Upcoming Seminars

Title: Riemannian Geometry and Biomedical Data
Seminar: Mathematics
Speaker: Sima Ahsani of Emory University
Contact: Bree Ettinger, betting@emory.edu
Date: 2022-01-28 at 10:00AM
Venue: MSC W201 and Zoom
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Abstract:
Statistics is a science for everyone who wishes to collect, analyze, interpret, and understand data. Over the last few years, due to rapid technological developments, we handle increasingly large and complex data. For example, understanding biomedical data, that lie on matrix manifolds, in order to early detection of disease to prevent, control, or provide improved health care with low costs. Therefore, one of the most important steps in analyzing this type of data is understanding the structure of the surfaces where data live on them. To this end, differential geometry allows us to develop local methods to understand the global properties of surfaces that data lie on them. In this talk, after giving some examples of datasets that lie on curved spaces, I will provide an intuitive definition of Riemannian manifolds and their basic properties. Then, I will describe matrix manifolds and explain how to measure distances between two points and challenges that may arise when we want to calculate the mean of datasets and mention techniques that can be used to tackle these challenges. In the end, some resources and content will be provided to engage undergraduate students to know more about this research area to find the right way to develop their ideas and interest and take steps to build their future research areas.
Title: Geometric Group Theory and Untangling Earphones
Seminar: Mathematics
Speaker: Neha Gupta of Georgia Institute of Technology
Contact: Bree Ettinger, betting@emory.edu
Date: 2022-02-02 at 10:00AM
Venue: MSC W201 and Zoom
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Abstract:
Suppose you get your earphones entangled around a doughnut with two holes... an entirely probable scenario, right?! Then how "big" does your doughnut need to be, for you to successfully untangle your earphones? This is going to be a gentle introduction to groups, and how they connect to geometry. We will slowly build up to answering our original question. No prior experience with groups, geometry, or topology is required or assumed. This is joint work with Ilya Kapovich.
Title: Euler’s Polyhedron Formula and The Euler Characteristic
Seminar: Mathematics
Speaker: Daniel Hess of University of Chicago
Contact: Bree Ettinger, betting@emory.edu
Date: 2022-02-04 at 10:00AM
Venue: MSC W201 and Zoom
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Abstract:
A standard soccer ball is constructed using 12 regular pentagons and 20 regular hexagons. Is it possible to build one using only pentagons? How about only hexagons? It turns out that one of these is possible and one is not! The key to answering these questions is Euler’s Polyhedron Formula, which expresses a certain relationship between the number of vertices, edges, and faces in any convex polyhedron. In this talk, we will discuss this formula, the more general Euler characteristic, and applications such as the classification of the Platonic solids and triangulations of surfaces.