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Prof: Robin Pemantle, DRLB 4N22, x8-5978, pemantle@math.upenn.edu

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Course description

Syllabus

Study guide for those using this as a major topic in the oral qualifying exam

Reserve list

Excerpt from Tsai on the Weyl closure

Announcement for 1-week summer school in Probabilitistic methods in Combinatorics (Graz, July 16-20)

Lecture notes for the last three lectures, with sketches of proofs only and no guarantee of correctness - these contain the open problems from Friday's lecture.

Lecture notes, posted by chapter, updated often

References (Bibliography, version of 23 MAR 06)

Introduction (Chapter 1, version of 06 JAN 06; typos corrected 13 FEB 06)
Generating functions (Chapter 2, version of 06 JAN 06; typos corrected 23 MAR 06)
Univariate asymptotics (Chapter 3, version of 06 JAN 06; typos corrected 23 MAR 06)
Manifolds (Chapter 4, version of 13 FEB 06; typos corrected 23 MAR 06)
Morse Theory (Chapter 5, version of 13 FEB 06; typos corrected 23 MAR 06)
Decomposing the Cauchy integral (Chapter 6, version of 10 MAR 06; typos corrected 23 MAR 06)
Techniques of symbolic computation (Chapter 7, Version of 10 MAR 06; typos corrected 23 MAR 06)
Saddle integrals in one variable (Chapter 9, Version of 23 MAR 06)

Tentative titles for remaining chapters