Tau-Functions and Monodromy Symplectomorphisms

Twisted L-Functions and Monodromy

Monodromy of A-hypergeometric functions

Using Mellin-Barnes integrals we give a method to compute a relevant subgroup of the monodromy group of an A-hypergeometric system of differential equations. Presumably this group is the full monodromy group of the system

Topology of polynomial functions and monodromy dynamics

Let f : C n ! C be a polynomial function. We deene global polar invariants associated to bres of f and we describe a CW-complex model of a bre. We show how to use aane polar curves in order to study the monodromy around atypical values of f, including the value innnity. We give a zeta-function formula for such a monodromy. Topologie des fonctions polynomiales et dynamique mono-dromique R esum e...

L-functions and monodromy: four lectures on Weil II-1 L-functions and monodromy: four lectures on Weil II

fu u u un n n nc c c ct t t ti i i io o o on n n ns s s s a a a an n n nd d d d m m m mo o o on n n no o o od d d dr r r ro o o om m m my y y Ka a a at t t tz z z z T T T Ta a a ab b b bl l l le e e e o o o of f f f C C C Co o o on n n nt t t te e e en n n nt t t ts s s s L L L Le e e ec c c ct t t tu u u ur r r re e e e I I I I Introduction Review of …-adic sheaves and …-adic cohomology Weight...

Tau Functions and Matrix Integrals

We consider solvable matrix models. We generalize Harish-Chandra-Itzykson-Zuber and certain other integrals (Gross-Witten integral and integrals over complex matrices) using the notion of tau function of matrix argument. In this case one can reduce matrix integral to the integral over eigenvalues, which in turn is certain tau function. The resulting tau functions may be analyzed either by the m...