Fall 2012 seminar on complex analysis and combinatorics
Nicolas and Sam are running a learning seminar on many complex variables with applications to asymptotic combinatorics. This learning seminar can be taken as a reading course; please contact me if you are interested.
We will be in K9509, 11:30-1:30 Mondays. See below for the schedule. Dates are subject to change, especially later in the semester.
Schedule
- Sept 17
- Wei Chen, Cauchy integral formula in higher dimensions. Summary: Sam Johnson
- Sept 24
- Sophie Burrill, Domains of Holomorphy. Summary: Himadri Ganguli
- Oct 1
- Himadri Ganguli, Topology of H(U). Summary: Brad Jones
- Oct 8
- Thanksgiving, no seminar
- Oct 15
- Sam Johnson, From C to C^{n}: counterexamples (particularly Riemann mapping theorem). Summary: Himadri Ganguli
- Oct 22
- Brad Jones, Some combinatorial examples part 1. Summary: Sam Johnson
- Oct 29
- Wei Chen, Weierstrass theorems. Summary: Brad Jones
- Nov 5
- Sam Johnson, Implicit and inverse mapping theorems (with a comparison to multivariate Lagrange inversion). Summary: Himadri Ganguli
- Nov 12
- Remembrance day, no seminar
- Nov 19
- Karen Yeats, Analytic Nullstellensatz part 1. Summary: Sam Johnson
- Nov 26
- Karen Yeats, Analytic Nullstellensatz part 2. Summary: Brad Jones
- Dec 3
- Himadri Ganguli, Multiple zeta functions. Summary: Sam Johnson
- Dec 10
- Brad Jones, Stokes theorem and MB formula
References
- Several Complex Variables with Connections to Algebraic Geometry and Lie Groups by Joseph Taylor, Graduate Studies in Mathematics
2002;
Volume: 46.
A lecture notes version.
- Twenty combinatorial examples of asymptotics derived from multivariate generating functions by Robin Pemantle and Mark C. Wilson. arXiv:math/0512548 or SIAM Rev., 50(2), 199–272.
- Analytic combinatorics in d variables: an overview by Robin Pemantle.
- Multiple Hurwitz Zeta Functions by Ram Murty and Kaneenika Sinha.
Previous seminars
Older seminars on more motivic topics from when I was at Boston University. There are many broken links, but I consider these archived and so they will not be changed.