Sivaram Narayan
Sivaram Narayan
Professor
Operator Theory

Pearce Hall 218
989-774-3566
sivaram.narayan@cmich.edu

Education

  • Ph.D., Purdue University, 1988
  • M.S., University of Michigan, 1981
  • B.S., University of Madras, India, 1974

Affiliations

American Mathematical Society, Mathematical Association of America, International Linear Algebra Society

Honors and Awards

  • College of Science and Technology Outstanding Research Award, 2009
  • College of Science and Technology Outstanding Teaching Award, 2004
  • Central Michigan University Research Professorship, Spring 2004

Professional Interests

Operator Theory and Matrix Analysis

Teaching Areas

Calculus I-III, Linear Algebra, Differential Equations, Complex Analysis, Functional Analysis, and Real Analysis

Ph.D. Students

  • ​Kevin Dennis, May 2000
  • Patricia Egleston, December 2001
  • Dawn Sadir, August 2003
  • Animesh Sarker, May 2008
  • ​PalRamani Karthikeyan, May 2008
  • Waleed Al-Rawashdeh, August 2010
  • Yousra Sharawi, December 2011

Recent Publications

Note: An * after a name indicates the co-author was an undergraduate student at the time of collaboration.

  • (2013) The Koteljanski Inequalities for Mixed Matrices (with C.R. Johnson) to appear in Linear and Multilinear Algebra.
  • (2013) When the positivity of the leading principal minors implies the positivity of all principal minors of a matrix (with C.R. Johnson), to appear in Linear Algebra and its Applications.
  • (2013) Maximum robustness and surgery of frames in finite dimensions (with M. Copenhaver*, Y. Kim, C. Logan*, K. Mayfield*, and J. Sheperd*). Linear Algebra and its Applications 439 (2013) 1330-1339.
  • (2013) Diagram vectors and tight frame scaling in finite dimensions (with M. Copenhaver*, Y. Kim, C. Logan*, K. Mayfield*, M. Petro and J. Sheperd*), to appear in Operators and Matrices.
  • (2013) Difference of Composition Operators on Hardy Space (with W. Al-Rawashdeh), to appear in Journal of Mathematical Inequalities.
  • (2013) Bounds for minimum rank problems from superpositions and cut sets (with J. Beagley*, L. Mitchell, E. Radzwion*, S. Rimer*, R. Tomasino*, J. Wolfe*, and A. Zimmer*), Linear Algebra and its Applications 438 (2013) 4041-4061.
  • (2013) Commutators of Composition Operators with Adjoints of Composition Operators on Weighted Bergman Spaces (with B.D. MacCluer and R. J. Weir), Complex Variables and Elliptical Equations 58 (2013) 35-54.
  • (2012) Maximum induced trees and minimum semidefinite rank (with R. Cranfill*, L. Mitchell, and Taiji Tsutsui*), Involve 5 (2012) 411-420.
  • (2012) Subgraph Summability Number of Paths and Cycles (with D. Cochran*, R. Doshi*, M. Larson-Koester*, R. Ligo*, and J. Webster), AKCE Journal of Graphs and Combinatorics 9 (2012), 135-143.
  • (2012) On Nonsingular Regular Magic Squares of Odd Order (with M. Lee*, E. Love*, E. Wascher* and J. Webster), Linear Algebra and its Applications 437 (2012) 1346-1355.
  • (2012) Weighted composition operators on weighted Bergman spaces of the unit ball (with W. Al-Rawashdeh), International Journal of Pure and Applied Mathematics 78 (2012) 161-183.
  • (2012) Commutators of Composition Operators with Adjoints of Composition Operators (with J. Clifford and D. Levi), Complex Variables and Elliptic Equations 57 (2012) 677-686.
  • (2012) Lower bounds for minimum semidefinite rank from orthogonal removal and chordal supergraphs (with L.H. Mitchell, A.M. Zimmer), Linear Algebra and its Applications 436 (2012) 525-536.
  • (2011) On the minimum semi-definite rank of a simple graph (with M. Booth*, P. Hackney*, B. Harris*, C.R. Johnson, M. Lay*, T. Lenker, L. Mitchell, A. Pascoe*, B.D. Sutton) Linear and Multilinear Algebra 59 (2011), 483-506.
  • (2011) Minimum semidefinite rank of outerplanar graphs and the tree cover number (with F. Barioli, L. Mitchell and S. Fallat), Electronics Journal of Linear Algebra 22 (2011),
    10-21.
  • (2011) Robustness and Surgery of Frames (with E. Radzwion*, S. Rimer*, R. Tomasino*, J. Wolfe*, and A. Zimmer) Linear Algebra and its Applications 434 (2011) 1893-1901.
  • (2010) On the minimum vector rank of multigraphs (with L. Mitchell and I. Rogers*), Electronics Journal of Linear Algebra 20 (2010), 661-672.
  • (2010) Normal Weighted Composition Operators on the Hardy Space H2(U) (with P.S. Bourdon) Journal of Mathematical Analysis and its Applications 367 (2010), 278-286.
  • (2010) Lower bounds in minimum rank problems (with L.H. Mitchell, A.M. Zimmer), Linear Algebra and its Applications 432 (2010), 430-440.
  • (2009) Circular Symmetry of Spectra of Composition Operators (with Dawn E. Sadir), Far East Journal of Mathematical Sciences 35 (2009), 281-293.
  • (2009) Linearly independent vertices and minimum semi-definite rank (with P. Hackney*, B. Harris*, M. Lay*, L. Mitchell, A. Pascoe*), Linear Algebra and its Applications 431 (2009), 1105-1115.
National Science Foundation - Research Experience for Undergraduates (REU) site in Mathematics
  • 2012-2014. These sites are part of a 3-year, $283,537 grant from NSF awarded to Narayan as PI.
  • 2009-2011. These sites were part of a 3-year, $199,952 grant from NSF awarded to Narayan as PI.
  • 2009-2008. These sites were part of a 3-year, $175,000 grant from NSF awarded to Narayan as PI and Ken Smith as co-PI.
  • 2003-2005. These sites were part of a 3-year, $160,000 grant from NSF awarded to Narayan as PI and Ken Smith as co-PI.
  • 2002. This was the first NSF-REU site at CMU. The REU site was supported by an NSF grant of $36,000 awarded to Narayan as PI.
National Science Foundation Long-term Undergraduate Research Experience (LURE) site in Mathematics
  • 2007-2011. This site was part of a 4-year grant from NSF. The grant supported sites at 5 locations. The other sites were at Coppin State University, Olin College, Sam Houston State University, and the University of Richmond.
Undergraduate Student Research
Supervised undergraduate student research of 72 undergraduates since summer 1998. Among the 72 students, 45 came from various colleges and universities outside of Central Michigan University. They were funded by the NSF-REU grant or were international students supported by their home college/university. There were 27 CMU undergraduate students who have worked with me since 1998. 12 of the 27 received Summer Research Scholarships, 7 were supported by an NSF-REU matching grant from CMU, 4 were supported by the NSF-LURE grant, 1 student was supported by a McNair Scholarship, and the Dean of the CMU College of Science & Technology funded 3 students.

All students have made several oral and poster presentations at regional and national mathematics conferences. Many of them are co-authors on scholarly publications in refereed research journals.