### Research of George Androulakis

My ORCID identifier is 0000-0002-7237-6926 which contains my profile and links to all of my publications.

My arXiv public author identifier is androulakis_g_1 which contains the files of most of my publications.

Current Research Interests: Quantum information. I have also worked on Functional Analysis and Mathematical Physics.

Grant support:

College of Arts and Sciences, Dean's initiative for travel, 2023

College of Arts and Sciences, Dean's initiative for travel, 2022

College of Arts and Sciences, Dean's initiative for travel, 2020

College of Arts and Sciences, Dean's initiative for research, 2019

National Science Foundation, DMS-9970547.

Editorial Work:

Editor for Annals of Functional Analysis (2010-2023).

Associate Editor for Quanta (2021-present)

Some of my research presentations

Video of my talk and slides entitled "Optimal data compression using quantum dynamical entropy" for the Virtual APS March Meeting 2020. See also here.

My poster entitled "Optimal quantum data compression using dynamical entropy" presented in QIP 2020.

The slides for my talk entitled "The role of entropy in classical and quantum communications" presented in the 40th International Conference on Quantum Probability and Infinite Dimensional Analysis in 2019.

Video of my talk entitled "Quantum Kac's chaos" presented in the workshop "Quantum transport equantions and applications" (18w5059) in Oaxaca in 2018.

Video of my talk entitled "The form of the generator of a quantum Markov Semigroup" presented in the workshop "Quantum Markov semigroups in Analysis, Physics and Probability" (15w5086) in Oaxaca in 2015.

Ph.D. students in reverse chronological order

Theodoros Anastasiadis Current PhD student. Summer 2022-present.

Ryan McGaha Completed his Ph.D. in 2022. Thesis title: "The existence and quantum approximation of optimal pure state ensembles". Present position: Lockheed Martin.

Duncan Wright Completed his Ph.D. in 2019. Thesis title: "Dynamical entropy of quantum random walks". Present position: AMS Congressional Fellow.

Alexander Wiedemann Completed his Ph.D. in 2019. Thesis title: "On the generators of quantum dynamical semigroups". Present position: Visiting Assistant Professor at Rudolph-Macon College.

Rade Musulin Completed his Ph.D. in 2018. Thesis title: "Classical and Quantum Kac's chaos". Present position: Lecturer at Rowan University.

Matthew Ziemke Completed his Ph.D. in 2015. Thesis title: "Pettis Integration with applications to generators of Quantum Markov Semigroups". Present position: Assistant Teaching Professor at Drexel University.

Frank Sanacory Completed his Ph.D. in 2007. Thesis title: "The Richness of the space of operators on a Banach space". Present position: Associate Professor at SUNY College of Old Westbury.

Kevin Beanland Completed his Ph.D. in 2006. Thesis title: "A Hereditarily Indecomposable Banach Space and Embedding $\ell_\infty$ into the space of Operators". Present position: Professor at Washington and Lee University.

Postdoctoral Fellows

Tiju Cherian John Fulbright fellow 2/23/2021-12/31/2022.

Antoine Flattot, AY 2006-2010.

Bunyamin Sari AY 2004-2005, (co-advised by Prof. S.J. Dilworth).

Masters students

Rabins Wosti, Department of Computer Science and Engineering, UofSC, (officially a student of Professor Stephen A. Fenner.)

### PUBLICATIONS

 37. Relative Entropy via Distribution of Observables G. Androulakis, T.Ch. John Submitted. ArXiv. 36. Quantum f-divergences via Nussbaum-Szkoła Distributions and Applications to f-divergence Inequalities G. Androulakis, T.Ch. John Submitted. ArXiv. 35. A Variational Quantum Algorithm For Approximating Convex Roofs G. Androulakis, R. McGaha To appear in Quantum Information and Computation. ArXiv. 34. Some remarks on the entanglement number G. Androulakis, R. McGaha Quanta 2020; 9: 22–36. ArXiv, journal. 33. The induced semigroup of Schwarz maps to the space of Hilbert-Schmidt operators G. Androulakis, A. Wiedemann, M. Ziemke Mathematical Physics, Analysis and Geometry 23, 10 (2020). ArXiv, journal. 32. Optimality in Quantum Data Compression using Dynamical Entropy G. Androulakis, D. Wright Phys. Rev. A 100, (2019) 032301. ArXiv, journal. 31. GKSL generators and digraphs: Computing invariant states G. Androulakis, A. Wiedemann J. Phys. A: Math. Theor. 52 (2019) 305201. ArXiv, journal. 30. On the non-linearity of quantum dynamical entropy G. Androulakis, D. Wright J. Math. Phys. Vol. 60, (2019), 053504. ArXiv, journal. 29. A connection between mixing and Kac's chaos G. Androulakis, R. Musulin Dynamical Systems, An International Journal Vol. 34, No 1, (2019), 113-129. ArXiv, journal. 28. Quantum Kac's chaos G. Androulakis, R. Musulin Commun. Math. Sci. Vol. 16, No 7, (2018), 1801-1825. ArXiv, journal. 27. On the closedness of the generator of a semigroup G. Androulakis, M. Ziemke Semigroup Forum Vol. 93, No. 3, (2016), 589-606. ArXiv, journal. 26. Generators of Quantum Markov semigroups G. Androulakis, M. Ziemke J. of Math. Phys. Volume 56, (2015), 083512. ArXiv, journal. 25. Dissipative dynamics in semiconductors at low temperature G. Androulakis, J. Bellissard, C. Sadel J. Stat. Phys. Volume 147, Issue 2, (2012), 448-486. ArXiv, journal. 24. Hyperinvariant subspace for weighted composition operator on $L^p([0,1]^d)$ G. Androulakis, A. Flattot J. Operator Theory 66 (1) (2011), 125-144. ArXiv, journal. 23. On Banach spaces containing $\ell_p$ or $c_0$ G. Androulakis, N.J. Kalton, A. Tcaciuc Houston J. Math. 37 (3) (2011), 859-866. ArXiv, journal. 22. A new approach to the Ramsey-type games and the Gowers dichotomy in F-spaces G. Androulakis, S.J. Dilworth, N.J. Kalton Combinatorica 30 (4) (2010), 359-385. ArXiv, journal. 21. Almost invariant half-spaces of operators on Banach spaces G. Androulakis, A.I. Popov, A. Tcaciuc, V.G. Troitsky Integral Equations and Operator Theory 65 (2009), 473-484. ArXiv, journal. 20. Classes of strictly singular operators and their products G. Androulakis, P. Dodos, G. Sirotkin, V.G. Troitsky Israel J. Math. 169, (2009), 221-250. ArXiv, journal. 19. An extension of Schreier unconditionality G. Androulakis, F. Sanacory Positivity 12 (2008), no. 2, 313--340. pdf file, journal. 18. Descriptive set theoretic methods applied to strictly singular and strictly cosingular operators G. Androulakis, K. Beanland Quaestiones Mathematicae 31 (2008), 151-161. ArXiv, journal. 17. Some equivalent norms on the Hilbert space G. Androulakis, F. Sanacory Banach spaces and their applications in Analysis, de Gruyter 2007, 241-250. pdf file, journal. 16. A new method for constructing invariant subspaces G. Androulakis J. Math. Anal. Appl. 333 (2007) 1254-1263. ArXiv, journal. 15. A Hereditarily Indecomposable Asymptotic $\ell_2$ Banach Space G. Androulakis, K. Beanland Glasgow Mathematical Journal 48 (2006) 503-532. ArXiv, journal. 14. Embedding $\ell_\infty$ into the space of bounded operators on certain Banach spaces G. Androulakis, K. Beanland, S.J. Dilworth, F. Sanacory Bull. London Math. Soc. 38 (2006) 979-990. ArXiv, journal. 13. On the structure of the spreading models of a Banach space G. Androulakis, E. Odell, Th. Schlumprecht, N. Tomczak-Jaegermann Canadian J. Math. Vol. 57 (4), (2005), 673-707. ArXiv, journal. 12. Space averages and homogeneous fluid flows G. Androulakis, S. Dostoglou Math. Phys. Electronic J. Vol. 10 (4) (2004), 1-12. pdf file, journal. 11. A property of strictly singular 1-1 operators G. Androulakis, P. Enflo Ark. Mat. 41, (2003), 233-252. ArXiv, journal. 10. A note on the method of minimal vectors G. Androulakis Trends in Banach spaces and operator theory (Memphis, TN, 2001), 29-36, Contemp. Math., 321, Amer. Math. Soc., Providence, RI, 2003. ArXiv, journal. 9. The Banach space S is complementably minimal and subsequentially prime G. Androulakis, Th. Schlumprecht Studia Math. 156 (3) (2003), 227-242. ArXiv, journal. 8. Strictly singular non-compact operators exist on the Gowers-Maurey space G. Androulakis, Th. Schlumprecht J. London Math. Soc. (2) 64 (2001), no 3, 655-674. ArXiv, journal. 7. Some more weak Hilbert spaces G. Androulakis, P. Casazza, D. Kutzarova Canad. Math. Bull. 43 (2000), no 3, 257-267. ArXiv, journal. 6. Positivity results for the Yang-Mills-Higgs Hessian G. Androulakis, S. Dostoglou Pacific J. Math. 194 (2000), no 1, 1-17. pdf file, journal. 5. Distorting mixed Tsirelson spaces G. Androulakis, E. Odell Israel J. Math. 109 (1999) 125-149. ArXiv, journal. 4. On the stability of monopole solutions G. Androulakis, S. Dostoglou Nonlinearity 11 no. 3 (1998), 377-408. pdf file, journal. 3. Twisted sums, Fenchel-Orlicz spaces and property (M) G. Androulakis, C.D. Cazacu, N.J. Kalton Houston J. Math. 24 no. 1 (1998), 105-126. ArXiv, journal. 2. A counterexample to a question of R. Haydon, E. Odell and H. Rosenthal G. Androulakis Proc. Amer. Math. Soc. 126 no. 5 (1998), 1425-1428. ArXiv, journal. 1. A subsequence characterization of sequences spanning isomorphically polyhedral Banach spaces G. Androulakis Studia Math. 127 no. 1 (1998), 65-80. ArXiv, journal. 0. Isomorphically polyhedral Banach spaces and mixed Tsirelson spaces of arbitrary distortion G. Androulakis Ph.D. dissertation University of Texas, Austin, TX 1996. On the subsymmetric sequences in S G. Androulakis, Th. Schlumprecht Unpublished. pdf file.

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