epshteyn (at) math.utah.edu)
August 22 (Welcome Back and Group Photo!)
Speaker: Davit Harutyunyan, Department of Mathematics, The University of Utah
Title: Quantitative Wulff and Brunn-Minkowski inequalities for convex sets
Abstract: In this lecture we revisit the anisotropic isoperimetric (Wulff) and the Brunn-Minkowski inequalities for convex sets. The best know constant C(n)=Cn^8.5 depending on the space dimension n in both inequalities is due to Figalli, Maggi and Pratelli, 2010. We improve that constant to Cn^6 for convex sets and even better in some cases. We also conjecture, that the best constant in both inequalities must be of the form Cn^2, i.e., quadratic in n. The tools are the Brenier's mapping from the theory of optimal mass transportation combined with new sharp geometric-arithmetic mean and some algebraic inequalities plus a trace estimate by Figalli, Maggi and Pratelli.
Speaker: Alexander Kurganov, Department of Mathematics, Tulane University
Speaker: Noa Kraitzman, Department of Mathematics, The University of Utah
Speaker: Michael Ryvkin, The Iby and Aladar Fleischman Faculty of Engineering, Tel Aviv University
Title: ANALYSIS OF NON-PERIODIC STRESS STATE IN PERIODIC MATERIALS. Applications to fracture and optimization.
Abstract: Many man-made materials have a periodic microstructure, periodic materials are widely met also in nature. Study of overall elastic properties of such materials and their optimization is a well-developed topic. The corresponding problems are characterized by a periodic stress state, however, in many cases of interest the stress state in periodic material is non-periodic. The non-periodicity can result from a non-periodic applied loading, from presence of cracks, inclusions and other flaws, and from the finite dimensions of the sample to be considered.
In these cases a direct numerical simulation is computationally expensive due to a large number of degrees of freedom to be involved, but reducing the analysis domain to a single repetitive cell is not straightforward. This goal is achieved by applying the discrete Fourier transform, casted as the representative cell method. As a result, one has to resolve a number of representative(repetitive) cell problems in the transforms space and can obtain the sought elastic field by the inverse transformation. The important feature of these problems is that they are independent and, consequently, can be treated by the use of parallel computing. It is shown how to plug-in the method into an efficient multiscale analysis scheme for arbitrary shaped sample of periodic material.
The suggested approach is employed for the fracture analysis of beam lattices: two-dimensional honeycombs and spatial open cell Kelvin foam, both cracks nucleation and propagation problems are addressed. Solid periodically voided and composite materials with flaws are considered as well, the optimal parameter combinations maximizing the fracture toughness are determined.
Speaker: Orly Alter, Departments of Bioengineering and Human Genetics, The University of Utah
Title: Cancer Diagnostics and Prognostics from Comparative Spectral Decompositions of Patient-Matched Genomic Profiles
Abstract: I will, first, briefly review our matrix and tensor modeling of large-scale molecular biological data, which, as we demonstrated, can be used to correctly predict previously unknown physical, cellular, and evolutionary mechanisms that govern the activity of DNA and RNA. Second, I will describe our recent generalized singular value decomposition (GSVD) and tensor GSVD comparisons of the genomes of tumor and normal cells from the same sets of astrocytoma brain and, separately, ovarian cancer patients, which uncovered patterns of DNA copy-number alterations that are correlated with a patient's survival and response to treatment. Third, I will present our higher-order GSVD, the only mathematical framework that can create a single coherent model from, i.e., simultaneously find similarities and dissimilarities across multiple two-dimensional datasets, by extending the GSVD from two to more than two matrices.
Speaker: Fengyan Li, Department of Mathematical Sciences, Rensselaer Polytechnic Institute
Speaker: Lajos Horvath, Department of Mathematics, The University of Utah
Speaker: Vianey Villamizar, Department of Mathematics, BYU
November 28 (Student Talk)
Speaker: Qing Xia, Department of Mathematics, The University of Utah
epshteyn (at) math.utah.edu).
Past lectures: 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.