The first Symposium of this series was held in Goslar (Germany) in 1999, QTS-1, then it was held in Cracow (2001) QTS-2, Cincinnati (2003) QTS-3, Varna (2005) QTS-4, Valladolid (2007) QTS-5, Lexington (2009) QTS-6, Prague (2011) QTS-7, Mexico-city (2013) QTS-8, Yerevan (2015) QTS-9, Varna (2017) QTS-10 , Montreal (2019) QTS-11.

In 2021 QTS-12 will be held in Moscow at the Moscow Institute of Physics and Technology (August 2-6, 2021).

The QTS series started around the core concept that symmetries underlie all descriptions of quantum systems. It has since evolved to a symposium on the frontiers of theoretical and mathematical physics.

Currently the topics of applications are:

- Symmetries in String Theory, Supergravity, Quantum Gravity

- Gauge, Noncommutative, Conformal Field Theories

- Integrable Systems

- Quantum Computing, Information and Control

- Foundations of Quantum Theory

- Quantum Optics, Coherent States, Wigner Functions

- Dynamical Systems

- Symmetries in Statistical Physics

- Symmetries in Condensed Matter Physics

- Symmetries in Nuclear, Atomic and Molecular Physics

- Symmetries in Chemistry, Biology and other Sciences

It depends on the Local Organizer to add/subtract topics in view of the local traditions.

Symmetries are understood in the widest sense:

- Lie groups and Lie algebras, both finite- and infinite-dimensional,

- Superalgebras and Supergroups,

- Algebraic Geometry and Number Theory,

- Quantum groups,

- Noncommutative generalizations,

- Representation Theory,

- Special Functions,

- Symmetries of Linear and Nonlinear PDO.

The purpose of these meetings is to review the principal developments that have occurred in recent years, to present the main results leading to current work in the subject in a coherent form that will be accessible to graduate students and young researchers newly entering the domain, and to point out the most promising directions for future research.

V.K. Dobrev (Sofia), Chairman

H.-D. Doebner (Clausthal), Honorary chairman

M.A. del Olmo (Valladolid)

G.S. Pogosyan (Guadalajara and Yerevan)

A. Shapere (Lexington)

P. Suranyi (Cincinnati)

L.C.R. Wijewardhana (Cincinnati)

K.B. Wolf (Cuernavaca)

L.L. Boyle † (Canterbury)

E. Kapuscik (Cracow)

V.I. Manko (Moscow) (until 31.12.2017)

G. Marmo (Naples)

T.H. Seligman (Cuernavaca)

A.I. Solomon † (Paris and Open University)

The QTS Symposium in 1999 was not planned as a series, but in 2000 it became known that the series of Wigner Symposia (see below) is terminating. Thus, in August 2000 during a meeting in Dubna a group of eight people (L.L. Boyle, V.K. Dobrev, H.-D. Doebner, E. Kapuscik, V.I. Manko, M.A. del Olmo, G.S. Pogosyan, A.I. Solomon) decided to make a regular QTS Symposia series to be held in the odd years as the Wigner Symposia. These eight founding members constituted the first QTS Conference Board. They elected H.-D. Doebner as the first Chairman of the Board. He held this post until June 2014, when V.K. Dobrev was elected Chairman of the Board.

In the founding meeting in Dubna it was decided that QTS-2 will be organized in 2001 in Krakow with main organizers E. Kapuscik and A. Horzela. Further, the main organizers were: for QTS-3 - P. Suranyi and L.C.R. Wijewardhana, for QTS-4 - V.K. Dobrev, for QTS-5 - M.A. del Olmo, for QTS-6 - S. Das and A. Shapere, for QTS-7 - C. Burdik, for QTS-8 - K.B. Wolf, for QTS-9 - G.S. Pogosyan, for QTS-10 - V.K. Dobrev.

Related series:

The oldest series in the field of symmetries is the

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