Applied Mathematics Seminar, Fall 2018

## Mondays 4:00 PM - 5:00 PM, LCB 215

• 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 2018. 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 27
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.

September 10
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.

September 24
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.

October 1
Speaker: Jia Zhao, Department of Mathematics, Utah State University
Title: TBA
Abstract: TBA

October 15
Speaker: Akil Narayan, Department of Mathematics and SCI, The University of Utah
Title: TBA
Abstract: TBA

October 22
Speaker: Dong Wang, Department of Mathematics, The University of Utah
Title: TBA
Abstract: TBA

November 5
Speaker: Ellis Scharfenaker, Department of Economics, The 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