Professor Khai Nguyen Dept. of Mathematics, NC State University 
Title: Kolmogorov Entropy Compactness Estimates for nonlinear PDEs 
Abstract. Inspired by a question posed by Lax in 2002, in recent years it has received an increasing attention the study on the quantitative analysis of compactness for nonlinear PDEs. In this talk, I will present recent results on the sharp compactness estimates in terms of Kolmogorov epsilon entropy for hyperbolic conservation laws and HamiltonJacobi equations. Estimates of this type play a central roles in various areas of information theory and statistics as well as of ergodic and learning theory. In the present setting, this concept could provide a measure of the order of “resolution” of a numerical method for the corresponding equations. 
Updates
Monday, April 1, 11:00AM12:00 Noon, Conference room
Wednesday, March 27, 3:00PM4:00 Noon, Conference room
Professor Ernst Presman 
Title: 
Friday, April 12, 11:00AM12:00 Noon, Conference room
Professor Rakesh Dept. of Mathematical Sciences, University of Delaware 
Title: Inverse problems for hyperbolic PDEs 
Abstract: We state and motivate (oil prospecting, medical imaging, radar, etc.) some inverse problems for the wave equation. We then describe some of the important theoretical results and end with two important ideas in proving these results. 
Friday, March 29, 11:00AM12:00 Noon,
Professor Julie Mitchell,Bioscience Division, Oak Ridge National Lab 
Title: Feature Selection in Biomolecular Models 
Abstract: Proteinprotein interactions regulate many essential biological processes and play an important role in health and disease. The process of experimentally characterizing protein residues that contribute the most to proteinprotein interaction affinity and specificity is laborious. Thus, developing models that accurately characterize hotspots at proteinprotein interfaces provides important information about how to drug therapeutically relevant proteinprotein interactions. In this work, we combined the KFC2a proteinprotein interaction hotspot prediction features with Rosetta scoring function terms and interface filter metrics. A 2way and 3way forward selection strategy was employed to train support vector machine classifiers, as was a reverse feature elimination strategy. From these results, we identified subsets of KFC2a and Rosetta combined features that show improved performance over KFC2a features alone. The forward selection algorithm also helped elucidate the biophysical principles that determine whether a given amino acid is a binding hot spot. 
Monday, Feb 11, 11:00AM12:00 Noon, Conference room
Professor Hyungchun Lee of Dept. of Mathematics, Ajou University, South Korea 
Title: Uncertainty quantification for partial differential equations and their optimal control problems 
Abstract: In this talk, we consider UQ (Uncertainty quantification) and optimal control problems for partial differential equation with random inputs. First we introduce a general approach of studying UQ and then consider some optimal control problems.
To determine an applicable deterministic control $\hat{f}(x)$, we consider the four cases which we compare for efficiency and feasibility. We prove the existence of optimal states, adjoint states and optimality conditions for each cases. We also derive the optimality systems for the four cases. The optimality system is then discretized by a standard finite element method and sparse grid collocation method for physical space and probability space, respectively. The numerical experiments are performed for their efficiency and feasibility. 
Wednesday, Jan 16, 11:00AM12:00 Noon, Conference room
Inbo Sim, University of Ulsan, South Korea 
Title: Symmetrybreaking bifurcation for the onedimensional H\'{e}non and MooreNehari differential equations 
Abstract: We show the existence of a symmetrybreaking bifurcation point for the onedimensional H\'{e}non and the MooreNehari differential equation.
Employing a variant of Rabinowitz’s global bifurcation, we obtain the unbounded connected set (the first of the alternatives about Rabinowitz’s global bifurcation), which emanates from the symmetrybreaking bifurcation point. Moreover, we give an example of a bounded branch connecting two symmetrybreaking bifurcation points (the second of the alternatives about Rabinowitz’s global bifurcation) and show that a bifurcation point for MooreNehari equation is explicitly represented as a function of \p\ which is an exponent of nonlinear term. 
Monday, Nov 26, 11:00AM12:00 Noon, Fretwell 315
Grace Stadnyk, NC State University 
Title: Some Combinatorial Results on the EdgeProduct Space of Phylogenetic Trees 
Abstract: I will discuss a topological space that arises in evolutionary biology called the edgeproduct space of phylogenetic trees. In particular, I will discuss some of the combinatorial properties of a particularly natural CW decomposition of this space. It is known that intervals in the resulting face poset are shellable, but the manner in which the maximal faces intersect is still not wellunderstood. In particular, the poset in its entirety is not known to be shellable. I will introduce a partial order on the maximal faces of the edgeproduct space of phylogenetic trees called the enriched Tamari poset, which can be viewed as a generalization of the Tamari lattice. I will use this poset to show that the edgeproduct space of phylogenetic trees is galleryconnected. I will conclude by discussing the question of whether the face poset of this topological space is shellable. I will define most of the notions that appear in the talk, so it should be accessible to all. 
Monday, Nov 12, 11:30AM12:30 PM, Fretwell 315
Dr. Min Hyung Cho, University of Massachusetts at Lowell 
Title: Fast Integral equation methods for wave scattering in layered media 
Abstract: Many modern electronic/optical devices rely on waves such as solar cells, antennae, radar, and lasers. These devices are mostly built on a patterned layered structure. For optimizing and characterizing these devices, numerical simulations play a crucial role. In this talk, an integral equation method in 2 and 3D layered media Helmholtz equation will be presented. In 2D, the boundary integral equation with the periodizing scheme is used. This method uses near and farfield decomposition to avoid using the quasiperiodic Green’s function. By construction, the farfield contribution can be compressed using Schur complement with minimal computational cost. The new method solved the scattering from a 1000layer with 300,000 unknown to 9digit accuracy in 2.5 minutes on a workstation. In 3D, a LippmannSchwinger type volume integral equation is used with layered media Green’s function to include interface condition between layers and reduces the problem to only scatterers.
In both 2 and 3D layered media, a fast integral operator application is required because integral equation methods usually yield a dense matrix system. A heterogenous fast multipole method (HFMM) is developed. This is a hierarchical method and uses recursivelygenerated treestructure. The interactions from far fields are compressed with freespace multipole expansion. All the spatially variant information are collected into the multipoletolocal translation operators. As a result, many freespace tools can be adapted directly without any modification to obtain an optimal O(N) algorithm for low frequency.
This is a joint work with Jingfang Huang (UNC), Alex Barnett (Dartmouth College), Duan Chen (UNC Charlotte), and Wei Cai (Southern Methodist University)

Friday, Nov 2, 11:30AM12:30 PM, Fretwell 116
Dr. Dat Cao, Texas Tech University 
Title: Asymptotic expansions for solutions of NavierStokes equations in a general class of decaying forces 
Abstract: We discuss the long time behavior of solutions to the threedimensional NavierStokes equations with periodic boundary conditions. We introduce appropriate systems of decaying functions and the asymptotic expansion with respect to those systems. It is shown that if the force has a longtime asymptotic expansion in SobolevGevrey spaces in such a general system then any LerayHopf weak solution admits an asymptotic expansion of the same type. Particularly, we obtain the expansions in terms of the logarithmic and iterated logarithmic decay and recover the case of power decay obtained earlier. This is a joint work with Luan Hoang 
Thursday, Sept 20, 11:00AM12:00 noon, Fretwell 315
Dr. Jeanne Atwell, National Defense, Ball Aerospace, USA 
Title: Math in Industry: Examples from Aerospace 
Abstract: Degrees in math often lead to careers in teaching or academia, but not always. Dr. Jeanne Atwell, a UNCC math department alumni, will share how her math degree led to a career in the Aerospace industry, and compare and contrast problem solving as a math student vs. an industry professional. 