# Van Winter Lecture Series

### The 2016-17 van Winter Memorial Lecture in Mathematical Physics

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**Speaker**: Michael Weinstein, Department of Mathematics, Department of Applied Physics and Applied Mathematics, Columbia University

**Title:** Energy on the edge**Date, time, location**: 4pm in CP 155, refreshments at 3:30 in CP 179**Abstract:** In many applications, e.g. photonic and quantum systems, one is interested in controlled localization of wave energy.

Edge States are a type of localization along a line-defect or interface between media. We study edge states in honeycomb structures (such as graphene and its photonic analogues) and discuss their novel properties. In particular, we examine the formation of Topologically Protected Edge States, which persist and are stable against strong local distortions of the edge, and are therefore potential vehicles for robust energy-transfer in the presence of defects and random imperfections.

We further discuss rigorous results and conjectures for families of continuum PDE models (Schroedinger and Maxwell) admitting edge states which are topologically protected, edge states which are not protected, and states which remain localized near an edge for a very long time, but likely decay eventually.

Past van Winter lecturers

- 2015-2016, John Cardy, University of California, Berkeley
- 2014-2015, Ingrid Daubechies, Duke University
- 2013-2014, Juan Maldacena, Institute for Advanced Study
- 2012-2013, Israel Michael Sigal, University of Toronto
- 2011-2012, Paul Steinhardt, Princeton University
- 2010-2011, Gunther Uhlmann, University of Washington
- 2009-2010, Christopher Hill, Fermilab
- 2008-2009, Percy Deift, Courant Institute, NYU
- 2007-2008, Joel Lebowitz, Rutgers University
- 2006-2007, Barry Simon, California Inst. of Technology
- 2005-2006, Eric Heller, Harvard University
- 2004-2005, Maciej Zworski, University of California, Berkeley
- 2003-2004, Roger Blandford, Stanford University
- 2002-2003, Clifford Taubes, Harvard University
- 2001-2002, Elliot Lieb, Princeton University

### About the van Winter Memorial Lecture in Mathematical Physics

The van Winter Memorial Lecture honors the memory of Clasine van Winter, who held a professorship in the Department of Mathematics and the Department of Physics and Astronomy from 1968 to her retirement in 1999. Professor Van Winter specialized in the study of multiparticle quantum systems; her contributions include the Weinberg-van Winter equations for a multiparticle quantum system, derived independently by Professor van Winter and Professor Steven Weinberg, and the so-called HVZ Theorem which characterizes the essential spectrum of multiparticle quantum systems. She died in October of 2000.