Title:  On the flag enumeration of the subspace lattice

Abstract:  We consider the q-analogue of the Boolean algebra: the lattice of subspaces of an n-dimensional vector space over the finite field of q elements. Using the quasi-symmetric function of this lattice, we can evaluate a q-analogue of the classical descent set statistic in two cases. In one case, we express the values in terms of the classical descent set statistic and find the maximal value, extending De Bruijn and Niven's results in permutation enumeration. In the other, we compute the values for certain descent sets and conjecture when the maximum is obtained. Finally, when evaluating the quasi-symmetric function using a root of unity, we obtain a version of the cyclic sieving phenomenon on the Boolean algebra, due to Reiner, Stanton and White. This talk, which is based on joint work with Richard Ehrenborg, will include abundant examples and be accessible to anyone who has a minimal knowledge of combinatorics.

Title:  Homological Algebra with Filtered Module

Abstract:  Classical homological algebra begins with the study of projective and injective modules.  In this talk I will discuss analogous notions of projectivity and injectivity in a category of filtered modules.  In particular, projective and injective objects with respect to the restricted class of strict morphisms are defined and characterized.  Additionally, an analogue to the injective envelope is discussed with examples showing how this differs from the usual notion of an injective envelope.

Title:  Eigenvalue Multiplicities of the Hodge Laplacian on Coexact 2-Forms for Generic Metrics on 5-Manifolds

Abstract:  In 1976, Uhlenbeck used transversality theory to show that on a closed Riemannian manifold, the eigenvalues of the Laplace-Beltrami operator are all simple for a residual set of C^r metrics. In 2012, Enciso and Peralta-Salas established an analogue of Uhlenbeck's theorem for differential forms, showing that on a closed 3-manifold, there exists a residual set of C^r metrics such that the nonzero eigenvalues of the Hodge Laplacian on k forms are all simple.  We continue to address the question of whether Uhlenbeck's theorem can be extended to differential forms by proving that for a residual set of C^r metrics, the nonzero eigenvalues of the Hodge Laplacian acting on coexact 2-forms on a closed 5-manifold have multiplicity 2.  We structure our argument around a study of the Beltrami operator, using techniques from perturbation theory to show that the Beltrami operator has only simple eigenvalues for a residual set of metrics.  We further establish even eigenvalue multiplicities for the Hodge Laplacian acting on coexact k-forms in the more general setting n=4m+1 and k=2m.

"Dopaminergic and activity-dependent modulation of mechanosensory responses in Drosophila melanogaster larvae"

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While neutrons within nuclei may be stable, the free neutron is unstable against beta decay and has a mean lifetime of ~15min. Free neutron beta decay is, perhaps, the simplest weak nuclear process as it is uncomplicated by many body effects that are present in the decay of nuclei. As a result, it can be directly understood in terms of rather simple fundamental weak interaction theory. Additionally, because free neutron decay is the "prototype" for all nuclear beta decays, the neutron lifetime is a fundamental parameter whose value is important not only in nuclear physics, but also in astrophysics, cosmology, and particle physics. I will give an introduction to the theory of weak nuclear decay and briefly discuss the importance of the neutron lifetime as a parameter in the Big Bang. A review of the experimental strategies for the measurement of the neutron lifetime will be given as well as a discussion of the puzzling discrepancy among the measurements with the lowest quoted uncertainty. Finally, I present a very new result recently obtained at the NIST Cold Neutron Research Facility in Gaithersburg Md.

Diane Negra, Professor of Film Studies and Screen Culture and Head of Film Studies at University College Dublin, is an internationally prominent film scholar and feminist critic who has lectured on five continents about the political and economic dynamics of race and gender in contemporary film. She is the author, editor or co-editor of seven books: Off-White Hollywood: American Culture and Ethnic Female Stardom (2001), A Feminist Reader in Early Cinema (2002); The Irish in Us: Irishness, Performativity and Popular Culture (2006); Interrogating Postfeminism: Gender and the Politics of Popular Culture (2007); What a Girl Wants?: Fantasizing the Reclamation of Self in Postfeminism (2008); Old and New Media After Katrina (2010); and In the Limelight and Under the Microscope: Forms and Functions of Female Celebrity (2011).

Differing Perspectives on the Reconstruction of Proto-Indo-European's Accent and Ablaut System