Tom Cooney - Research

Name: Tom Cooney

Office: 454 Plaza De Ciencias, 3, Universidiad Complutense De Madrid

Email: tomcooney1@gmail.com

I graduated with a Ph.D. in Mathematics from the University of Illinois in August 2010. I currently hold a postdoctoral position at the Institute for Interdiscipinary Mathematics at the Universidad Complutenese de Madrid. My research interests lie in functional analysis, especially operator algebras and operator spaces. I am currently interested in the application of operator space theory to problems in quantum information theory and quantum game theory. I am also interested in noncommutative harmonic analysis and how ideas from harmonic analysis on groups can be extended to harmonic analysis on quantum groups. My Ph.D. thesis was on this subject. My thesis advisor was Professor Zhong-Jin Ruan.
Before coming to the University of Illinois, I was at University College Cork, National University of Ireland, Cork.

A Hausdorff-Young Inequality for Locally Compact Quantum Groups, International Journal of Mathematics, Vol. 21, No. 12 (2010)

"A Hausdorff-Young Inequality for Locally Compact Quantum Groups"(Slides for a talk given at Wabash Modern Analysis Conference)

"Fourier Multipliers acing on Noncommutative Lp-spaces" (Slides for a talk given at the Banff workshop on "Noncommutative Lp-spaces, Operator Spaces and Applications")

"Noncommutative Lp-spaces Associated with Locally Compact Quantum Groups" (Ph.D. Dissertation)

Research Statement

My research interests include:

  • Operator algebras and operator spaces
  • Quantum Information theory
  • Quantum Game theory
  • The operator algebra approach to quantum groups
  • Non-commutative Lp spaces and their vector-valued counterparts
  • Approximation properties for operator algebras
  • Operator algebras generated by q-Gaussian operators or the corresponding creation operators

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    Department of Mathematics
    College of Liberal Arts and Sciences
    University of Illinois at Urbana-Champaign
    273 Altgeld Hall, MC-382
    1409 W. Green Street, Urbana, IL 61801 USA
    Department Main Office Telephone: (217) 333-3350 Fax (217) 333-9576