| Wed, Aug 26, 2026
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Lie Groups Seminar
3:30 PM
MSCS 514 | | Organizational Meeting
| | | Abstract: We will meet to plan the semester's talks. If you're interested in giving a talk, please feel free to come by, or reach out to Melissa Emory via e-mail.
The seminar covers Lie groups, representation theory, invariant theory, combinatorics, and automorphic forms — five deeply interconnected areas at the heart of modern mathematics. Lie groups sit at the crossroads of algebra, geometry, and analysis: they are groups that are also smooth manifolds, making them the natural language for describing continuous symmetry. Representation theory studies these and other algebraic structures by realizing them as linear transformations of vector spaces, allowing abstract symmetry to be analyzed using the tools of linear algebra. Invariant theory examines the quantities and structures that remain unchanged under group actions, providing a powerful bridge between abstract symmetry and concrete algebraic and geometric objects. Combinatorics contributes the discrete structures — such as root systems, Weyl groups, and crystal bases — that encode and organize much of this symmetry, offering combinatorial models for objects that are otherwise defined analytically or algebraically. Automorphic forms are highly symmetric functions that connect number theory and representation theory by encoding arithmetic information in forms that can be studied through symmetry. The interaction among these areas has led to major advances on longstanding problems and remains one of the central themes of modern mathematics, with connections reaching from number theory and harmonic analysis to the symmetries underlying quantum mechanics and particle physics. |
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Mathematics Seminars and Colloquia