Mathematics & Computer Science

Seminars and Colloquia

Monday, September 26, 2016

04:45 pm - 06:00 pm

Logic Seminar

Philip Scowcroft, Wes: " Abelian lattice-ordered groups with at most finitely many pairwise disjoint elements." Abstract : Conrads characterization (1960) of the lattice-ordered groups with at most finitely many pairwise disjoint elements yields model-completions for various theories of such groups. A corresponding Nullstellensatz, and various quantifier-elimination results, assume stronger forms when restricted to special groups in the class.

Exley Science Center Tower ESC 638

Tuesday, September 27, 2016

04:15 pm - 05:15 pm

Algebra Seminar

Bweong-Kweon Oh (Seoul National University): The number of representations of squares by integral quadratic forms Abstract: Let f be a positive definite integral ternary quadratic form and let r ( k , f ) be the number of representatives of an integer k by f . We say that the genus of f is indistinguishable by squares if for any integer n , r ( n 2 , f ) = r ( n , f ) for any quadratic form f in the genus of f . In this talk, we will give some examples of non trivial genera of ternary quadratic forms which are indistinguishable by squares. Also, we give some relations between indistinguishable genera by squares and a conjecture by Cooper and Lam, and we resolve their conjecture completely. This is a joint work with Kyoungmin Kim.

Exley Science Center Tower ESC 618

Wednesday, September 28, 2016

04:20 pm - 05:30 pm

Topology Seminar

Dave Constantine, Wes: " Hausdorff dimension and the CAT(K) condition for surfaces" Abstract: A geodesic metric space satisfies the CAT(K) condition if its geodesic triangles are all `thinner' than triangles with the same side lengths in the model space of constant Riemannian curvature K. This condition allows one to extend many arguments relying on an upper curvature bound from Riemannian geometry to the metric space setting. How `strange' can a metric be while still satisfying the CAT(K) property? One way to measure this is with the difference between the topological dimension of the space and its Hausdorff dimension with respect to the metric. In this talk I'll show that, at least for surfaces, a CAT(K) metric is tame in the sense that it yields Hausdorff dimension 2. I'll also provide some motivation for this question by showing how results like this allow one to extend volume entropy rigidity statements to the CAT(-1) setting.

Exley Science Center Tower ESC 638