Mini Course / Dynamics Learning Seminar

from Thursday
June 01, 2017 to Sunday
December 31, 2017
Show events for:
Instructions for subscribing to Stony Brook Math Department Calendars

Wednesday
September 20, 2017

2:30 PM - 3:30 PM
Math Tower P-131
Tali Pinsky, TIFR
On the volumes of modular geodesics

A closed geodesic gamma on the modular surface is a knot in the complement of a trefoil knot in S^3. It is always a hyperbolic knot, and thus has a well defined volume. I will show how to construct the modular template, due to Ghys, and use it to obtain an upper bound for this volume.


Wednesday
September 27, 2017

2:30 PM - 3:30 PM
Math Tower P-131
Liviana Palmisano, Institut Mittag-Leffler
The rigidity conjecture

A central question in dynamics is whether the topology of a system determines its geometry, whether the system is rigid. Under mild topological conditions rigidity holds in many classical cases, including: Kleinian groups, circle diffeomorphisms, unimodal interval maps, critical circle maps, and circle maps with a break point. More recent developments show that under similar topological conditions, rigidity does not hold for slightly more general systems. We will discuss the case of circle maps with a flat interval. The class of maps with Fibonacci rotation numbers is a C1 manifold which is foliated with co dimension three rigidity classes. Finally, we summarize the known non-rigidity phenomena in a conjecture which describes how topological classes are organized into rigidity classes.


Wednesday
October 04, 2017

2:30 PM - 3:30 PM
Math Tower P-131
Adi Glücksam, Tel Aviv University
Measurably entire functions and their growth

Let (X,B,P) be a standard probability space. Let T:C-> PPT(X) be a free action of the complex plane on the space (X,B,P). We say that the function F:X-> C is measurably entire if it is measurable and for P-a.e x the function F_x(z):=F(T_zx) is entire. B. Weiss showed in '97 that for every free C action there exists a non-constant measurably entire function. In this talk I will present upper and lower bounds for the growth of such functions. The talk is partly based on a joint work with L. Buhovsky, A.Logunov, and M. Sodin.


Wednesday
October 11, 2017

2:30 PM - 3:30 PM
Math Tower P-131
Carlos Cabrera, Instituto de Matemáticas UNAM, Unidad Cuernavaca
On the Hurwitz class of rational maps

In this talk we discuss both geometrical and algebraic aspects of Hurwitz classes of rational maps. The first aspect is related to cobordisms of rational maps while the other is given in terms of isomorphisms of sandwich semigroups. In particular, sandwich semigroups characterize also the conjugacy relation on rational maps.


Wednesday
November 08, 2017

2:30 PM - 3:30 PM
Math Tower P-131
Leon Takhtajan, Stony Brook University
Schwarz equation and symplectic geometry of the space of complex projective structures

The space of complex projective connections on Riemann surfaces is an affine bundle, modeled on the holomorphic cotangent bundle of the moduli space, and carries a holomorphic symplectic form - a differential of the Liouville 1-form on the cotangent bundle. The monodromy map is a holomorphic mapping of this space into the PSL(2,C)-character variety of a Riemann surface. It has a natural symplectic form, introduced by Bill Goldman for compact surface. The PSL(2,C)-character is non-abelian analog of a C*-character variety, the set of one-dimensional representations of the fundamental group of a surface. The symplectic nature of the latter variety was studied by Riemann.

I will explain how variational theory of Schwarz equation allows to determine the differential of the monodromy map and to prove the non-abelian analog of the Riemann bilinear relations, the relation between symplectic structures on the holomorphic tangent bundle of the moduli space of Riemann surfaces and on the PSL(2,C)-character variety of a given surface. This relation holds for the general case of orbifold Riemann surface.


Wednesday
November 15, 2017

2:30 PM - 3:30 PM
Math Tower P-131
Leon Takhtajan, Stony Brook University
Schwarz equation and symplectic geometry of the space of complex projective structures

The space of complex projective connections on Riemann surfaces is an affine bundle, modeled on the holomorphic cotangent bundle of the moduli space, and carries a holomorphic symplectic form - a differential of the Liouville 1-form on the cotangent bundle. The monodromy map is a holomorphic mapping of this space into the PSL(2,C)-character variety of a Riemann surface. It has a natural symplectic form, introduced by Bill Goldman for compact surface. The PSL(2,C)-character is non-abelian analog of a C*-character variety, the set of one-dimensional representations of the fundamental group of a surface. The symplectic nature of the latter variety was studied by Riemann.

I will explain how variational theory of Schwarz equation allows to determine the differential of the monodromy map and to prove the non-abelian analog of the Riemann bilinear relations, the relation between symplectic structures on the holomorphic tangent bundle of the moduli space of Riemann surfaces and on the PSL(2,C)-character variety of a given surface. This relation holds for the general case of orbifold Riemann surface.


Show events for:
Instructions for subscribing to Stony Brook Math Department Calendars