Tagungen und Workshops zum Thema Mathematische Physik

CIRM – Centre International de Rencontres Mathématiques

Analysis,    Wissenschaftliches Rechnen

CIRM – Centre International de Rencontres Mathématiques

Wissenschaftliches Rechnen,    Angewandte Mathematik (allgem.)

CIRM – Centre International de Rencontres Mathématiques

The conference will bring together leading experts and research scholars to exchange and share their experience and research results on all aspects of mathematical physics and to promote transference of knowledge at the crossroads of mathematics and physics. There will be plenary sessions (30 to 40min), short talks and posters for student presentations. The scope of the conference will be quite broad, including in particular the following topics: polyanalytic function theory, harmonic analysis, representation theory and quantization, Clifford analysis and applications, coherent states, time-frequency analysis and wavelets, orthogonal polynomials, special functions and q-analogues, Hopf algebras and quantum groups, geometric mechanics and symmetry, exact solvable systems, spectral theory and quantum systems, topological methods. With the goal of encouraging communication and collaborative research between the participants, a feature of ICMMP2021 will be the inclusion of specific time-slots for scientific discussion.

Tel.: [(212) (0) 663564850];     Email: mouayn@gmail.com

Harmonic analysis, representation theory and quantization, Clifford algebras, Clifford analysis and applications, Coherent states & wavelets, q-deformation, Hopf algebras and quantum groups, Geometric mechanics and symmetry, Orthogonal Polynomials, special functions and exact solvable systems, Spectral theory and quantum systems, Topological Methods

Geometrie und Topologie,    Gruppentheorie

The workshop Quantum resources: from mathematical foundations to operational characterisation is concerned with the theoretical investigation of quantum resources, and in particular on bridging the gap between the abstract mathematical description of resource theories and the protocols for their practical exploitation.

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

An essential paradigm in science is solving a problem through the study of its symmetries. Whether dealing with a chemical, physical, or mathematical system, its symmetries are intimately related to the conservation laws characterizing the system itself. Therefore, their study leads us to its full understanding. Quantum groups are deformations of the most elementary symmetries in Nature, describing, for example, infinitesimal layers of ice. They first appeared in the eighties as symmetries of one and two-dimensional statistical mechanical models and are nowadays ubiquitous objects in mathematics. Quantum groups represent only an instance of the more general Theory of Quantization, in which the procedure of "deforming" classical structures gives rise to their "quantum" analog. This theory proved soon to have spectacular connections with many and only apparently unrelated areas of mathematics and physics, especially in representation theory (as described above), algebraic geometry (in particular the theory of moduli spaces), and theoretical physics (e.g. gauge theory). The present workshop aims to provide a survey of the state of the art of the Quantization Theory, with a special emphasis on using advanced techniques from (derived) algebraic geometry to the realm of Quantization.

Organised by IOP West Midlands Branch, Hereford & Worcester Centre

Maxwell's discovery of the laws of electromagnetism represents one of the key events in the history of physics, resulting in a paradigm shift from Newtonian physics to a Universe dominated by fields. Maxwell's discovery provides the link between the physics of Newton and Einstein. The revolutionary nature of Maxwell's insights will be highlighted. This event may also be delivered as an online webinar. If necessary due to Coronavirus or venue restrictions it will be an online webinar only.

Systemtheorie, Regelung und Automatisierung,    Geschichte und Philosophie von Wissenschaft und Technik

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

The presence of singularity in mathematics and physics is an omnipresent phenomena which is the subject of an enormous amount of current research. One reason for this is that techniques which are useful and well understood in the context of smooth spaces do not carry over automatically to singular spaces in general. Depending on the type of singularity involved, one might find that a theorem which is true in the smooth setting requires modification even to make sense in a particular singular setting, and a singular object with extra structure may lead to a generalization of a theorem in which that extra structure plays a role.

Kurse und Veranstaltungen für Studenten der Mathematik,    Analysis

The conference “Analytic Number Theory, Quantum Chaos and their Interfaces” aims at gathering distinguished researchers working in either of the disciplines to discuss recent research advances in these fields, and serve as a playground for the exchange of ideas between these, rather diverse, research communities. Another purpose of our conference is to provide a solid educational platform for more junior researchers (PhD students, postdoctoral researchers and early career permanent faculty) who aspire to conduct research in the relevant fields and expose them to some of the outstanding results and open problems as well as to meet other researchers with similar academic interests, with high potential to start new research collaborations. Being a home to Professor Zeev Rudnick, who has contributed greatly to unifying the main subjects of the conference and established some relevant fundamental results in these fields, Tel Aviv University is a natural place for such a meeting to take place.

Zahlentheorie, Arithmetik,    Komplexe Systeme und Chaos

Kavli Institute for Theoretical Physics (KITP)

Thin elastic films can be found everywhere: they occur naturally (lipid membranes, viral capsids, plant leaves, epithelial tissues, seashells, etc.) and as man-made materials (paper, graphene, fabrics, concrete shells, etc.). Since their resistance to bending must obey purely geometric surface constraints, stress and geometry are intricately coupled, often leading to unexpected and very nonlinear responses to perturbations. Recent progress in theoretical and experimental approaches, as well as novel technological applications, have advanced the frontier of this field, but also brought challenging new problems into focus, to which this conference is dedicated. Examples of interest include extreme mechanics, the cross-talk between stress and geometry, fluctuations in and out of equilibrium, frustrated internal stresses, and wetting of deformable sheets. We strive for a highly multidisciplinary meeting, in which experimentalists, theorists, and numerical simulators explore open questions in both biological and man-made model systems, examine the promise of novel theoretical and numerical techniques, identify the current frontier of understanding, and speculate on what type of new ideas or tools might be needed to push it further.

Festkörperphysik,    Computerphysik und Numerische Simulation

Sponsored by the SIAM Activity Group on Mathematical Aspects of Materials Science

Since 1994, every 2 to 4 years the SIAM Materials Activity Group organizes the SIAM Conference on Mathematical Aspects of Materials Science. This conference focuses on interdisciplinary approaches that bridge mathematical and computational methods to the science and engineering of materials. The conference provides a forum to highlight significant advances as well as critical or promising challenges in mathematics and materials science and engineering. In keeping with tradition, the conference seeks diversity in people, disciplines, methods, theory, and applications.

Festkörperphysik,    Angewandte Mathematik (allgem.)

CIRM – Centre International de Rencontres Mathématiques

Simulation,    Wissenschaftliches Rechnen

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

The topic of our programme is the string landscape and the swampland and should be understood in a broad sense.

Johannes Gutenberg University Mainz

The aim of the topical workshop is to bring together particle physicists, string theorists and mathematicians working on elliptic functions, with the grand goal of advancing our understanding of elliptic functions required to make precise predictions for future particle physics experiments.

CIRM – Centre International de Rencontres Mathématiques

Simulation,    Mechanik, Rheologie und Tribologie

The aim of the meeting is to present the state of the art in some challenging open problems in Quantum Mechanics from the point of view of Mathematical Physics. It is addressed to young people interested in working on the subject but also to experienced researchers willing to exchange the newest ideas and methods in the field. Among the topics covered: spectral and scattering theory for Schrödinger operators, effective behavior in many particles quantum systems, Bose-Einstein condensation, nonlinear Schrödinger equation, semiclassical analysis, numerical analysis of quantum systems, quantum graphs. Three courses of 6 hours will be given in a series of lectures scheduled in the morning of each day. In the afternoon short contributed talks will be given by young participants, followed by plenary talks given by invited speakers.

Quantenmechanik und Quanteninformation,    Kurse und Veranstaltungen für Physikstudenten

UC Santa Barbara, Kavli Institute for Theoretical Physics (KITP)

This conference will explore many aspects of entangled quantum states of matter, with an eye towards their eventual experimental realization. These include non-Fermi liquids, symmetry-protected topological states, and topologically-ordered quantum matter such as gapped and gapless quantum spin liquids. Some of these states harbor nontrivial boundary or edge modes which will also be highlighted. Different topics will be covered including: the classification of entangled topological states which provide a roadmap of what is possible; investigations on how to engineer models built with realistic ingredients guided by theoretical explorations of their phase diagrams; and proposals for the right observables to detect and manipulate these states which can bring them closer from an abstract idea to reality. This conference will bring together experts on many aspects of highly-entangled quantum matter and help connect experts on mathematical aspects of classification and those with numerical expertise that provide information on phase diagrams with experimentalists striving to engineer these states in the lab.

Quantenmaterialien, Tieftemperaturphysik,    Quantenmechanik und Quanteninformation

Tel-Aviv University

The goal of the conference is to bring together leading experts, as well as promising students and young researchers, in order to exchange ideas and share methods of study of different problems in integrable systems. The conference is designed to cover many aspects of the field, to provide an opportunity for perspective participants to present their recent results in the area. Moreover, we aim at creating a learning environment, and setting the ground for a fruitful exchange of ideas generating new visions and collaborations between experts and students alike.

Bulgarian Academy of Sciences - Institute for Nuclear Research and Nuclear Energy

The meeting covers the whole field of Lie Theory in its widest sense together with its applications in many facets of physics. As interface between mathematics and physics the workshop serves as a meeting place for mathematicians and theoretical and mathematical physicists.

Representation Theory - Infinite-Dimensional Lie Groups and Algebras - Algebraic Geometry and Number Theory - Cluster Algebras, Quiver Representations - Superalgebras and Supergroups - Quantum Groups and Noncommutative Geometry - Symmetries in Quantum Computing, Entanglement - Operator Algebras - Symmetries of Linear and Nonlinear PDO - Special Functions - Symmetries in String Theory - Supergravity, Quantum Gravity - Conformal Field Theories - Integrable Systems - Relativistic and Nonrelativistic Holography - Neural Networks, Deep Learning - Gauge Field Theories - Noncommutative Quantum Theories - Symmetries in Dynamical Systems - Symmetries in Condensed Matter and Statistical Physics

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

This workshop will study this question for systems of geometric origin. One example of this is a particle bouncing inside a region -- think of a ball bouncing around a billiard table, or a light beam bouncing around a room whose walls are mirrors. If the walls are flat then the behavior is fairly predictable, but if they are curved then one often observes random-looking behavior in the long run. Or imagine walking in a straight line along a surface; if the surface is flat then changing the starting point a little will lead to a predictable change in the trajectory. However, if the surface is curved like a saddle then different trajectories will spread out and your location after walking for a long time will eventually seem to be random. The task of giving precise descriptions of systems such as these requires a more complete development of the theory of thermodynamic formalism for systems of geometric origin, which is precisely the goal of this workshop.

Kurse und Veranstaltungen für Studenten der Mathematik,    Thermodynamik, Hydrodynamik und Statistische Mechanik

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

The workshop brings together top experts in the field, and creates an environment where all the latest ideas, intuition and techniques can be shared and refined. Another important goal of the proposed workshop is to introduce junior researchers to a highly active area of research in PDEs of fluid dynamics. We will give preferences to young researchers when inviting speakers to the workshop.

Kurse und Veranstaltungen für Studenten der Mathematik,    Thermodynamik, Hydrodynamik und Statistische Mechanik

International Association of Mathematical Physics (IAMP)

ICMP 2021 will be preceded by the Young Researchers Symposium (YRS) from 29-31 July 2021.

International Association of Mathematical Physics (IAMP)

On behalf of the International Association of Mathematical Physics (IAMP), the International Scientific Committee, and the Local Organizing Committee we invite you to participate in the XX International Congress on Mathematical Physics to be held in Geneva, Switzerland from 2-7 August 2021. The International Congress on Mathematical Physics (ICMP), on its three year cycle, is the most important conference of the International Association of Mathematical Physics. It will be a major event, where new results and future challenges will be discussed, illustrating the richness and vitality of Mathematical Physics. ICMP 2021 will be preceded by the Young Researchers Symposium (YRS) from 29-31 July 2021.

Mathematical Sciences Research Institute, Berkeley

Mathematical Sciences Research Institute, Berkeley

This workshop will focus on cutting-edge research in random matrices and integrable probability. We will explore connections with other branches of mathematics and applications to sciences and engineering. The workshop will feature presentations by both leading researchers and promising newcomers.

Algebra,    Kurse und Veranstaltungen für Studenten der Mathematik

Mathematical Sciences Research Institute, Berkeley

The introductory workshop aims at providing participants with an overview of some of the recent developments in the topics of the semester, with a particular emphasis on universality and applications. This includes universality for Wigner matrices and band matrices and quantum unique ergodicity, universality for beta ensembles and log/coulomb gases, KPZ universality class, universality in interacting particle systems, the connection between random matrices and number theory.

Algebra,    Kurse und Veranstaltungen für Studenten der Mathematik

This school is intended for young researchers (master students, PhD students and young postdocs) involved in the global effort of investigating the large excess of the measured value of the muon anomalous magnetic moment over the Standard Model prediction. The lecture schedule will be complemented by dedicated sessions for discussions, exercises and posters along with social activities to encourage networking and a vivid exchange of ideas.

Kurse und Veranstaltungen für Physikstudenten,    Teilchenphysik und Felder

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Kurse und Veranstaltungen für Studenten der Mathematik,    Astronomie, Astrophysik und Kosmologie

UC Santa Barbara, Kavli Institute for Theoretical Physics (KITP)

Several communities of experimental and theoretical physics are devoted to studying the problem of transport and energy conversion in quantum systems away from equilibrium. In statistical physics, these topics have been traditionally addressed mainly in the classical realm. In condensed matter and atomic physics, the traditional context has been quantum charge and spin transport. Recent progress includes the application of ideas from quantum information to understand the emergence of thermodynamical concepts and the creation in experiments of quantum coherent systems of various scales with a novel degree of control. These developments motivate work on fundamental challenges like the creation of optimal protocols for energy/information transport as well as state preparation. The aim of this conference is to provide a survey of the most recent advances in the area, bringing together experts across all these fields.

When many quantum particles interact, they can organize themselves into highly entangled states with unexpected properties that transcend those of the individual constituents. The description of those states and their properties is typically rather challenging - not only from a mathematical point of view. In the last 15 years, concepts and tools from quantum information theory (QIT) have proven highly useful in investigating such systems. This new perspective aims to characterize and classify the complexity in large quantum systems.

Mainz Institute for Theoretical Physics, Johannes Gutenberg University

Recently, there has been great interest in determining criteria which differentiate between effective low-energy field theories which can be consistently completed in the ultraviolet into quantum gravity, said to be in the ‘Landscape’, from theories which appear consistent but nonetheless defy such a coupling to quantum gravity, the so-called ‘Swampland’. A number of such criteria, or Swampland Conjectures, have been proposed in the literature and attracted considerable interest in the high energy physics community. If confirmed, they have far-reaching consequences for physics and cosmology, such as for the structure of large field inflation in early time cosmology or for the mechanism responsible for the observed late-time acceleration of the universe, to name but the most striking ones. On the other hand, the Swampland Conjectures translate, in the context of string theory, into conjectures regarding the structure of possible compactifications, or string geometries. String theory is therefore in a unique position to quantitatively test - and possibly refine - such general Swampland Conjectures. This Scientific Program proposes to study these intriguing connections between general properties of quantum gravity and the geometry of string compactifications. It aims to bring together world experts working at the forefront of research in string theory, field theoretic aspects of quantum gravity, and geometry at this unique time in which our understanding of the Swampland is quickly evolving.

Institute for Advanced Study in Mathematics (IASM) in Hangzhou, China, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

Subfactors and vertex operator algebras are mathematical structures that at first glance appear very different, but both are used in the mathematical study of quantum field theory. In particular, vertex operator algebras are algebraic structures arising in two-dimensional conformal field theory (CFT), a quantum field theory with applications ranging from string theory to condensed matter physics to quantum computing. On the other hand, subfactors are closely related to conformal nets, which are a functional-analytic approach to CFT. Because they are both mathematical descriptions the same quantum field theory, the theories of vertex operator algebras and conformal nets are widely believed to be equivalent, but only in the last few years has there been substantial progress in establishing an equivalence. As many important results in conformal field theory have been established for either vertex operator algebras or conformal nets, but not necessarily both, developing connections and equivalences will be useful for answering open questions in both mathematical formulations of CFT.

Kurse und Veranstaltungen für Studenten der Mathematik,    Algebra

UC Santa Barbara, Kavli Institute for Theoretical Physics (KITP)

The advent of quantum simulators have ushered a new era of non-equilibrium many-body physics and has sparked a dialogue between seemingly disparate fields. This conference will explore universal aspects of many-body systems far from equilibrium at the interface of statistical physics, AMO, condensed matter and high-energy physics, by bringing together scientists from these diverse communities. Our focus is on novel phases of matter far from equilibrium and their associated universality classes that emerge beyond equilibrium paradigms. Diverse topics will be covered including short-time universality, entanglement dynamics, and mapping between classical and quantum non-equilibrium systems. Our goal is to identify aspects of high-energy physics that can inform non-equilibrium condensed and AMO systems and vice versa, with an eye towards realizing experiments which can sharpen our understanding of far-from-equilibrium universality.

Mainz Institute for Theoretical Physics, Johannes Gutenberg University

Boundaries and defects have been at the heart of crucial developments in theoretical physics in the last 20 years: holography (field theories could live at the boundary of a higher- dimensional gravitational theory), entanglement (the entangling surface can be treated as a defect), black holes (the horizon is a boundary), topological insulators and semi-metals (the topologically-protected massless modes live at the boundary), and non-local operators such as Wilson and ‘t Hooft lines (defects defined by appropriate boundary conditions). Additionally, many other areas have made major advances in recent years whose implications for quantum field theory with boundaries and defects have yet to be explored fully: the conformal bootstrap, dualities among (2+1)d quantum field theories, supersymmetric localization, integrability, and so on. However, progress in these areas has largely been carried out by separated communities working in isolation from the others. This scientific program thus aims to bring together a diverse group of leading theorists interested in boundaries and defects in quantum field theory, from the formal/mathematical to the applied, to forge collaborations between different areas, identify common subjects and complementary approaches, and set the agenda for future developments and new applications.

The three broad focus areas will be: Conformal field theories with boundaries and defects Supersymmetry and Duality with boundaries and defects Curved space, gravity and entanglement

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Kurse und Veranstaltungen für Studenten der Mathematik,    Quantenmechanik und Quanteninformation

ETH Zürich - EPF Lausanne - Universität Bern - Université de Genève

Understanding quantum gravity is one of the main open questions in modern theoretical physics. Holographic duality constitutes a major advance in this direction linking together quantum field theory and quantum gravity and in particular string theory. This meeting aims to bring together a diverse set of international experts working on the intersecting fields of string theory, quantum field theory and holography.

Strings, Branes and Holograms

Astronomie, Astrophysik und Kosmologie,    Teilchenphysik und Felder

Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Canada

In this workshop, experts in the physics and mathematics of string theory shall gather together to discuss the current progress on the study of the physical consequences (for particle physics and cosmology) of string models, and to explore new exciting formal (and informal) proposals that may constitute important tools to gain a better understanding of string theory and its possible predictions. Besides traditional overview talks and seminars on the ongoing research in this field, the workshop will provide an adequate environment for fruitful discussion and collaboration.

Kurse und Veranstaltungen für Studenten der Mathematik,    Erneuerbare Energien und Wäremekraftwerke

CIRM – Centre International de Rencontres Mathématiques

CIRM – Centre International de Rencontres Mathématiques

Infinitesimalrechnung, Differentialgleichungen, Integralrechnung,    Quantenmechanik und Quanteninformation

UC Santa Barbara, Kavli Institute for Theoretical Physics (KITP)

Understanding how color is confined in QCD, and the binding of quarks into hadrons, is one of the major unresolved challenges in fundamental physics. The central piece in this puzzle is the chromoelectric flux tube, or confining string, which holds quarks together. In recent years, tantalizing new insights into the dynamical properties of confining strings have been obtained using various theoretical tools such as effective string theory, integrability, the modern S-matrix bootstrap, and gauge/gravity duality. Lattice gauge theory supplies important information about the spectrum of flux tube excitations. Finally, the recent experimental discovery of heavy flavor tetraquarks provides a direct observational probe of flux tube junctions. This conference will bring together experts in these different fields to initiate the exchange of ideas and stimulate future cross-disciplinary developments.

UC Santa Barbara, Kavli Institute for Theoretical Physics (KITP)

Binary systems are ubiquitous in nature, from stars to the supermassive black holes expected to reside in galactic nuclei. In many circumstances, the binary system is enveloped by circumbinary gas. How does circumbinary gas evolve and influence the embedded binary? What observational signatures of this gas are most informative? What novel numerical techniques must we deploy to better model these systems? This conference will bring together two distinct communities: those working on massive black hole binaries with those working on stellar binaries. Because recent years have seen remarkable progress in observations of stellar binaries, and numerical modeling of both stars and black holes, now is the ideal time to bring together these two groups. The conference will highlight the remarkable similarities of problems at such varied astrophysical scales, and shed light on the crucial next steps for pushing the boundaries of our knowledge.

UC Santa Barbara, Kavli Institute for Theoretical Physics (KITP)

The goal of this conference is to survey the interdisciplinary avenues in modern neutrino physics, with a threefold overarching set of aims: (1) to maximize the new physics potential of present and upcoming experimental data, (2) to understand new directions in the quest for high-precision neutrino cross sections, including synergy with lattice QCD; and, (3) to ensure that the impact of neutrinos on astrophysical and cosmological processes is comprehensively addressed. Particular attention will be given to exploring connections between neutrinos and gravitational waves, cosmological data, sources for IceCube’s astrophysical neutrino events, implications of the latest sterile searches for cosmology and astrophysics, and an assessment of the role of the neutrino detectors as astrophysical observatories.

UC Santa Barbara, Kavli Institute for Theoretical Physics (KITP)

The detection of gravitational waves by Advanced LIGO/Virgo has opened a new frontier in physics, with impact on areas ranging from field theory through stellar evolution and cosmology. It has also seeded new connections between theoretical communities, especially between field theorists and classical relativists. An even brighter future lies ahead, with more sensitive ground-based detectors and, eventually, a space-based observatory. Current and future experiments demand precision modelling of gravitational-wave signals in order to interpret the strongest gravitational-wave events and to enable sensitive searches for new physics which may be embedded in these signals. The conference will bring together experts from three communities: classical relativity, effective field theory, and scattering amplitudes. Building on the current state of the art, we will discuss the needs of the next generation of gravitational-wave experiments; identify which challenges theory must overcome; highlight recent advances in gravitational wave modelling for more detailed study; and uncover the most promising emerging tools and techniques from classical and quantum field theory for further development.

UC Santa Barbara, Kavli Institute for Theoretical Physics (KITP)

This conference will bring together a diverse set of scientists interested in the broad topic of few-body physics, providing a snapshot of the current status of few-body physics near unitarity, where the two-body scattering length is the largest length scale in the problem. Successes and open challenges in the area of atomic and nuclear physics, which are--despite the vastly different length and energy scales--intimately linked through, e.g., the three-body Efimov effect, will be highlighted. A major objective is to provide a platform for cross-fertilization between theory and experiment as well as between different research areas (such as nuclear, atomic, molecular, condensed matter, high-energy, and mathematical physics), with universality and its implied organizing principles as a unifying connection.

UC Santa Barbara, Kavli Institute for Theoretical Physics (KITP)

This conference will explore many aspects of classical and quantum fluctuating electromagnetic fields in the presence of matter, which impact a wide range of fundamental and practical phenomena in domains of physics, chemistry end engineering. Building upon the significant milestones achieved in the realms of the Casimir interactions between bodies, and the role of quantum field fluctuations in heat transfer in the near- and far-fields, we plan to address a plethora of novel questions and remaining puzzles: the ramifications of 2D (topological) and non-reciprocal materials, the possibility of detecting quantum friction, the discord between different experimental and theoretical results. Unraveling these puzzles will have profound impacts from fundamental science to novel applications of materials. The conference will bring together theorists and experimentalists who will address unsettled topics and possible new experimental directions that could elucidate them.

Optoelektronik und Anzeigetechnik,    Quantenmechanik und Quanteninformation

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Kurse und Veranstaltungen für Studenten der Mathematik,    Numerische Analysis