Assistant Professor |

My research focuses on several areas of harmonic and functional analysis

Analysis on cones of matrices

Analysis of large graphs and graph limits

High-dimensional statistics

Spaces of analytic functions

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**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), SÃ©minaire Lotharingien de Combinatoire, in press, 2017.**D. Guillot**, A. Khare, B. Rajaratnam,*Preserving positivity for rank-constrained matrices*, Trans. Amer. Math. Soc., 369(2017):6105--6145, arXiv:1406.0042A. Belton,

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

**D. Guillot**, A. Khare, M. Putinar,*Schur polynomials and matrix positivity preservers*, FPSAC '16 Proceedings (DMTCS), 155--166, 2016.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**D. Guillot**, A. Khare, B. Rajaratnam,*Critical exponents of graphs*, J. Combin. Theory Ser. A, Volume 139, 2016, Pages 30--58, arXiv:1504.04069**D. Guillot**, A. Khare, B. Rajaratnam,*Preserving positivity for matrices with sparsity constraints*, Trans. Amer. Math. Soc., 368 (2016), 8929--8953, arXiv:1406.3408.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.**D. Guillot**, B. Rajaratnam,*Functions preserving positive definiteness for sparse matrices*, Trans. Amer. Math. Soc. 367 (2015), 627-649, arXiv:1210.3894.**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.**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.**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.**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.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.**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:1309.6702J. 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.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.**D. Guillot**, N. Chevrot, T. J. Ransford,*De Branges-Rovnyak spaces and Dirichlet spaces*, J. Funct. Anal., 259 (2010), 2366-2383.**D. Guillot**,*Blaschke condition and zero sets in weighted Dirichlet spaces*, Arkiv for Matematik, Volume 50, Issue 2 (2012), 269-278.**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.**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.**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.**D. Guillot**, T.J. Ransford,*Bloch's theorem for algebroid multifunctions II*, Math. Proc. R. Ir. Acad., 105A(2) (2005), 103-109.

D. Guillot, J. Wu,

*Total nonnegativity of GCD matrices and kernels*, submitted, arXiv:1901.01947A. Belton, D. Guillot, A. Khare, M. Putinar,

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

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

*Moment-sequence transforms*, submitted, arXiv:1610.05740P. Diao, D. Guillot, A. Khare, B. Rajaratnam,

*Model-free consistency of graph partitioning*, submitted, arXiv:1608.03860

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

Fall 2018.

MATH 451: Abstract Algebra.

MATH 350: Probability Theory and Simulation Methods.

Fall 2017. MATH 245: An Introduction to Proof.

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

Fall 2016.

MATH 349: Elementary linear algebra (honors section).

MATH 450: Mathematical Statistics.

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

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

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).

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).

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).

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).

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).