Weekly Colloquium
The Department hosts a weekly colloquium on Fridays at 2pm, usually in Southern Hall, room 303. If you would like to present, please contact Dr. Huiqing Zhu with a title and abstract. Please see our tips on abstracts below. You can also find links to previous years' titles and abstracts below.
Date  Presenter, Affiliation  Title, Abstract 
28 Apr 2017  Jiu Ding, USM  From Unit Circle to Mean Ergodic Theorem Starting from the powers of points on the unit circle in the complex plane, we present and prove the Mean Ergodic Theorem, a fundamental mathematical tool for the statistical and stochastic study of dynamical systems. 
21 Apr 2017  Zhisheng Shuai, University of Central Florida  Disease Invasion and Control in a Heterogeneous Environment Consider a set of communities in a heterogeneous environment, connected to one another according to a weighted network. When can a disease such as cholera invade this network? The answer depends on both the network structure and the properties of the communities. In particular, the rooted spanning intrees of the network and a generalization of the group inverse of the graph Laplacian play fundamental roles in determining the ability of disease to invade. The rooted spanning outtrees are used to construct Lyapunov functions to establish global disease dynamics. Disease control strategies can be measured in terms of closed walks of the network. 
7 Apr 2017  Yong Wang, Washington University School of Medicine  Method of Fundamental Solution and its Applications in Electrophysiological Imaging of Excitable Organs Electrophysiological imaging (EPI) is a type of novel functional imaging modality. The Method of fundamental solution (MFS) has been employed to discretize 3D Laplace’s Equation with Cauchy boundary conditions underlying EPI. MFSbased EPI has demonstrated multiple advantages over traditional meshbased numerical methods in terms of computation speed, accuracy, clinical applicability, etc. MFS has also been employed as the core numerical technique in Electrocardiographic Imaging (ECGI) and Electromyometrial Imaging (EMMI). The bridge among mathematics, engineering and medicine will enable more exciting inventions to benefit health care. 
31 Mar 2017  Dr. Gareth Roberts, College of the Holy Cross  Existence and Stability of Vortex Crystals In the weather research and forecasting models of certain hurricanes (e.g., Hurricane Rita), vortex crystals are found within a polygonalshaped eyewall. These configurations are special formations of mesovortices that rigidly rotate as a solid body. One example is the remarkably stable hexagonal cloud structure circling about the North Pole of Saturn. These special configurations can be interpreted mathematically as relative equilibria (rigidly rotating periodic solutions) of the point vortex problem introduced by Helmholtz. We will discuss some interesting examples of relative equilibria, including the wide range of mathematical techniques used to find them and study their stability. This talk is accessible to students with some background in ordinary differential equations and linear algebra. 
30 Mar 2017  Dr. Gareth Roberts, College of the Holy Cross  Special Location and time: Polymer Science Auditorium, 4 pm Math and Music: The Greatest Hits The connections between mathematics and music are numerous, deep, and fun to investigate. While this may sound surprising to some, early educational traditions, such as those proposed by Plato and later Boethius, grouped music with the subjects of arithmetic and geometry. Using a “music first” approach, I will reveal the hidden connections between these two fields, and in the process, encourage a greater appreciation and desire for mathematical thinking. Many musical transformations naturally lead to a discussion of mathematical concepts such as symmetry and the dihedral group (e.g., the symmetries of the square). We will explore these, as well as some other favorites, demonstrating how mathematics can help us understand music at a more profound level. 
24 Mar 2017  Dr. Yulia Gel, University of Texas at Dallas  Special Location: LAB 103, but same time The Role of Modern Social Media Data in Surveillance and Prediction of Infectious Diseases: from Time Series to Networks The prompt detection and forecasting of infectious diseases are critical in the defense against these diseases. Despite many promising approaches, the lack of observations for near realtime forecasting is still the key challenge for operational disease prediction and control. In contrast, online social media has a great potential for realtime epidemiological forecasting and could revolutionize modern biosurveillance capabilities. We investigate utility of Twitter to serve as a proxy for unavailable data on flu occurrence and propose a predictive platform for disease dynamics by accounting for heterogeneous social network interactions, spacetime, and sociodemographic information. 
24 Mar 2017  Dr. Jiuyi Zhu  Nodal geometry of Steklov eigenfunctions The Steklov problem is an eigenvalue problem with its spectral parameter at the boundary of a compact Riemannian manifold. Recently the study of Steklov eigenfunctions has been attracting much attention. We consider the quantitative properties: Doubling inequality and nodal sets. We obtain the sharp doubling inequality for Steklov eigenfunctions on the boundary and interior of manifolds using delicate Carleman estimates. Nodal sets are where the eigenfunctions vanish. We can ask Yau's type conjecture for the Hausdorff measure of nodal sets of Steklov eigenfunctions on the boundary and interior of the manifold. I will describe some recent progress about this challenging direction. Part of work is joint with C. Sogge and X. Wang. 
10 Mar 2017  Dr. Alan Baker, Swarthmore College  Bamboos, cicadas, and number theory Bamboos may wait for as long as 120 years before flowering and producing seeds. Periodical cicadas emerge only once every 13 years or 17 years. Biologists have long sought evolutionary explanations for the extended lifecycles and synchronized behavior of these species. But it has only been relatively recently that mathematical explanations have been proposed for why the particular numbers selected are significant. In this talk, I examine some of these explanations, explore their numbertheoretic basis, and draw some broader philosophical conclusions about the nature of mathematics. 
3 Mar 2017  Dr. James Lambers  Three Effective Compromises in Numerical Analysis This talk presents three problems in which effective numerical methods are obtained by novel compromises between competing criteria. First, I will discuss Krylov subspace spectral (KSS) methods, which apply techniques for computing elements of functions of matrices in order to solve timedependent partial differential equations in a more efficient way for highresolution simulation. Second, I will present new models for denoising and sharpening images by nonlinear diffusion. Third, I will present an approach to modeling of flow in porous media, particularly for oil reservoir simulation, in which wellknown techniques are tightly integrated in order to ensure that computational effort is expended where it is needed most. 
10 Feb 2017  Dr. Xu Zhang, Mississippi State University  Immersed finite element methods for interface problems: basic idea, development, analysis, and applications Multiscale/multiphysics phenomena often involve domains with different materials, leading to “interface problems” for PDEs: convergence for classical methods can be impaired if the mesh does not align with the interfaces. Immersed finite element (IFE) methods allow the interface's immersion, so they can use Cartesian meshes with nontrivial interface geometry. This talk briefly introduces IFE methods for the secondorder elliptic equation, describes the challenges of classical methods, introduces recent advances in designing more accurate and robust schemes, and presents mathematical convergence theories and some numerical experiments. Finally, we demonstrate how IFE methods can apply to more complicated interface model problems. 
25 Jan 017  Dr. Angela Hodge, University of Nebraska Omaha  Top 10 ways to recruit and retain strong mathematics and mathematics education majors

Tips on abstracts
Dear speaker: We like to maintain a list of titles, topics, and abstracts, so that we (and you) have a record of who has visited and talked about which topic.
 The topic should be short, similar to the headlines in the AMS subject classifications.
 Please aim for no more than 100 words in your abstract. We're not fanatically rigorous about this, but an abstract should summarize the essence of a presentation, not give every detail. It’s a sales pitch, not a business plan. Keeping the abstract at 100 words also is a good preparatory step for a concise and informative talk that communicates the salient points of your work.
 You may notice that we are MathJaxenabled, so feel free to use \(\mathrm{\LaTeX}\) markup in your abstract when appropriate.