What exactly do mathematics researchers think about all day? The Lab of Geometry at Michigan, LoG(M), invites you to meet, explore, and answer questions posed by today's mathematicians.

LoG(M) is a semester-long mathematics research and computing experience for qualified undergraduates at the University of Michigan. LoG(M) projects are developed and mentored by various faculty and graduate students in the mathematics department at the University of Michigan. The topics of each project vary widely, but are unified by experimental methods that involve some visualization, computing, or examples, and are motivated by open questions in modern mathematics research. Researchers work in a team of three or four undergraduates.

Researchers in LoG(M) enroll in the course Math 440 and meet weekly with the Director of LoG(M), who supports the researchers in their professional development, project management, and technical skill acquisition. LoG(M) researchers enrolled in the same semester will follow their peers’ progress closely in weekly meetings; they have the opportunity to learn not just about their own mathematics research, but also that of their peers in other fields. In this course, teams are expected to complete a midterm progress presentation, a final poster presentation advertised to the public, and a final project report. Students receive a final letter grade based on these outputs. [link to Math 440 for more info?]

Prerequisite qualifications vary widely for the projects, though nearly all projects require proof-writing experience or linear algebra (Math 217 or equivalent). Interested students complete an application process. Applicants indicate which project(s) they find most interesting in this process. The application process is competitive, and students who are not admitted are strongly encouraged to apply again in future semesters.

Our LoGM students have made visualizations and formed, proved, and disproved conjectures in many fields of mathematics, including: complex analysis, complex dynamics, combinatorics, topology, homology groups, projective geometry, moduli spaces, mathematical games, algebraic geometry, billiard dynamics, origami, mathematical physics, commutative algebra, and more. Read more about our past projects [link]

Join us as we shape and explore the mathematics of tomorrow!

See the projects tab for Winter 2022 projects and application!

Email us at logm-info [at] umich [dot] edu.