# ICMAT Laboratory "Marius Junge"

Marius Junge

Marius Junge

Marius Junge was born in 1962 in Hannover, Germany. He defended his Ph.D. Thesis at Christian-Albrechts Universität at Kiel, under the supervision of Herman König. In 2007, Junge received full professorship at the University of Illinois at Urbana-Champaign.

Marius Junge is worldwide known for his work in quantum probability, operator space theory, noncommutative harmonic analysis and more recently quantum information theory. Of special interest are his contributions on noncommutative maximal Doob’s and ergodic theorems, the Grothendieck program for von Neumann algebras, the cb-embedding theory for noncommutative Lp spaces and more recently on Fourier multipliers for group von Neumann algebras and violation of Bell inequalities.

The aim of the project is to accept the quantum mechanical perspective in the context of harmonic analysis and information theory. We are interested in extending classical estimates for Fourier multipliers to group von Neumann algebras and other noncommutative scenarios. Among other topics, this includes Hörmander-Mihlin multiplier type theorems, Calderón-Zygmund and Littlewood-Paley methods, hypercontractivity and log-Sobolev inequalities, transference techniques… Additionally, some of these problems lead us to new viewpoints in classical harmonic analysis. Regarding quantum information, we will be focussing on quantum channels, Bell inequalities and entanglement theory and quantum games via operador spaces.

Selected publications of Marius Junge

[1] Integral mappings and the principle of local reflexivity for noncommutative L1-spaces (with E. Effros and Z-J. Ruan). Ann. of Math. (2) 151 (2000), no. 1, 59–92.

[2] Doob's inequality for non-commutative martingales. J. Reine Angew. Math. 549 (2002), 149–190.

[3] Noncommutative Burkholder/Rosenthal inequalities (with Q. Xu). Ann. Probab. 31 (2003), no. 2, 948–995.

[4] Embedding of the operator space OH and the logarithmic `little Grothendieck inequality'. Invent. Math. 161 (2005), no. 2, 225–286.

[5] Noncommutative maximal ergodic theorems (with Q. Xu). J. Amer. Math. Soc. 20 (2007), no. 2, 385–439.

[6] Rosenthal's theorem for subspaces of noncommutative Lp (with J. Parcet). Duke Math. J. 141 (2008), no. 1, 75–122.

[7] Operator space embedding of Schatten p-classes into von Neumann algebra preduals (with J. Parcet). Geom. Funct. Anal. 18 (2008), no. 2, 522–551.

[8] Representation of certain homogeneous Hilbertian operator spaces and applications (with Q. Xu). Invent. Math. 179 (2010), no. 1, 75–118.

[9] Unbounded violations of bipartite Bell inequalities via operator space theory (with C. Palazuelos, D. Pérez-García, I. Villanueva and M. M. Wolf). Comm. Math. Phys. 300 (2010), no. 3, 715–739.

[10] Large violation of Bell inequalities with low entanglement (with C. Palazuelos). Comm. Math. Phys. 306 (2011), no. 3, 695–746.

Selected work by Marius Junge and his LAB collaborators at ICMAT

RECENT PUBLICATIONS WITH M. JUNGE

T. Cooney, M. Junge, C. Palazuelos and D. Pérez-García,
Rank-one Quantum Games.
To appear in Comput. Complexity. ArXiv:1112.3563.

M. Junge, T. Mei and J. Parcet,
An invitation to harmonic analysis associated to semigroups of operators.
Proceedings 9th Int. Conf. Harmonic Analysis and PDEs. Contemp. Math. 612, 2014.

M. Junge, T. Mei and J. Parcet
Smooth Fourier multipliers in Group von Neumann algebras.
Arxiv:1010.5320.

M. Junge, T. Mei y J. Parcet,
Noncommutative Riesz transforms --- Dimension free bounds and Fourier multipliers.
Arxiv:1407.2475.

M. Junge and C. Palazuelos,
Channel capacities via p-summing norms.
ArXiv:1305.1020.

M. Junge and C. Palazuelos,
CB-estimates for maps between noncommutative Lp-spaces and quantum channel theory.
ArXiv:1407.7684.

M. Junge, C. Palazuelos, J. Parcet and M. Perrin,
Hypercontractivity in group von Neumann algebras.
ArXiv:1304.5789.

M. Junge, C. Palazuelos, J. Parcet and M. Perrin,
Hypercontractivity in finite-dimensional matrix algebras.
Preprint.

M. Junge, C. Palazuelos, J. Parcet, M. Perrin and É. Ricard,
To appear in Annales Scientifiques de l’ENS. ArXiv:1211.4759.

M. Junge and M. Perrin,
Theory of Hp-spaces for continuous filtrations in von Neumann algebras.
Astérisque, nº 362 (2014).

HISTORY OF COLLABORATION - FORMER PUBLICATIONS

M. Junge, C. Palazuelos, D. Pérez-García, I. Villanueva and M.M. Wolf,
Operator Space theory: a natural framework for Bell inequalities.
Phys. Rev. Lett. 104, 170405 (2010).

M. Junge, C. Palazuelos, D. Pérez-García, I. Villanueva and M.M. Wolf.
Unbounded violations of bipartite Bell Inequalities via Operator Space theory,
Comm. Math. Phys. 300 (3),715-739 (2010).

M. Junge, M. Navascues, C. Palazuelos, D. Pérez-García, V. B. Scholz and R. F. Werner, Connes' embedding problem and Tsirelson's problem.
J. Math. Phys. 52, 012102 (2011).

M. Junge and C. Palazuelos,
Large violation of Bell inequalities with low entanglement.
Comm. Math. Phys. 306 (3), 695-746 (2011).

M. Junge y J. Parcet,
The norm of sums of independent non-commutative random variables in $L_p(\ell_1)$.
J. Funct. Anal. 221 (2005), 366-406.

M. Junge y J. Parcet,
Rosenthal's theorem for subspaces of noncommutative $L_p$.
Duke Math. J. 141 (2008), 75-122.

M. Junge y J. Parcet,
Operator space embedding of Schatten p-classes into von Neumann algebra preduals.
Geom. Funct. Anal. 18 (2008), 522-551.

M. Junge y J. Parcet,
Mixed-norm inequalities and operator space Lp embedding theory.
Mem. Amer. Math. Soc. 952, 2010.

M. Junge y J. Parcet,
A transference method in quantum probability.