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 mechanics and Quantum information.

Relevant ArXiv sections: Quantum Physics, Statistical Mechanics, Mathematical Physics, Dynamical Systems, Information Theory, Operator Algebras, Functional Analysis.

Relevant 2010 Mathematics Subject Classifications: Quantum Physics: 81Pxx (81P15, 81P16, 81P40, 81P45, 81P70), 81Qxx (81Q50), 81Sxx (81S22), Information Theory: 94Axx (94A17, 94A24, 94A40), Ergodic Theory: 28Dxx (28D05, 28D10), 37Axx (37A05, 37A10, 37A30, 37A35, 37A50, 37A60), Functional Analysis: 46Bxx (46B03, 46B06, 46B25, 46B28, 46B45), 46Cxx (46C05, 46C07), Operator Theory: 47Axx (47A07, 47A15, 47A20, 47A80), 47Dxx (47D06, 47D07, 47D60).


Grant support:

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:

Annals of Functional Analysis (2010-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

Ryan McGaha Current PhD student.

Duncan Wright Completed his Ph.D. in 2019. Thesis title: "Dynamical entropy of quantum random walks". Present position: Post-Doctoral Scholar, Worcester Polytechnic Institute.

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

Rade Musulin Completed his Ph.D. in 2018. Thesis title: "Classical and Quantum Kac's chaos". Present position: Instructor, Florida Atlantic 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.

PUBLICATIONS

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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