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 Cⁿ: 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

1. 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.
2. 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.
3. Analytic combinatorics in d variables: an overview by Robin Pemantle.
4. Multiple Hurwitz Zeta Functions by Ram Murty and Kaneenika Sinha.

Previous seminars

• Fall 2011 multiple zeta values
• Summer 2011 the Dynkin operator and renormalization Hopf algebras
• Spring 2011 integrable models in combinatorics and physics
• In Fall 2010, Samson Black and I organied a learning seminar on knots and quantum field theory.
• In late April and May 2010 I gave a series of 5 lectures on Renormalization Hopf Algebras, and the participants kindly took notes.
• Spring 2010 workgroup on Random matrices, symmetric functions, and graph enumeration.

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.

• Fall 2006 seminar on motives with applications in physics
• Spring 2006 Motives-Arithmetic-Physics Seminar (organized by Obi Rej).
• Fall 2005 learning seminar on motives