Profile picture

Andrei Khrennikov

Professor, Subject Representative
Department of Mathematics
andrei.khrennikov [at] lnu [dot] se
+46 470 70 87 90
Hus B 2049
Save contact Download hi-resolution image

Andrei Khrennikov is Professor of Mathematics at the Department of Mathematics at Linnaeus University. Andrei is also director of the research group International Center for Mathematical Modeling (ICMM) at Linnaeus University.

My research activity can be characterized as extensively multi-disciplinary. (Sometimes I am surprised by myself that all these diverse studies covering so different areas of science were done by the same person). Research activities are split in the basic disciplines: MATHEMATICS, PHYSICS, BIOLOGY, COGNITION, PSYCHOLOGY and BEHAVIORAL ECONOMICS.

MATHEMATICS, pure and applied: Infinite-Dimensional Analysis and Feynman Integration; Functional Superanalysis; P-adic and non-Archimedean Analysis, the Q_p to Q_p; P-adic dynamical systems; P-adic and Ultrametric Analysis, Wavelets, Distributions, Pseudo-differential Operators, the Q_p to C case; Foundations of Probability Theory.

PHYSICS, mathematical and theoretical:Quantization of systems with infinite number of degrees of freedom; Quantization of p-adic and non-Archimedean physical systems; Probabilistic foundations of quantum mechanics and Bell’s inequality; Classical random field model of quantum mechanics.

BIOLOGY, COGNITION, PSYCHOLOGY and BEHAVIORAL ECONOMICS: Quantum-like models:molecular biology, cognition, psychology, behavioral economics, social science; Econophysics: modeling of price dynamics on the basis of expectations of traders of the financial market; P-adic dynamical models of cognitive and biological processes.

P. Grangier, Closing the Door on Einstein and Bohr's Quantum Debate

G. Weihs, Violation of Bell¹s Inequality under Strict Einstein Locality Conditions

R. Hensen, From the first loophole - free Bell test to a quantum Internet

M. Giustina and M. Versteegh, Significant-loophole-free test of local realism with entangled photons

K. Shalm,  A strong loophole - free test of Bell's inequalities

H. Weinfurter,
Event ready loophole free Bell test using heralded atom-atom entanglement

P. Grangier, Violation of Bell's Inequalities in a quantum realistic framework

A. Zeilinger, The Future of Bell Experiments

The Växjö series of conferences is arranged by ICMM, International Centre for Mathematical Modelling in physics, engineering and cognitive sciences, at Linnaeus University in Växjö, Sweden. Obs! Link till ICMM site It is devoted to quantum foundations, information and novel quantum technologies (cryptography, random generators, imaging, computing) and probabilistic foundations. The main point is that quantum mechanics is essentially about a novel representation of probabilistic data and predictions about the results of random experiments.  

This is the longest continuous series of conferences on quantum foundations, since creation of quantum mechanics.  It was started in 2000 and goes annually. This series was generated by revolution in quantum information theory at the end of 20th century.

This series of conferences can be characterized by two distinguishing features:

A). Openness for expression of opinions on the origin or problems of quantum mechanical foundations and their relation to the problems of probability theory and the possible ways of their resolution.

B). Creation of actively interacting mixture of top experts in theory and experiments and even a few philosophers.

From this viewpoint this conference-series is definitely unique. One cannot find anything similar anywhere in the world. At the first stage, I even try to involve pure mathematicians to create knowledge transfer between mathematics and physics.

Experimenters working in quantum optics and neutron interferometry, quantum information technologies represent an important part of the team of invited speakers. In general, the conferences are planned as events unifying the efforts of experts in foundations, mathematical methods, and experimenters to clarify the fundamental questions of quantum theory and its future applications.

Historically, I can mention Christopher Fuchs as one of the creators of the series. In 2001  he came to Växjö with the great team, including Asher Pers, David Mermin, Daniel Greenberger, Lev Vaidman, Carlton Caves, Richard Josza, Lucien Hardy, Hery Folse, Arkady Plotnitsky and other bright physicists and philosophers. This event lifted the conference status enormously and attracted other top experts with the interest to quantum foundations, especially from USA. I also point to the “Austrian-branch” of the conference organizational efforts. Here Helmut Rauch and Gregor Weihs contributed a lot, during the last years the active participation of Anton Zeilinger and people from his lab also played the important role.

I also want to mention the stormy debates between Richard Gill and Jan-Åke Larsson from one side and Luigi Accardi and later also Karl Hess and Walter Philipp from another side during the initial stage of the conference series which were extremely important for clarification of positions of various groups of experts with respect the probabilistic structure of violations of Bell’s inequality.

The participation of Gerard ´t Hooft supported essentially the position of researchers rejecting the conventional interpretation of quantum mechanics.

Växjö definitely played the crucial role in development of QBism. Here the Bayesian approach to quantum probabilities was actively advertised and debated.

Växjö-presentations also contributed a lot to development of the information approach to quantum theory by Mauro D’Ariano and his students.

I personally enjoyed lectures of Arkady Plotnitsky about views of Born, Heisenberg, and Schrödinger and recently Pauli. Nowadays not so many even experts read the original sources, so such lecturing is useful.

I really appreciate recent efforts of Alan Migdall and Sergey Polyakov from NIST, USA, to organize the top level experimental sessions.

Of course, the Växjö-series of conferences is the project of the great complexity and not without problems. For example, consider openness. Here I have to filter originality of mind from craziness. In some cases this is really a difficult task, because the difference is tinny, especially in the case of quantum foundations.

Another problem, at least for some physicists, that there are “too many philosophers”. (In fact, they are one-three…) Some theoreticians are angry that there are too many experimental talks and so on. However, in general people are satisfied and many of them come to Växjö again and again.


Article in journal (Refereed)

Article in journal (Other academic)

Conference paper (Refereed)

Conference paper (Other academic)

Book (Refereed)

Chapter in book (Refereed)

Chapter in book (Other academic)

Collection (editor) (Other academic)

Article, review/survey (Refereed)

Conference proceedings (editor) (Refereed)

Conference paper (Other (popular science, discussion, etc.))

Chapter in book (Other (popular science, discussion, etc.))

Conference proceedings (editor) (Other (popular science, discussion, etc.))