Department of Mathematics
Applied Mathematics Seminar, Fall 2015

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

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

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

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

Seminar organizer: Yekaterina Epshteyn (epshteyn (at)

Past lectures: Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007, Spring 2007, Fall 2006, Spring 2006, Fall 2005, Spring 2005, Fall 2004, Spring 2004, Fall 2003, Spring 2003, Fall 2002, Spring 2002, Fall 2001, Spring 2001, Fall 2000, Spring 2000, Fall 1999, Spring 1999, Fall 1998, Spring 1998, Winter 1998, Fall 1997, Spring 1997, Winter 1997, Fall 1996, Spring 1996, Winter 1996, Fall 1995.

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