Georgia Institute of Technology College of Sciences

Lopsided bipartite graphs naturally appear in advertising setting. One side is all the eyeballs and the other side is all the advertisers. An edge is when an advertiser wants to reach an eyeball, aka, ad targeting. Such a bipartite graph is lopsided because there are only a small number of advertisers but a large number of eyeballs. We give algorithms which have running time proportional to the size of the smaller side, i.e., the number of advertisers. One of the main ideas behind our algorithm and as well as the analysis is a property, which we call, monotonic quality bounds. Our algorithm is flexible as it could easily be adapted for different kinds of objective functions. Towards the end of the talk we will describe a new matching polytope. We show that our matching polytope is not only a new linear program describing the classical matching polytope, but is a new polytope together with a new linear program. This part of the talk is still theoretical as we only know how to solve the new linear program via an ellipsoid algorithm. One feature of the polytope, besides being intriguing, is that it has some notion of fairness built in. This is important for advertising since if an advertiser wants to reach 10 million users of type A or type B, advertiser won't necessarily be happy if we show the ad to 10 million users of type A only (though it fulfills the advertising contract in a technical sense).

East Coast Computer Algebra Day (ECCAD) is an informal one-day meeting for those active or interested in computer algebra. It provides opportunities to learn and to share new results and work in progress.  The schedule includes invited speakers, a panel discussion, and contributed posters and software demonstrations. Importantly, plenty of time is allowed for unstructured interaction among the participants.  Researchers, teachers, students, and users of computer algebra are all welcome! Visit ECCAD for more details.

Abstract expressionism is a post–World War II art movement in American painting, developed in New York in the 1940s. It was the first specifically American movement to achieve international influence and put New York City at the center of the western art world, a role formerly filled by Paris.

Let k be a global field or a local field. Class field theory says that every central division algebra over k is cyclic. Let l be a prime not equal to the characteristic of k. If k contains a primitive l-th root of unity, then this leads to the fact that every element in H^2(k, µ_l ) is a symbol. A natural question is a higher dimensional analogue of this result: Let F be a function field in one variable over k which contains a primitive l-th root of unity. Is every element in H^3(F, µ_l ) a symbol? In this talk we answer this question in affirmative for k a p-adic field or a global field of positive characteristic. The main tool is a certain local global principle for elements of H^3(F, µ_l ) in terms of symbols in H^2(F µ_l ). We also show that this local-global principle is equivalent to the vanishing of certain unramified cohomology groups of 3-folds over finite fields.