epshteyn (at) math.utah.edu)
Speaker: Eugene Mishchenko, Department of Physics and Astronomy, The University of Utah
Title: The puzzling phenomenon of minimal conductivity of graphene
Abstract: graphene is a two-dimensional crystal of carbon atoms arranged in a honeycomb lattice. Graphene happens to be a semi-metal that can, in some instances, display insulating properties yet reveal metallic behavior in others. For example, conductivity of graphene is predicted by the band theory to be metallic. In contrast, screening of Coulomb interaction between electrons is expected to be rather weak, very much like in typical insulators. Accordingly, one would expect interactions to be strong and result in significant corrections to the conductivity. Surprisingly, experiments show little such corrections, if any. I will discuss theoretical efforts expended over the last decade to understand this phenomenon.
Speaker: Braxton Osting, Department of Mathematics, The University of Utah
Title: Diffusion generated methods for target-valued maps
Abstract: A variety of tasks in inverse problems and data analysis can be formulated as the variational problem of minimizing the Dirichlet energy of a function that takes values in a certain target set and possibly satisfies additional constraints. These additional constraints may be used to enforce fidelity to data or other structural constraints arising in the particular problem considered. I'll present diffusion generated methods for solving this problem for a wide class of target sets and prove some stability and convergence results. I'll give examples of how these methods can be used for the geometry processing task of generating quadrilateral meshes, finding Dirichlet partitions, constructing smooth orthogonal matrix valued functions, and solving inverse problems for target-valued maps. This is joint work with Dong Wang and Ryan Viertel.
Speaker: Lajos Horvath, Department of Mathematics, The University of Utah
Title: Change Point Detection in the Conditional Correlation Structure of Multivariate Volatility Models
Abstract: We propose semi-parametric CUSUM tests to detect a change point in the correlation structures of non--linear multivariate models with dynamically evolving volatilities. The asymptotic distributions of the proposed statistics are derived under mild conditions. We discuss the applicability of our method to the most often used models, including constant conditional correlation (CCC), dynamic conditional correlation (DCC), BEKK, corrected DCC and factor models. Our simulations show that, our tests have good size and power properties. Also, even though the near--unit root property distorts the size and power of tests, de--volatizing the data by means of appropriate multivariate volatility models can correct such distortions. We apply the semi--parametric CUSUM tests in the attempt to date the occurrence of financial contagion from the U.S. to emerging markets worldwide during the great recession.
Joint work with Marco Barassi, Department of Economics, University of Birmingham UK and Yuqian Zhao, Department of Statistics and Actuarial Science, University of Waterloo, Canada.
Speaker: Jia Zhao, Department of Mathematics, Utah State University
Speaker: Akil Narayan, Department of Mathematics and SCI, The University of Utah
Speaker: Dong Wang, Department of Mathematics, The University of Utah
Speaker: Ellis Scharfenaker, Department of Economics, The University of Utah
epshteyn (at) math.utah.edu).
Past lectures: Spring 2018, Fall 2017, Spring 2017, Spring 2016, Fall 2015, 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.