This page contains a list of seminars that I am co-organizing within the Department of Computer Science and Department of Applied Mathematics
at CU Boulder. For a list of seminars that I gave, please see my CV.

This series of talks aims at encouraging networking among postdocs and promoting the exchange of ideas for potential collaborations.
We have started this series of relatively informal seminars where the postdocs from the two Departments, and occasionally from other local universities,
can showcase their research and foster relationships and collaborations between the two Departments and other universities.

**Please note:** These seminars are given by postdocs, but are intended for all types of audience (students are welcome!).

**APPM + CS Postdoc Seminar:**

**Fri. Nov. 16, 2018:**

**Time:**1 pm

**Location:**ECOT 831

**Speaker: Giacomo Capodaglio**, Florida State University, Visiting Scholar at the Department of Applied Mathematics, CU Boulder

**Title:**

*Approximation of probability density functions for SPDEs using truncated series expansions*

**Abstract:**The probability density function (PDF) of a random variable associated with the solution of a stochastic partial differential equation (SPDE) is approximated using a truncated series expansion. The SPDE is solved using two stochastic finite element (SFEM) methods, Monte Carlo sampling and the stochastic Galerkin method with global polynomials. The random variable is a functional of the solution of the SPDE, such as the average over the physical domain. The truncated series are obtained considering a finite number of terms in the Gram-Charlier (GC) or Edgeworth (ED) series expansions. These expansions approximate the PDF of a random variable in terms of another PDF, and involve coefficients that are functions of the known cumulants of the random variable. While the GC and ED series have been employed in a variety of fields such as chemistry, astrophysics and finance, their use in the framework of SPDEs has not yet been explored. This is a joint work with Max Gunzburger and Henry P. Wynn.

**Fri. Nov. 30, 2018:**

**Time:**1 pm

**Location:**ECOT 831

**Speaker: Tahra Lucene Eissa**, Department of Applied Mathematics, CU Boulder

**Title:**

*Spatiotemporal Dynamics of Neocortical Seizure Activity*

**Abstract:**Seizures are defined as sudden, abnormal electrical disturbances in the brain. Patients diagnosed with epilepsy have chronic, recurrent seizures and often require clinical intervention to prevent these episodes. Unfortunately, a large portion of epilepsy patients do not respond to current treatment options, in part due to a lack of understanding on how seizures develop in the brain. This talk will discuss some of the complex dynamics associated with seizure activity and how these dynamics can educate epilepsy treatment. Using a combination of human electrical recordings, biological experiments and computational modeling, we studied the dynamics of seizures at various spatial scales, ranging from a single neuron up to large neuronal networks (centimeter scale). At each scale, we analyzed the interactions between the seizure-producing neurons and the surrounding tissue to determine how the interactions can define a seizure's trajectory and the activity observed clinically. The findings were then used to identify representative electrical markers that could be applied to clinical treatment.

**Fri. Dec. 14, 2018:**

**Time:**1 pm

**Location:**ECOT 831

**Speaker: Jeffrey Hokanson**, Department of Computer Science, CU Boulder

**Title:**

*H2-optimal Model Order Reduction Using Projected Nonlinear Least Squares*

**Abstract:**In many applications throughout science and engineering, model reduction plays an important role replacing expensive large-scale linear dynamical systems by inexpensive reduced order models that capture key features of the original, full order model. One approach to model reduction is to find reduced order models that are locally optimal approximations in the H2 norm, an approach taken by the Iterative Rational Krylov Algorithm (IRKA) and several others. Here we introduce a new approach for H2-optimal model reduction using the projected nonlinear least squares framework. At each iteration, we project the H2 optimization problem onto a finite-dimensional subspace yielding a weighted least rational approximation problem. Subsequent iterations append this subspace such that the least squares rational approximant asymptotically satisfies the first order necessary conditions of the original, H2 optimization problem. This enables us to build reduced order models with similar error in the H2 norm as competing methods but using far fewer evaluations of the expensive, full order model. Moreover our new algorithm only requires access to the transfer function of the full order model, unlike IRKA which requires a state-space representation or TF-IRKA which requires both the transfer function and its derivative. This application of projected nonlinear least squares to the H2-optimal model reduction problem suggests extensions of this approach related model reduction problems.