SATURDAY, APRIL 9, IUPUI, INDIANAPOLIS, IN
Speakers:
Eric Bedford (Stony Brook U)
Michael Klug (U Chicago)
Nattalie Tamam (U Michigan)
Jane Wang (Indiana U)
Schedule:
Times below are given in Eastern Daylight Time.
10:30-11:00 Welcome, Coffee
11:00-11:50 Eric Bedford
12:00-1:30 Lunch
1:30-2:20 Nattalie Tamam
2:30-2:45 Coffee
2:45-3:35 Jane Wang
4:00-4:50 Michael Klug
5:00 farewells
Parking and Local Info:
Parking is available in the Gateway Garage, 525 N Blackford St.
Talks will take place in the Science Building in room LD 136. Coffee and breaks will be in the Math Lounge, LD 259.
Organizers:
Support:
This GGD workshop is funded with the support of the IU Mathematics Journal, IUPUI and its School of Science.
Titles and Abstracts
Eric Bedford
Title: Henon maps: Horseshoes and crossed mappings
Abstract: I will discuss real and complex Henon mappings from the point of view of real and complex horseshoes.
Michael Klug
Title: Z/2 in Low-dimensional Topology
Abstract: I will discuss a connection between several different Z/2 invariants in low-dimensional topology (the Arf invariant of a knot, the Arf of a surface with a spin structure, the Rochlin invariant of a homology 3-sphere, and the Arf invariant of a characteristic surface in a 4-manifold, the Kirby-Siebenmann invariant of a 4-manifold). I will consider some unifying perspectives on these different invariants.
Nattalie Tamam
Title: Classification of divergence of trajectories
Abstract: As shown by Dani, diophantine approximations are in direct correspondence to the behavior of orbits in certain homogeneous spaces. We will discuss the interpretation of the divergent trajectories and the obvious ones, the ones diverging due to a purely algebraic reason. As conjectured by Barak Weiss, there is a complete classification of divergent trajectories when considering the action of subgroups of the diagonal group. We will discuss the proof of the last part of this conjecture, showing that for a 'large enough' such subgroup, every divergent trajectory diverges obviously. This is a joint work with Omri Solan.
Jane Wang
Title: The topology of the moduli space of dilation surfaces
Abstract: Translation surfaces are geometric objects that can be defined as a collection of polygons with sides identified in parallel opposite pairs by translation. If we generalize slightly and allow for polygons with sides identified by both translation and dilation, we get a new family of objects called dilation surfaces. While translation surfaces are well-studied, much less is known about dynamics on dilation surfaces and their moduli spaces. In this talk, we will survey recent progress in understanding the topology of moduli spaces of dilation surfaces. This talk represents joint work with Paul Apisa and Matt Bainbridge.