Magdalena E. Musat

My main mathematical interests are in the fields of Functional Analysis and Operator algebras, and their interplay with analytic, geometric and probabilistic aspects of group theory, noncommutative probability theory, analysis in quantum information theory.

Head of studies (Studieleder) for the Master’s Program in Mathematics.

Organizer of the Department colloquium and of the Harald Bohr Lectures.

Education

• Ph.D. 2002, University of Illinois at Urbana-Champaign. Thesis advisors: Donald Burkholder and Marius Junge.
  Title of Ph.D. thesis: On the Operator Space UMD Property and Non-commutative Martingale Inequalities.

• M.S. 1997, University of Illinois at Urbana-Champaign.

• Diploma in Mathematics 1993, University of Bucharest.

Curriculum Vitae

Publications

1. Extreme Points and Factorizability for New Classes of Unital Quantum Channels (with U. Haagerup and M.B. Ruskai),
   Annales H. Poincare, to appear. arXiv:2006.03414

2. Factorizable maps and traces on the universal free product of matrix algebras (with M. Rørdam),
   Int. Math. Res. Not. IMRN., to appear. arXiv:1903.10182

3. Non-closure of quantum correlation matrices and factorizable channels that require infinite dimensional (with M. Rørdam),
   Comm. Math. Phys., 375 (2020), no. 3, 1761-1776. arXiv:1806.10242

4. Just-infinite C*-algebras (with R. Grigorchuk and M. Rørdam),
   Commentarii Math. Helvetici, 93 (2018), no. 1, 157-201. arXiv:1604.08774

5. An asymptotic property of factorizable completely positive maps and the Connes embedding problem (with U. Haagerup),
   Comm. Math. Phys.338 (2015), 721-752. arXiv:1408.6476

6. Factorization and dilation problems for completely positive maps on von Neumann algebras (with U. Haagerup),
   Comm. Math. Phys. 303 (2011), 555-594. arXiv:1009.0778

7. Classification of hyperfinite factors up to completely bounded isomorphism of their preduals (with U. Haagerup),
   J. Reine Angew. Math. 630 (2009), 141-176. arXiv:0706.3463

8. The Effros-Ruan conjecture for bilinear maps on C*-algebras (with U. Haagerup),
   Inventiones Mathematicae 174 (2008), 139-163. arXiv:0711.1851

9. On the best constants in noncommutative Khintchine-type inequalities (with U. Haagerup),
   J. Funct. Analysis 250, no. 2, (2007), 588-624. arXiv:0611160

10. A noncommutative version of the John-Nirenberg theorem (with M. Junge),
    Trans. Amer. Math. Soc. 359, no. 1 (2007), 115-142. arXiv:0410121

11. On the operator space UMD property for noncommutative L_p-spaces
    Indiana Univ. Math. J. 55, no. 6 (2006), 1857-1892.

12. The condenser problem (with J. Bliedtner),
    Potential Analysis 21 (2004), 177-192.

13. Interpolation between non-commutative BMO and non-commutative L_p-spaces,
    J. Funct. Analysis 202 (2003), 195-225.

14. On strong Darboux property
    Stud. Cerc. Mat. 44 (1992), no. 4, 305-307.

Oberwolfach reports

1. Infinite dimensional aspects of the analysis of quantum information theory, with M. Rørdam, Oberwolfach Reports (2019), to appear.
2. Factorization and dilation problems for completely positive maps on von Neumann algebras, with U. Haagerup, Oberwolfach Reports 7, issue 1 (2010), 718-719.
3. The Effros-Ruan conjecture for bilinear maps on C*-algebras, with U. Haagerup, Oberwolfach Reports 5, issue 3 (2008), 2157-2159.

Preprints and papers in preparation

1. Infinite dimensional phenomena in quantum information theory and the Connes Embedding Problem. Survey paper for the Proceedings of the IWOTA 2021, Lancaster, in preparation.
2. On factorizable quantum channels with finite dimensional ancillas, in preparation.
3. Finite dimensional approximations of hyperfinite martingales, in preparation.
4. Notes on noncommutative L_p-spaces (the tracial case) (with Bruce Driver), Preprint, 2005.

Conferences Organized (selected)

• ICM Satellite conference: Operator algebras, dynamics and groups (July 1-4, 2022) at the University of Copenhagen. Organizers: Søren Eilers, Magdalena Musat, Mikael Rørdam and Asger Tornquist.
• Richard Kadison and his mathematical legacy - A memorial conference. (November 29-30, 2019) at the Carlsberg Academy (University of Copenhagen). Organizers: Magdalena Musat and Mikael Rørdam.
• Symposium: The mathematical legacy of Uffe Haagerup. (June 24-26, 2016) at the University of Copenhagen. Organizers: Magdalena Musat, Mikael Rørdam and Wojciech Szymanski.
• Masterclass: Expanders and rigidity of group actions. (May 2-6, 2016) at the University of Copenhagen. Organizers: Chris Cave and Magdalena Musat.
• Masterclass on Groups, boundary actions and group C*-algebras. (April 13-17, 2015) at the University of Copenhagen. Organizers: Magdalena Musat and Mikael Rørdam.
• Ergodic Theory and von Neumann Algebras: Master Class (October 14-18, 2013) at the University of Copenhagen. Organizers: Steven Deprez and Magdalena Musat.
• Sofic Groups and Applications to Operator Algebras: Master Class (November 5-9, 2012) at the University of Copenhagen. Organizers: Uffe Haagerup, Magdalena Musat and Mikael Rørdam.
• Von Neumann Algebras and Group Actions: Master Class (January 25-29, 2010) and Workshop (February 1-5, 2010) at the University of Copenhagen. Organizers: Uffe Haagerup and Magdalena Musat.

Postdocs

• Chris Cave (2015-2018).

Ph.D. students

• Rasmus Kløvgaard Stavenuiter, current.
• Borys Clemens (2020), Ph.D thesis: Groups, Actions, and C*-algebras (joint supervision with M. Rørdam).
• Rasmus Sylvester Bryder (2017). Ph.D. thesis: Boundaries, injective envelopes, and reduced crossed products, (joint supervision with M. Rørdam).
• Kristian Knudsen Olesen (2016). Ph.D. thesis: Analytic aspects of the Thompson groups, (joint supervision with U. Haagerup).
• Tim de Laat (2013), (joint supervision with U. Haagerup). Ph.D. thesis: Approximation properties for Lie groups and noncommutative L_p-spaces
  Currently Juniorprofessor für Theoretische Mathematik, Westfälische Wilhelms-Universität Münster.

Masters students

• Rasmus Kløvgaard Stavenuiter (2020, September). M. S. Thesis: Poincare Inequalities, non-linear spectral calculus and superexpanders.
• Emilie Mai Elkiær (2019, December). M. S. Thesis: Rigidity of group actions on Banach spaces.
• Mikkel Strunge (2017, February). M. S. Thesis: Expansion in groups: Coarse geometry and analytic aspects.
• Sanne Winther (2016, March), M. S. Thesis: Inner Amenability, Cost and Central Sequences in Factors.
• Anne Munk Ebbesen (2016, March), M. S. Thesis: Superreflexivity and property (T) for group actions on Banach spaces.
• Andreas Midjord (2015, July), M. S. Thesis: Poisson boundaries of groups: Entropy, growth and amenability.
• Rasmus Sylvester Bryder (2014, May), M. S. Thesis: Simplicity and uniqueness of trace for reduced group C*-algebras, (joint supervision with M. Rørdam).
• Marcus Dorph De Chiffre (2013, November), M. S. Thesis: Quasidiagonality of Group C*-algebras, (joint supervision with M. Rørdam).
• Kristian Knudsen Olesen (2012, November), M. S. Thesis: The Connes Embedding Problem: Sofic Groups and the QWEP Conjecture

Masters projects and PUKs

• Nadja Lausen and Victoria Snow (2021, November), PUK: Tricks and Treats with Hilbert Spaces.
• Chris Søndergaard Gassner Nielsen (2020), PUK: Groups, Operator algebras and Dynamics.
• Rasmus Kløvgaard Stavenuiter (2019), PUK.
• Peter M. R. Rasmussen (2019, August), Fagprojekt: A mathematical introduction to spectral expansion.
• Malthe M Karbo (2018, April), Fagprojekt: Fourier Analysis and the Theory of Representations of Topological Groups.
• Moritz Korte-Stapff (2016, November), Fagprojekt: Introduction to free probability.
• Malthe M Karbo & Magnus B Kristensen (2016, June), Fagprojekt: Reflexivity in Banach spaces, (joint supervision with R. S. Bryder).
• Michael Staal-Olsen (2016, June), Fagprojekt: Khintchine inequalities and applications: Embedding a Hilbert space into L₁ - From classical to noncommutative.
• Jacob Emil Friis Frølich (2016, April), Fagprojekt: Groups with property RD.
• Mikkel Munkholm (2016, January), Fagprojekt: Property A, expanders and exactness of groups, (joint supervision with C. Cave).
• Andreas Midjord (2014), Fagprojekt: Random walks on groups: amenability and convolution operators.
• Rasmus Sylvester Bryder (2013, February), Fagprojekt: Injective and Semidiscrete von Neumann Algebras.
• Isak Wulff Mottelson (2012, January), Fagprojekt: Introduction to Non-commutative Probability.

Bachelor students

• Sophia Josephine Lundgreen Stone (2022), B. S. Thesis: Weak convergence of probability measures, Fourier-Stieltjes transforms and Bochner's theorem.
• Christian Jonas Peifer (2020), B. S. Thesis: Choquet Theory: Representation of compact convex sets.
• Emilie Mai Elkiær (2017), B. S. Thesis: The asymptotic quantum Birkhoff conjecture.
• Kevin Aguyar Brix (2013, June), B. S. Thesis: Amenability and Growth of Finitely Generated Groups.
• Anna Munk Ebbesen (2012, June), B. S. Thesis: Convex Sets and their Integral Representations.
• Frederik Riis Mikkelsen (2012, June), B. S. Thesis: Probabilistic Aspects of Moment Sequences: The Method of Moments.
• Marcus Dorph De Chiffre (2011, June), B. S. Thesis: The Haar Measure.
• Julie Pedersen (2010, July), B. S. Thesis: The Little Grothendieck Inequality - From Classical to Non-Commutative.
• May Louise Wetke Nielsen (2009, May), B. S. Thesis (at the University of Southern Denmark): The Haar Measure.

Current teaching

• Fall 2021/Winter 2022 (Blok 2)
  • Functional Analysis (FunkAn).
• Fall 2021 (Blok 1)
  • Lebesgueintegralet og Maalteori (LIM) (joint with Mikael Rørdam).
  • Groups, Operator Algebras and Dynamics (GOADyn).

• Fall 2018/Winter 2019 (Blok 2)
  • Functional Analysis (FunkAn).
• Fall 2018 (Blok 1)
  • Analysis 2 (An2) (joint with Mikael Rørdam).
  • Approximation Properties for Operator Algebras and Groups (Approx). (Reading course)
• Fall 2017/Winter 2018 (Blok 2)
  • Approximation Properties for Operator Algebras and Groups (Approx).
  • Functional Analysis (FunkAn).
• Fall 2016/Winter 2017 (Blok 2)
  • Functional Analysis (FunkAn).
• Fall 2016 (Blok 1)
  • Approximation Properties for Operator Algebras and Groups (Approx).
  • Analysis 2 (An2) (joint with Mikael Rørdam).
• Fall 2015/Winter 2016 (Blok 2)
  • Approximation Properties for Operator Algebras and Groups (Approx).
  • Functional Analysis (FunkAn).
• Fall 2015 (Blok 1)
  • Analysis 2 (An2) (joint with Mikael Rørdam).
• Fall 2014/Winter 2015 (Blok 2)
  • Approximation Properties for Operator Algebras and Groups (Approx) (joint with U. Haagerup).
• Fall 2014 (Blok 1)
  • Functional Analysis (FunkAn).
  • Analysis 2 (An2) (joint with Mikael Rørdam).
• Fall 2013/Winter 2014 (Blok 2)
  • Approximation Properties for Operator Algebras and Groups (Approx) (joint with U. Haagerup).
• Fall 2012/Winter 2013 (Blok 2)
  • Approximation Properties for Operator Algebras and Groups (Approx) (joint with U. Haagerup).
• Fall 2012 (Blok 1)
  • Functional Analysis (FunkAn).
  • Analysis 2 (An2) (joint with Mikael Rørdam).
• Fall 2011/Winter 2012 (Blok 2)
  • Measure and Integration Theory (MI).
• Fall 2011 (Blok 1)
  • Functional Analysis (FunkAn).
• Fall 2010/Winter 2011 (Blok 2)
  • Measure and Integration Theory (MI) (joint with Ernst Hansen).
• Fall 2010 (Blok 1)
  • Approximation Properties for Operator Algebras and Groups (Approx) (joint with U. Haagerup).
• Spring 2010 (Blok 3)
  • Banach spaces.
• Fall 2009 (Blok 1)
  • Large Deviations (AS 100).

Previous teaching