A full abstract list for all plenary and contributed speakers is now available, as well as a full PDF schedule. Our plenary speakers for ORAM 8 are:
Matthew Badger, University of Connecticut
Title: Open problems in curves, sets, and measures
Abstract: This talk will serve as an introduction to recent work and open problems on the geometry of sets and measures in Euclidean space. One goal of this inquiry is to understand how general measures interact with canonical families of lower dimension sets such as rectifiable curves, Hölder curves, or Lipschitz surfaces. Along the way, one must develop tests to identify subsets of the canonical sets. Our tour will highlight classical theorems in topology, modern results in quantitative geometry, and recent advances in geometric measure theory and harmonic analysis with an emphasis on open problems. This is joint work with R. Schul and with L. Naples and V. Vellis.
Andreas Seeger, University of Wisconsin
Title: Spherical maximal functions on the Heisenberg groups
Abstract: Let $V$ be a hyperplane in the Heisenberg group $\mathbb H^n$ and $\mu$ the surface measure of a sphere in $V$. In the talk I will discuss old and new results on $L^p(\mathbb H^n)$-boundedness for the maximal operator $f\mapsto \sup_t |f*\mu_t|$ generated by the automorphic dilations.
Plamen Stefanov, Purdue University
Title: Local and global boundary rigidity
Abstract: The boundary rigidity problem consist of recovering a Riemannian metric in a domain, up to an isometry, from the distance between boundary points. We show that in dimensions three and higher, knowing the distance near a fixed strictly convex boundary point allows us to reconstruct the metric inside the domain near that point, and that this reconstruction is stable. We also prove semi-global and global results under certain an assumption of the existence of a strictly convex foliation. The problem can be reformulated as a recovery of the metric from the arrival times of waves between boundary points; which is known as travel-time tomography. The interest in this problem is motivated by imaging problems in seismology: to recover the sub-surface structure of the Earth given travel-times from the propagation of seismic waves. In oil exploration, the seismic signals are man-made and the problem is local in nature. In particular, we can recover locally the compressional and the shear wave speeds for the elastic Earth model, given local information. The talk is based on joint work with G.Uhlmann (UW) and A.Vasy (Stanford). We will also present results for a recovery of a Lorentzian metric from red shifts motivated by the problem of observing cosmic strings.
Catherine Sulem, University of Toronto
Title: Surface water waves over a variable bottom
Abstract: We examine the effect of a periodic bottom on the free surface of a fluid linearized near the stationary state, and we develop a Bloch theory for the linearized water wave system. This analysis takes the form of a spectral problem for the Dirichlet-Neumann operator of the fluid domain with periodic bottom. We find that, generically, the presence of the bottom results in the splitting of double eigenvalues creating a spectral gap.
(This is joint work with W. Craig, M. Gazeau, and C. Lacave).
Sijue Wu, University of Michigan
Title: On the motion of two dimensional water waves with angled crests
Abstract: We will discuss recent progress on the study of two dimensional water waves with angled crests.