Dominique Guillot

 

Assistant Professor
Department of Mathematical Sciences
University of Delaware
534 Ewing Hall
Newark, DE, 19716
Phone: (302)-831-4444
email: dguillot [@] udel [DOT] edu

Research

My research focuses on several areas of harmonic and functional analysis

CV

My CV in pdf (last updated 04/16/2019).

Publications

Peer-reviewed

  1. A. Belton, D. Guillot, A. Khare, M. Putinar, Simultaneous kernels of matrix Hadamard powers, Linear Algebra and its Applications, in print, 2018, arXiv:1709.03280

  2. D. Guillot, A. Khare, B. Rajaratnam, The critical exponent: a novel graph invariant, 29th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC '17), Séminaire Lotharingien de Combinatoire, in press, 2017.

  3. D. Guillot, A. Khare, B. Rajaratnam, Preserving positivity for rank-constrained matrices, Trans. Amer. Math. Soc., 369(2017):6105--6145, arXiv:1406.0042

  4. A. Belton, D. Guillot, A. Khare, M. Putinar, Matrix positivity preservers in fixed dimension. I, Advances in Mathematics, 298, 2016, Pages 325--368, arXiv:1504.07674

  5. A. Belton, D. Guillot, A. Khare, M. Putinar, Schur polynomials and matrix positivity preservers, FPSAC '16 Proceedings (DMTCS), 155--166, 2016.

  6. A. Belton, D. Guillot, A. Khare, M. Putinar, Matrix positivity preservers in fixed dimension, C. R. Acad. Sci. Paris, Volume 354, Issue 2, 2016, Pages 143--148. link

  7. D. Guillot, A. Khare, B. Rajaratnam, Critical exponents of graphs, J. Combin. Theory Ser. A, Volume 139, 2016, Pages 30--58, arXiv:1504.04069

  8. D. Guillot, A. Khare, B. Rajaratnam, Preserving positivity for matrices with sparsity constraints, Trans. Amer. Math. Soc., 368 (2016), 8929--8953, arXiv:1406.3408.

  9. P. Diao, D. Guillot, A. Khare, B. Rajaratnam, Differential calculus on graphon space, J. Combin. Theory Ser. A, Volume 133, 2015, Pages 183--227, arXiv:1403.3736.

  10. D. Guillot, B. Rajaratnam, Functions preserving positive definiteness for sparse matrices, Trans. Amer. Math. Soc. 367 (2015), 627-649, arXiv:1210.3894.

  11. D. Guillot, A. Khare, B. Rajaratnam, Complete characterization of Hadamard powers preserving Loewner positivity, monotonicity, and convexity, J. Math. Anal. Appl., 425(1):489-507, 2015, arXiv:1311.1581.

  12. D. Guillot, A. Khare, B. Rajaratnam, The critical exponent conjecture for powers of doubly nonnegative matrices, Linear Algebra and its Applications, Volume 439, Issue 8, 2013, Pages 2422-2427, arXiv:1303.4701.

  13. D. Guillot, B. Rajaratnam, Retaining positive definiteness in thresholded matrices, Linear Algebra and its Applications, Volume 436, Issue 11, 1 June 2012, Pages 4143-4160, arXiv:1108.3325.

  14. D. Guillot, A. Maleki, B. Rajaratnam, B. Rolfs, I. Wong, Iterative thresholding algorithms for sparse inverse covariance estimation, NIPS, Lake Tahoe, 2012, arXiv:1211.2532.

  15. J. Wang, J. Emile-Geay, D. Guillot, N. McKay, B. Rajaratnam, Fragility of reconstructed temperature patterns over the Common Era: Implications for model evaluation, Geophysical Research Letters, in print, 2015, link.

  16. D. Guillot, B. Rajaratnam, J. Emile-Geay, Statistical paleoclimate reconstructions via Markov random fields, Ann. Appl. Stat., Volume 9, Number 1, 2015, Pages 324--352, arXiv:1309.6702

  17. J. Wang, J. Emile-Geay, D. Guillot, J. E. Smerdon, and B. Rajaratnam, Evaluating climate field reconstruction techniques using improved emulations of real-world conditions, Clim. Past, 10, 1-19, 2014 link.

  18. J. Wang, J. Emile-Geay, D. Guillot, B. Rajaratnam, Spatiotemporal Pattterns of low-frequency variability in a 2000-year long global temperature reconstruction, 4th International Workshop on Climate Informatics, National Center for Atmospheric Research, Boulder, CO, 2014.

  19. D. Guillot, N. Chevrot, T. J. Ransford, De Branges-Rovnyak spaces and Dirichlet spaces, J. Funct. Anal., 259 (2010), 2366-2383.

  20. D. Guillot, Blaschke condition and zero sets in weighted Dirichlet spaces, Arkiv for Matematik, Volume 50, Issue 2 (2012), 269-278.

  21. D. Guillot, Fine boundary behavior and invariant subspaces of harmonically weighted Dirichlet spaces, Complex Analysis and Operator Theory, 2012, Volume 6, Issue 6, 1211-1230.

  22. D. Guillot, Comportement au bord dans les espaces de Dirichlet avec poids harmoniques et espaces de de Branges-Rovnyak (Boundary behavior in Dirichlet spaces with harmonic weights and de Branges–Rovnyak spaces), Doctoral dissertation, Universite Laval, 2010.

  23. D. Guillot, La visibilite du spectre des algebres de Banach et le probleme de l'inversion controlee (Visibility of the spectrum in Banach algebras and the problem of controlled inversion), Master thesis, Universite Laval, 2007.

  24. D. Guillot, T.J. Ransford, Bloch's theorem for algebroid multifunctions II, Math. Proc. R. Ir. Acad., 105A(2) (2005), 103-109.

In submission

  1. D. Guillot, J. Wu, Total nonnegativity of GCD matrices and kernels, submitted, arXiv:1901.01947

  2. A. Belton, D. Guillot, A. Khare, M. Putinar, A panorama of positivity, submitted, arXiv:1812.05482

  3. A. Belton, D. Guillot, A. Khare, M. Putinar, Total positivity preservers, submitted, arXiv:1711.10468

  4. A. Belton, D. Guillot, A. Khare, M. Putinar, Moment-sequence transforms, submitted, arXiv:1610.05740

  5. P. Diao, D. Guillot, A. Khare, B. Rajaratnam, Model-free consistency of graph partitioning, submitted, arXiv:1608.03860

Teaching

  1. Spring 2019. MATH 350: Probability Theory and Simulation Methods.

  2. Fall 2018.

    MATH 451: Abstract Algebra.

    MATH 350: Probability Theory and Simulation Methods.

  3. Fall 2017. MATH 245: An Introduction to Proof.

  4. Spring 2017. MATH 567: Mathematical Techniques in Data Science.

  5. Fall 2016.

    MATH 349: Elementary linear algebra (honors section).

    MATH 450: Mathematical Statistics.

  6. Spring 2016. MATH 829: Introduction to data mining and analysis.

  7. Fall 2015. MATH 349: Elementary linear algebra (honors section).

Conference Organization

  1. AMS Special Session on Interplay between Analysis and Combinatorics, AMS Fall Eastern Sectional Meeting, U. Delaware, September 29-30, 2018, Co-organizer: Mahya Ghandehari (U. Delaware).

  2. Positivity with Applications to Data Science, ILAS 2017 Meeting Invited Minisymposium, July 24-27, 2017, Co-organizers: Apoorva Khare (IISc Bangalore) and Bala Rajaratnam (UC Davis).

  3. Positivity, graphical models, and modeling of complex multivariate dependencies, American Institute of Mathematics (Palo Alto), October 13-17, 2014. Co-organizers: Apoorva Khare (Stanford), Helene Massam (York), and Bala Rajaratnam (Stanford).

  4. AMS Special Session on Positivity and Matrix Inequalities, Joint Mathematics Meetings, San Antonio, January 10-13, 2015. Co-organizers: Apoorva Khare (Stanford), and Bala Rajaratnam (Stanford).

  5. AMS Special Session on Limits of Discrete Structures, Joint Mathematics Meetings, San Antonio, January 10-13, 2015. Co-organizers: Peter Diao (Stanford), Apoorva Khare (Stanford), and Bala Rajaratnam (Stanford).