Department of Mathematical Sciences
Events
People
Colloquia and Seminars
Conferences
Centers
Positions
Areas of Research
About the Department
Alumni 
Faculty
Dejan Slepčev, Professor Ph.D., University of Texas at Austin Email: slepcev AT math DOT cmu DOT edu Office: Wean Hall 7123 Phone: 4122682562 Personal web site Research:My research is in applied analysis. It has two main themes. One of them is investigation of energydriven systems  that is systems whose dynamics is driven by dissipating an associated free energy. The dissipation mechanism endows the underlying configuration space with a geometric structure. Investigating the geometry of the energy landscape enables one to obtain important information about the behavior of the given system. With collaborators, I have studied dynamics of thinliquid films, demixing of fluids, evolution of interfaces, systems with nonlocal interactions, and analyzed models of collective behavior in biological systems. The phenomena I have studied include dynamical scaling in coarsening processes, singularity formation, diffuse interface models and their sharp interface limits, evolution of grainboundary networks and fundamental questions of existence, uniqueness, and asymptotic behavior in nonlocal interaction equations. Studies of these phenomena connect partialdifferential equations, fluid mechanics, calculus of variations, optimal transport, and applied fields. The other line of my research, which involves a broad collaboration, is on application of variational techniques to problems of analysis of large data sets. The task of data and image analysis is to enable scientists to analyze often high dimensional, datasets and interpret the information they contain. Many of these tasks like classification, clustering, data parameterization, and representation have a variational description, where the goal is to minimize an objective functional. Motivated by variational approaches to image analysis, I am studying totalvariation based approaches to analysis of data clouds. As the natural data structure is often a graph, this involves building tools to analyze variational problems on graphs. In particular I have studied behavior of functionals and algorithms on graphs as the number of data points goes to infinity. I am also working on using optimaltransportationbased techniques for studies of medical images, for tasks such as cancer detection. Another research topic is the use of energy based approaches to find optimal ways to parameterize highdimensional datasets by low dimensional objects. This research involves modeling, rigorous analysis of nonlocal energy functionals and design of efficient numerical algorithms. Recent CNA Publications:
