Applied Mathematics Seminar, Fall 2015

## Mondays 3:55 PM - 5:00 PM, LCB 219

• This seminar can be taken for credit: Students can get 1-3 credits by registering to the Applied Math Seminar class Math 7875 Section 010 for Fall 2015. Students should talk to the seminar organizer before taking it for a credit. Grading is based on attendance and giving a talk by presenting an applied-mathematics paper (not necessarily your own). Student talks will be appropriately labeled to distinguish them from visitor talks. The seminar organizer is available to review your slides, for dry-runs etc.
• Please direct questions or comments about the seminar (or its class) to Yekaterina Epshteyn (epshteyn (at) math.utah.edu)
• Talks are announced through the applied-math mailing list. Please ask the seminar organizer for information about how to subscribe to this list.

August 24 (Welcome Back!)
Speaker: Andrej Cherkaev, Department of Mathematics, University of Utah
Title: Optimal Multicomponent Composites: Amazing 3d Structures and hint for new bounds.
Abstract:I will review the latest results concerning optimal multicomponent 2D- and 3D composite structures. These structures are minimizing sequences of a variational problem with a multiwell Lagrangian; their energy represents a relaxed energy of an optimal composite or a quasiconvex envelope of the Lagrangian. Analysis of the fields in optimal structures provides hints for modification of a lower bound for the relaxed energy.

September 14
Speaker: Jack Xin, Department of Mathematics, University of California, Irvine
Title: Minimizing the Difference of L1 and L2 Norms and Applications
Abstract:L1 norm minimization is a widely used convex method for enforcing sparsity in signal recovery and model selection. In this talk, we introduce a non-convex Lipschitz continuous function, the difference of L1 and L2 norms (DL12), and discuss its sparsity promoting properties. Using examples in compressed sensing and imaging, we show that there can be plenty of gain beyond L1 by minimizing DL12 at a moderate level of additional computation via the difference of convex function algorithms. We shall draw a connection of DL12 with penalty functions in statistics and machine learning.

September 21
Speaker: Michael Meylan, School of Mathematical and Physical Sciences, The University of Newcastle, Australia
Title: Wave - Ice interaction, field measurements, laboratory experiments, and mathematical models
Abstract: The attenuation and scattering of sea ice is a complex process and the current state of our knowledge is quite limited. This in turn makes it difficult to make even the most basic predictions of wave induced melting or to forecast the wave state in the frozen ocean. The key process which we need to model is the interaction of ocean waves with a single ice floe (or small groups of floes). However, we only have field measurements of large scale wave attenuation (over hundreds of ice floes) and it is actually not obvious how to scale from single floe models to multiple floe problems. Therefore the models are lacking validation at both the large and small scale. In a recent series of experiments performed in a wavetank we have tried to validate and test the range of applicability of our numerical models. I will present results and comparisons from these experiments and discuss their implications for accurate modelling of wave-ice interactions.

September 28
Speaker: Francois Monard, Department of Mathematics, University of Washington
Title: TBA
Abstract:TBA

October 19
Speaker: Andrej Cherkaev, Department of Mathematics, University of Utah
Title: TBA
Abstract:TBA

November 9
Speaker: Fernando Guevara Vasquez, Department of Mathematics, University of Utah
Title: TBA
Abstract:TBA

Seminar organizer: Yekaterina Epshteyn (epshteyn (at) math.utah.edu).

155 South 1400 East, Room 233, Salt Lake City, UT 84112-0090, T:+1 801 581 6851, F:+1 801 581 4148