Brian Munson NSF Postdoctoral Fellow Department of Mathematics Stanford University

I study algebraic topology. I am currently using the calculus of functors to study spaces of smooth embeddings and spaces of "link maps" to get information about their homotopy type. I am also interested in the connections between these more geometric problems and homotopy theory. Recently I have been trying to apply calculus methods to study the mapping class group of a Riemann surface. Here is my latest Research Statement.

I have been working on putting the linking number in a calculus of functors framework, which you can find a preprint of here. That work also identifies secondary obstructions (to the primary one of intersections) to separating the image of smooth maps. I have also been developing a surface calculus to study things like the mapping class group, which you can find a very rough draft of here.

• Excision estimates for cubical diagrams of link maps, in preparation.
• Surface calculus, in preparation (preprint).
• Homotopy theory of cubical diagrams, with Ismar Volic, in preparation.
• Excision estimates for spaces of classical knots with Ismar Volic, in preparation.
• A manifold calculus approach to link maps and the linking number, submitted (preprint).
• Embeddings in the 3/4 range, Topology 44 (2005), no. 6, 1133-1157.
• Cost-minimizing networks among immiscible fluids in R^2, with David Futer, Andrei Gnepp, David McMath, Ting Ng, Sang-Hyoun Pahk, and Cara Yoder, Pacific J. Math. 196 (2000), no. 2, 395-414.

I am not teaching any courses this year.

Last spring I taught Math 147: Differential Topology. Click on the link to view the syllabus and course materials.

Last fall I taught Math 283, a topics course on the Calculus of Functors. The syllabus I wrote turned into a descriptive essay. There is a much shorter and less informative version posted around the department. Three of the four papers we will follow most closely can be found online. Here are the links which will allow you to locate the appropriate files: Calculus III, Embeddings from Immersion Theory I, and Embeddings from Immersion Theory II. I will distribute copies of the fourth paper, Calculus II, in class. Although there is no official text for the course, much of the background which I will only touch on is detailed in the following: "Simplicial Objects in Algebraic Topology" by Peter May, "Categories for the Working Mathematician" by Saunders MacLane, "Homotopy Limits, Completions, and Localizations" by A. Bousfield and D. Kan, and "Infinite Loop Spaces" by Frank Adams. All of these texts may be found in the library.

Some time ago Ben Brubaker and I taught Math 263A: Lie Groups and Lie Algebras. Homework problems are available as .pdf files which can be obtained from the following links: homework 1, homework 2, homework 3. These problems will be discussed and presented by students in three evening sessions. Office hours for this class are by appointment. A course announcement can be found here.

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Seminars

• Topology Seminar

• Topology Progress Seminar

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Links

• MathSciNet.
• Brown University.
• The University of Oregon.
• Eric Weisstein's World of Mathematics An online mathematics encyclopedia.
• Google.

Last change: January 2005.