# Lie Theory

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More about Lie theory

Lie theory is a branch of mathematics devoted to the study of symmetries that occur throughout mathematics and science.

For example the ancient classification of Platonic solids is seen nowadays as an instance of finding all ''finite symmetries`` in three-dimensional space. More recently the study of "continuous symmetries" of mathematical objects and structures known as Lie groups, introduced by Sophus Lie in the 1880's to study differential equations, has influenced many scientific disciplines.

One fundamental problem involves describing and classifying the structure and geometry of those symmetries and their various generalizations. Lie theory is also vital to number theory, differential equations, differential geometry, dynamical systems, and many other areas of mathematics and its applications.

## Seminars

- Geometric methods in Langlands program seminar: Mondays from 4:30–6pm
- HAAR (Harmonic Analysis and Automorphic Representations) seminar: Mondays at 7pm
- Lie Theory Seminar

## Faculty

### Scot Adams

Professor

adams005@umn.edu

dynamical systems, foliations, ergodic theory, hyperbolic groups, trees, Riemannian geometry

### Benjamin Brubaker

Professor

brubaker@umn.edu

automorphic forms, p-adic representations, combinatorial representation theory, statistical lattice models

### Michelle Chu

Assistant Professor

mchu@umn.edu

hyperbolic geometry, low-dimensional topology, geometric group theory, and arithmetic groups

### Paul Garrett

Professor

garrett@umn.edu

automorphic forms, L-functions, representations, harmonic analysis, number theory

### Dihua Jiang

Professor

dhjiang@umn.edu

automorphic forms, L-functions, number theory, harmonic analysis, representation theory

### William Messing

Professor Emeritus

messing@umn.edu

p-adic Galois representations associated with algebraic varieties via étale cohomology, the connections between the latter and de Rham cohomology

### Peter Olver

Professor

olver@umn.edu

Lie groups, differential equations, computer vision, applied mathematics, differential geometry, mathematical physics

_{Photo: © 2007 John Stembridge}