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for events the day of Thursday, November 17, 2016.

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Thursday, November 17, 2016

11:00 am in 241 Altgeld Hall,Thursday, November 17, 2016

Consecutive primes and Beatty sequences

William Banks (University of Missouri)

Abstract: Beatty sequences are generalized arithmetic progressions which have been studied intensively in recent years. Thanks to the work of Vinogradov, it is known that every Beatty sequence S contains "appropriately many" prime numbers. For a given pair of Beatty sequences S and T, it is natural to wonder whether there are "appropriately many" primes in S for which the next larger prime lies in T. In this talk, I will show that this is indeed the case if one assumes a certain strong form of the Hardy-Littlewood conjectures. This is recent joint work with Victor Guo.

12:00 pm in Altgeld Hall 243,Thursday, November 17, 2016

The horofunction boundary of the lamplighter group

Gregory Kelsey (Bellarmine University)

Abstract: The horofunction boundary of a metric space is defined by embedding it in the space of continuous functions. This boundary frequently behaves more nicely than the visual boundary for spaces that are neither hyperbolic nor CAT(0). The lamplighter group is an amenable group with exponential growth that is neither hyperbolic nor CAT(0) and has provided many interesting examples and counterexamples in group theory. In joint work with Keith Jones, we fully describe the horofunction boundary of the lamplighter group with the word metric arising from its finite state automaton generating set.

12:30 pm in 464 Loomis Laboratory,Thursday, November 17, 2016

To Be Announced

Liam Fitzpatrick

2:00 pm in 243 Altgeld Hall,Thursday, November 17, 2016

Non-manifold monodromy spaces of branched covers between manifolds

Martina Aaltonen (University of Helsinki)

Abstract: Bernstein and Edmonds showed that every proper branched cover F between manifolds is a factor of a branched covering orbit map from a locally connected and locally compact Hausdorff space called the monodromy space of F. For proper branched covers between 2-manifolds the monodromy space is known to be a manifold. Together with Pankka we show that this does not generalize to dimension $3$ by constructing a self-map of the 3-sphere for which the monodromy space is not a locally contractible space.

3:00 pm in 243 Altgeld Hall,Thursday, November 17, 2016

Resolutions for powers of homogeneous ideals and applications to symbolic powers

Alexandra Seceleanu (University of Nebraska-Lincoln)

Abstract: I will discuss strategies for constructing graded free resolutions for powers of homogeneous ideals. It turns out that in the case of perfect ideals of height two the most naive strategy is also the most effective one. Knowledge of the resolutions obtained in this situation can be applied to classify ideals satisfying equality between their ordinary and symbolic powers. This is based on joint work with Cooper, Fatabbi, Guardo, Lorenzini, Migliore, Nagel, Szpond, and Van Tuyl.