazil, the University of Manchester (as Leverhulme Visiting Professor), and the City University of New York CUNY). For a number of years, he was a freelance writer living in France, where he wrote biographies of Guy Debord and Henri Lefebvre, as well as a bestselling "existential" travelogue, The Wisdom of Donkeys. He is author of nine books; his articles, essays, and reviews have appeared in the Times, The Nation, Harper's Magazine, New Left Review, Adbusters, Harvard Design Magazine, Radical Philosophy, Monthly Review, and Dissent, amongst others.