CURRICULUM VITAE DAVID GEORGE CARABALLO. Associate Professor Department of Mathematics and Statistics Georgetown University

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1 CURRICULUM VITAE DAVID GEORGE CARABALLO Associate Professor Department of Mathematics and Statistics Georgetown University RESEARCH INTERESTS: My primary field of research is geometric measure theory, an extension of differential geometry using measure theory which makes it possible to rigorously model complex geometrical and topological structures arising in applications. I work primarily on problems concerning lower semicontinuity, existence of minimizers, and regularity and singularity structure of minimizers, for problems in application areas such as materials science and, more recently, image processing. I have also been working to establish strong connections between geometric measure theory and other fields, most notably topology and convex analysis. EDUCATION: PRINCETON UNIVERSITY (Ph.D. in Mathematics, 1997) Thesis title: A Variational Scheme for the Evolution of Polycrystals by Curvature Advisor: Frederick J. Almgren, Jr. RUTGERS COLLEGE, RUTGERS UNIVERSITY B. A. in Math, graduated with Highest Honors POSITION: GEORGETOWN UNIVERSITY Associate Professor, 2011 present Assistant Professor, (I have also taught at MIT and at Embry-Riddle University.) 1

2 GRANTS, FELLOWSHIPS, AND SCHOLARSHIPS: Awarded Junior Faculty Research Fellowship, Spring year award (2006) from Los Alamos National Laboratory, $74, Awarded grant for project Anisotropic energies, polycrystals and partitions: associated steepest descent evolutions from the Consiglio Nazionale delle Ricerche (CNR), Italy (jointly) Participants: G. Bellettini (Rome), M. Novaga (Pisa), C. Mantegazza (SNS, Pisa), I. Fragala (Poletecnico Milano), M.S. Gelli (Pisa), G. Riey (Rome), A. Stancu (NYU), K. Vixie (LANL), D. Caraballo (Georgetown) Office of Naval Research (ONR) Graduate Fellowship Department of Education GAANN Fellowship Princeton University Graduate Assistantship National Merit Scholarship Dr. Scholl Worldwide Foundation Scholarship Rutgers Le Clear Scholarship Rutgers College Merit Scholarship Elks Foundation Scholarship OTHER FINANCIAL SUPPORT FOR RESEARCH: I received funding, through the Verification and validation of largescale complex simulations project with Los Alamos National Laboratories, for several meetings/workshops of the MRGA (Metrics, Regularization, and Geometric Analysis) working group from the DDMA (Data Driven Modeling and Analysis) team at Los Alamos National Laboratories. 2

3 HONOR SOCIETIES AND SOME AWARDS: Nominated for the Mathematical Association of America Deborah and Franklin Tepper Haimo Award for Distinguished College or University Teaching of Mathematics, academic year Nominated by the Mathematics Department for the Georgetown College Dean s Award for Excellence in Teaching, academic year Nominated by the Mathematics Department for the Georgetown College Dean s Award for Excellence in Teaching, academic year Elected to the Phi Beta Kappa Society Elected to the Pi Mu Epsilon National Mathematics Honor Society Elected to the Phi Eta Sigma National Honor Society Won John Bogart Prize for being the best student majoring in mathematics at Rutgers, the State University Won Bogart-Bradley-Hoyt university-wide mathematics competition at Rutgers University Won Weiss mathematics competition for first-year students at Rutgers University 3

4 REFEREED JOURNAL PAPERS SINCE 2005: * Caraballo, David G., Existence of surface energy minimizing partitions of R n satisfying volume constraints, submitted to Transactions of the American Mathematical Society; update: I am shortening the paper at the request of the editor. * Caraballo, David G., BV-ellipticity and lower semicontinuity of surface energy of Caccioppoli partitions of R n, Journal of Geometric Analysis (2011). * Caraballo, David G., Reduced boundaries and convexity, Proceedings of the AMS (2013) (accepted, to appear). * Caraballo, David G., Local simplicity, topology, and sets of finite perimeter, Interfaces and Free Boundaries 13 Issue 2 (2011), pp * Caraballo, David G., B2-convexity implies strong and weak lower semicontinuity of partitions of R n, Pacific Journal of Mathematics 253 No. 2 (2011), pp * Caraballo, David G., Convexity, local simplicity, and reduced boundaries of sets, Journal of Convex Analysis 18 No. 3 (2011), pp * Caraballo, David G., B2-convexity and surface energy of space partitions, Journal de Mathématiques Pures et Appliquées, 94 (2010), * Caraballo, David G., Uniform local energy estimates and partial regularity for space partitions, Applicable Analysis, special issue on Variational Analysis and Related Topics, * Caraballo, David G., Flat φ curvature flow of convex sets, Taiwanese Journal of Mathematics 16 No. 1 (2012), pp

5 * Caraballo, David G., The triangle inequalities and lower semicontinuity of surface energy of partitions, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 139 (2009), pp * Caraballo, David G., Crystals and polycrystals in R n : lower semicontinuity and existence, Journal of Geometric Analysis, 18 Number 1 (2008), pp * Caraballo, David G., 2-Dimensional flat curvature flow of crystals, Interfaces and Free Boundaries: Mathematical Modelling, Analysis, and Computation, Vol. 7, No. 3, (2005), pp * Caraballo, David G., Estimates on the areas of level sets of distance functions induced by asymmetric norms, Pacific Journal of Mathematics, Vol. 218, No. 1, (2005), pp TECHNICAL REPORTS: (TR2) Caraballo, David G. and Esedoglu, Selim, Metric selection via expert opinion on training data set, LANL Data Driven Modeling & Analysis Team (DDMA) technical report, (TR1) Caraballo, David G., The Geomeasures Toolkit, LANL Data Driven Modeling & Analysis Team (DDMA) technical report, and 75+ Matlab programs,

6 SOME INVITED RESEARCH TALKS: Existence, regularity, and singularity structure for energy minimizing partitions of space into regions having prescribed volumes, Functional Analysis seminar, Catholic University of America, April 6, Existence of surface energy minimizing partitions of space satisfying volume constraints and having independent surface energy density functions, AMS Joint Meetings, New Orleans, LA, January Convexity and Geometric Measure Theory, AMS Special Session on Convexity and Combinatorics, AMS Conference, Richmond, VA, November 7, On Surface Energy Minimizing Partitions of R n into Regions Having Specified Volumes, AMS Conference, Richmond, VA, November 6, Existence of Surface Energy Minimizing Partitions of Space Satisfying Volume Constraints, George Mason University Department of Mathematical Sciences Colloquium, September 17, Local Simplicity, Topology, and Geometric Measure Theory, Topology Seminar at George Mason University, May 7,

7 OLDER INVITED RESEARCH TALKS: Princeton University The Geometry Center at the University of Minnesota Brown University MIT Los Alamos National Laboratory (several) LANL DDMA (presentations) AMS Joint Meetings in the Special Session on Geometric Analysis Georgetown University (several) Jean Taylor Symposium at Rutgers University Catholic University NIST LONG RESEARCH WORKSHOPS (~40 hours each), involving research and talks/presentations: Los Alamos National Laboratories DDMA Workshop: Jan Los Alamos National Laboratories DDMA Workshop: Mar Los Alamos National Laboratories DDMA Workshop: Feb Los Alamos National Laboratories DDMA Workshop: Mar Los Alamos National Laboratories DDMA Workshop: May 2006 REVIEWING/EDITING: I have served as an anonymous reviewer for several math journals. I have served as a reviewer for one textbook: Calculus: Early Transcendentals, 7 th Edition, by Edwards and Penney. I have also been an editor of one textbook: Stats, Data, and Models by De Veaux, Velleman, and Bock. 7

8 TEXTBOOKS BEING DEVELOPED: Introduction to Mathematical Probability: this is a rigorous and thorough introduction to the field, at the advanced undergraduate or beginning graduate level. Calculus: the art of making curved things straight: this is a short book on first-semester calculus. Mathematical Thinking: an introduction to proofs and problemsolving: this is a book designed to help students make the transition from single-variable calculus to more advanced courses emphasizing proof and problem-solving. PROFESSIONAL MEMBERSHIPS: AMS (American Mathematical Society) MAA (Mathematical Association of America) ADVISING: I have served as advisor for many students, both undergraduates and Master s students. 8

9 SERVICE: Georgetown College Admissions Committee (academic year ) Departmental Curriculum Committee (Fall 2004 Spring 2010, Fall 2011 present) University research committee (Internal Grant Review committee, Fall 2012 present) Graduate Steering Committee (Fall 2011 present) Math Department Hiring Committee (2005, 2006, 2007) Pi Mu Epsilon (Math Honor Society) Chapter President (2004 present) Merit Review Committee (2005) Representative to the College Board of Advisors; gave presentation on Innovations in the Mathematics Department (academic year ) Departmental Math Club/Contest Problems Committee (2004 present) Departmental Library Committee ( ) Joseph S. Lepgold Award Committee (2010) Phi Beta Kappa selection committee (2011) various miscellaneous events (Majors Fairs, GAAP Open House, etc.) 9

10 TEACHING (Georgetown courses taught or scheduled): Math 003: Short Course in Calculus Math 004: Math in Society Math 035: Calculus I Math 036: Calculus II Math 040: Probability and Statistics Math 137: Multivariable Calculus Math 150: Linear Algebra Math 200: Introduction to Proof and Problem-Solving (also taught this course as Math 208: Foundations of Mathematics) Math 212: Number Theory Math 310: Analysis I Math 501: Probability Theory and Applications (graduate) Math 301/2: Tutorial: Advanced Calculus Math 301/2: Tutorial: Fibonacci Numbers and Number Theory Math 301/2: Tutorial: Modern Mathematics Math 301/2: Tutorial: Ordinary Differential Equations Math 301/2: Tutorial: Mathematical Statistics 10