Plenary Speakers
Louis Block, University of Florida
IP3: The Dynamics of Two Families of Maps of the Interval. Abstract
Sunday, March 30, 8:10am9:00am
We look at continuous maps of a space $X$ to itself considered as discrete dynamical systems. For a point $x\in X$ and a map $f:X \to X$ the orbit of $x$ is given by $\{x, f(x), f^2(x), \dots \},$ where $f^2$ denotes the map $f \circ f$ and so on. We are interested in describing the global orbit structure for a given map $f$. We focus the talk on two oneparameter families of maps of the interval $[0,1]$ to itself which are defined by simple formulas. These are the quadratic family given by $f_a(x)=ax(1x),$ where the parameter $a$ runs from $0$ to $4$ and the tent family family, given by $f_s(x) = sx$ if $x \in [0,\frac{1}{2}],$ and $f_s(x) = s(1x),$ if $x \in [\frac{1}{2},1],$ where the parameter $s$ runs from $0$ to $2$. We discuss some results in dynamics and topology which arise out of the study of these two families. The results involve periodic orbits, $\omega$limit sets, adding machines, topological entropy, and inverse limit spaces. Louis Block is a Professor of Mathematics at the University of Florida, where he has proudly served since 1973. He received his Doctoral Degree from Northwestern University, under the supervision of R.F. Williams. He has been a Visiting Fellow on three occasions at Australian National University, and he was a Van Vleck Visiting Professor at Wesleyan University twice during sabbatical years. Most of his research has been in the area of OneDimensional Dynamics. Professor Block is the author or coauthor of 54 publications which have been reviewed by Mathematical Reviews. His most frequently cited publications are his 1992 book (with W. A. Coppel), "Dynamics in one dimension," (Lecture Notes in Mathematics Volume 1513, 1992, MR1176513), and his 1980 paper (with J. Guckenheimer, M. Misiurewicz, and L. S. Young), "Periodic points and topological entropy of onedimensional maps," pages 1834, Lecture Notes in Mathematics Volume 819, MR0591173). Professor Block has had the good fortune of being able to visit and give lectures in numerous countries. In addition to mathematics, he enjoys playing tennis and spending time with family, especially his grandchildren.
Emmanuele DiBenedetto, Vanderbilt University
IP2: On the Local Behavior of NonNegative Solutions to a Logarithmically Singular Equation. Abstract
Saturday, March 29, 1:10pm2:00pm
The local positivity of solutions to logarithmically singular diffusion equations is investigated in some spacetime domain $E\times(0,T]$. It is shown that if at some time level $t_o\in(0,T]$ and some point $x_o\in E$ the solution $u(\cdot,t_o)$ is not identically zero in a neighborhood of $x_o$, in a measuretheoretical sense, then it is strictly positive in a neighborhood of $(x_o,t_o)$. The precise form of this statement is by an intrinsic Harnacktype inequality, which also determines the size of such a neighborhood. Recent results on the spaceanalyticity of solutions will also be presented.
Joel Smoller, University of Michigan
IP1: Gravitation. Abstract
Saturday, March 29, 8:10am9:00am
We discuss gravitation from Newton, to Einstein, to presentday. Dr. Joel Smoller is the Lamberto Cesari Chaired Professor at The University of Michigan. Dr. Smoller was a Guggenheim Fellow, a Senior Humboldt Fellow, and was the recipient of the 2009 Birkhoff Prize in Applied Mathematics.
Gunther Uhlmann, University of Washington and University of Helinski
IP4: Harry Potter's Cloak (Public Lecture). Abstract
Invisibility has been a subject of human fascination for millenia, from the Greek legend of Perseus versus Medusa to the more recent The Invisible Man, The Invisible Woman, Star Trek and Harry Potter, among many others. Over the years, there have been occasional scientific prescriptions for invisibility in various settings but the route to cloaking that has received the most attention has been transformation optics. To achieve invisibility one can design materials that would steer light around a hidden region, returning it to its original path on the far side. Not only would observers be unaware of the contents of the hidden region, they would not even be aware that something was being hidden. As Science Magazine stated in 2006 in naming cloaking one of the 10 breakthroughs of the year: "...no matter how you look at it the ideas behind invisibility are likely to cast a long shadow" Dr. Uhlmann studied mathematics as an undergraduate at the Universidad de Chile in Santiago, gaining his Licenciatura degree in 1973. He continued his studies at MIT where he received a PhD in 1976. He held postdoctoral positions at MIT, Harvard and NYU, including a Courant Instructorship at the Courant Institute in 19771978. In 1980, he became Assistant Professor at MIT and then moved in 1985 to the University of Washington. He has been the Walker Family Professor at the University of Washington since 2006. During 20102012 he was on leave at the University of California, Irvine, as the Excellence in Teaching Endowed Chair. Dr. Uhlmann has received several honors for his research including a Sloan Fellowship in 1984 and a Guggenheim fellowship in 2001. In 2001 he was elected a Corresponding Member of the Chilean Academy of Sciences. He is a Fellow of the Institute of Physics since 2004. He was elected to the American Academy of Arts and Sciences in 2009 and a SIAM Fellow in 2010. He was an Invited Speaker at ICM in Berlin in 1998 and a Plenary Speaker at International Congress on Industrial and Applied Mathematics in Zurich in 2007. He was named a Highly Cited Researcher by ISI in 2004. He was awarded the Bôcher Memorial Prize in 2011 and the Kleinman Prize also in 2011. Uhlmann delivered the American Mathematical Society (AMS) Einstein Lecture in 2012. He was awarded the Fondation Math'ematiques de Paris Research Chair for 20122013. He was elected to the Washington State Academy of Sciences in 2012 and is also an AMS Fellow since 2012. He was awarded a Simons Fellowship for 20132014.
