Mathematics Department

Student Colloquia

Most Tuesday afternoons during the academic year, the Mathematics students host a math talk. The talks are directed to our mathematics majors but are usually accessible on a variety of levels. Refreshments are served before the talks.

2018-19 Schedule

Fall

4:40 in Physics 123 (unless marked otherwise).

Sept 11Putting the "k" in Curvature: k-Plane Constant Curvature Conditions
Maxine Calle

Classical differential geometry studies curvature of manifolds using the tools of calculus and linear algebra.  As manifolds locally resemble Euclidean space, we can investigate properties of a representative model space in order to describe the behavior of the manifold at a point.  The focus of my research this summer was to generalize the curvature invariants known as constant sectional curvature and constant vector curvature.  While both properties are well understood for 3-dimensional model spaces, not much is known with regard to higher dimensions. We generalize these curvature conditions using k-planes for model spaces of arbitrary finite dimension, and many results are generalizations of known aspects of 2-plane constant curvature conditions. By studying k-plane curvature, we can further characterize model spaces by generating representative numbers for various subspaces.

Sept 18Improved Differentially Private Analysis of Variance
Marika Swanberg

What does privacy look like in a data-driven world? More data is collected about individuals than ever before, and this trend will only continue. Differential privacy emerged after countless failed attempts at rigorous privacy definitions. It provides a mathematically rigorous framework for thinking about privacy. This summer, the ANOVA research team* improved the differentially private algorithm for ANOVA, a very widely-used statistical test. The Analysis of Variance (ANOVA) test is used to determine whether there is a statistically significant difference between groups. The F-statistic was proved to be the most powerful ANOVA test in the public setting; however, our work this summer shows that this does not hold in the private setting. Our modified F-statistic is 14 times more powerful than the traditional F-statistic in the private setting. This talk will provide an introduction to differential privacy and ANOVA, and an in-depth explanation of the improvements that we made to the F-statistic.

*Marika Swanberg, Ira Globus-Harris, Iris Griffith, Adam Groce, Andrew Bray, Anna Ritz

Spring

4:40 in Physics 123 (unless marked otherwise).

Seminar schedule coming soon.

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