The talks will typically take place on Tuesdays at 4:00-5:00pm in Adel Room 164. Please contact Nandor Sieben if you would like to give a talk or have a question about the colloquium.
Short organizational meeting
Speaker: Jin Wang Title: Generalized Depth-Based Trimmed Means and Trimmed Scatter Matrices (Sabbatical report)
Abstract: Multivariate descriptive measures for location and scatter are the foundation of multivariate statistics and underpin almost all methods in the field. In this paper, we propose and study new general depth-based trimmed means and scatter matrices, along with their sample versions (estimators). In addition to their basic properties, we establish the strong consistency and asymptotic distributions of these estimators. Using the asymptotic distributions, we compute the asymptotic relative efficiencies of the sample trimmed means and sample trimmed scatter matrices based on the halfspace depth, with respect to the sample mean vector and the sample covariance matrix, respectively. Robustness is explored through influence function and finite-sample breakdown point. The results show that the sample trimmed means and scatter matrices are not only highly efficient but also exceptionally robust, making them highly competitive estimators for multivariate location and scatter.
Speaker: Annie Boyd, Ben Jefferies, Gina Nabours Title: LMC data
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Speaker: Mikhail Baltushkin Title: Isomorphism theorems for gamegraphs
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Speaker: Giorgio Cipolloni (UA) Title:
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Speaker: Andrew Schultz (Wellesley College) Title: Galois module structure of psth power classes of a field
Abstract: When a field $K$ contains a primitive $p$ th root of unity, Kummer theory tells us that the $\mathbb{F}_p$-space $K^{\times p}/K^\times$ is a parameterizing space for elementary $p$-abelian extensions of $K$. In previous work, the authors computed the Galois module structure of this set when the Galois group came from an extension $K/F$ whose Galois group is isomorphic to $\mathbb{Z}/p^n\mathbb{Z}$. In this talk we consider the more refined group $K^{\times p^s}/K^\times$ as a Galois module, and we determine its structure. Although the modular representation theory in this case is unwieldy, it turns out that there is only one summand in the decomposition of $K^{\times p^s}/K^\times$ which is not free (either under the full ring or one of its natural quotients). Furthermore, this “exceptional” summand’s structure is connected to the cyclotomic character and a certain family of embedding problems along the tower $K/F$. This work is joint with J'{a}n Min'{a}\v{c} and John Swallow.
Speaker: Jim Swift Title:
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Speaker: Joe Polman (CU Boulder) CSTL STEM Education speaker series Title:
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Speaker: Jeff Hovermill Title:
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Speaker: UGRADS Robert Title:
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