GRK 1493:  Mathematical Structures in Modern Quantum Physics

• Subject Area: Mathematics ; Particles, Nuclei and Fields
• Term: from 2008 to 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 51442683

• Final Report Year: 2017

Final Report Abstract

Die moderne Mathematik wird stark von Ideen stimuliert, die in Überlegungen und Theorien zur Physik von Materie, Zeit und Raum auf der Quantenskala wurzeln. Diet heoretische Behandlung der dort auftretenden Phänomene benötigt neue Konzepte und Methoden aus sehr verschiedenen Bereichen der Mathematik, von neuartigen Zugängen zu Geometrie und Topologie, etwa der groben und nichtkommutativen Geometrie, über neue Techniken in der Analysis unendlicher Systeme bis zur Theorie der Invarianten von Operatoralgebren und zur Kategorientheorie. Das Graduiertenkolleg befasst sich mit Themen an dieser Schnittstelle von Mathematik und Physik. Es hat zum Ziel, Doktorandinnen und Doktoranden in der reinen Mathematik und der theoretischen Physik ein inspirierendes Umfeld zu bieten, in dem einerseits die notwendige Spezialisierung in der eigenen fachlichen Thematik gelingt, andererseits der Blick geöffnet wird für andere Disziplinen und eine gewisse Breite der Ausbildung gewährleistet ist. Es unterstützt den wissenschaftlichen Nachwuchs dabei, früh wissenschaftliche Selbstständigkeit und Reife zu entwickeln.

Publications

• A sharpened nuclearity condition and the uniqueness of the vacuum in QFT. Comm. Math. Phys. 283 (2008), 523
  W. Dybalski
  (See online at https://doi.org/10.1007/s00220-008-0514-5)
• A sharpened nuclearity condition for massless fields. Lett. Math. Phys. 84 (2008), 217
  W. Dybalski
  (See online at https://doi.org/10.1007/s11005-008-0244-9)
• A short proof of the approximation conjecture for amenable groups. J. Funct. Anal. 255 (2008), 1102–1106
  D. Pape
  (See online at https://doi.org/10.1016/j.jfa.2008.05.018)
• Spectral theory of automorphism groups and particle structures in quantum field theory. Georg-August-Universität Göttingen (2008)
  W. Dybalski
  (See online at https://dx.doi.org/10.53846/goediss-2705)
• A new spectral triple over a space of connections. Comm. Math. Phys. 290 (2009), 389–398
  J. Aastrup, J. Grimstrup, R. Nest
  (See online at https://doi.org/10.1007/s00220-009-0758-8)
• Boundary integral method in the linear theory of micropolar thermoelasticity with microtemperatures. Proc. 8th Int. Congress on Thermal stresses, TS2009. 1–4 June, University of Illinois at Urbana-Champaign (2009), 469–472
  M. M. Svanadze
  
• Coincidence arrangements of local observables and uniqueness of the vacuum in QFT. J. Phys. A 42 (2009), 365201
  W. Dybalski
  (See online at https://doi.org/10.1088/1751-8113/42/36/365201)
• Conformally covariant quantization of Maxwell field in de Sitter space. Phys. Rev. D 80 (2009), 124005
  S. Faci, E. Huguet, J. Queva, J. Renaud
  (See online at https://doi.org/10.1103/PhysRevD.80.124005)
• Heat equation approach to an index theorem on odd-dimensional manifolds. Bull. Belg. Math. Soc. Simon Stevin 16 (2009), 647–664
  M. Esfahani Zadeh
  (See online at https://doi.org/10.36045/bbms/1257776240)
• Holonomy loops, spectral triples and quantum gravity. Classical Quantum Gravity 26 (2009), 165001, 17 pp.
  J. Aastrup, J. Grimstrup, R. Nest
  (See online at https://doi.org/10.1088/0264-9381/26/16/165001)
• Index theory for boundary value problems via continuous fields of C∗-algebras. J. Funct. Anal. 257 (2009), 2645–2692
  J. Aastrup, R. Nest, E. Schrohe
  (See online at https://doi.org/10.1016/j.jfa.2009.04.019)
• Landweber exact formal group laws and smooth cohomology theories. Algebr. Geom. Topol. 9 (2009), 1751–1790
  U. Bunke, T. Schick, I. Schröder, M. Wiethaup
  (See online at https://dx.doi.org/10.2140/agt.2009.9.1751)
• On spectral triples in quantum gravity. I. Classical Quantum Gravity 26 (2009), 065011, 53pp
  J. Aastrup, J. Grimstrup, R. Nest
  (See online at https://doi.org/10.1088/0264-9381/26/6/065011)
• On spectral triples in quantum gravity. II. J. Noncommut. Geom. 3 (2009), 47–81
  J. Aastrup, J. Grimstrup, R. Nest
  (See online at https://doi.org/10.4171/JNCG/30)
• On the Reeh–Schlieder property in curved spacetime. Comm. Math. Phys. 288 (2009), 271–285
  K. Sanders
  (See online at https://doi.org/10.1007/s00220-009-0734-3)
• Spectral theory of automorphism groups and particle structures in QFT. Ph.D. Thesis. Published by VDM
  W. Dybalski
  
• Bidifferentialkalküle und integable Systeme. Lviv/Ukraine (2010)
  O. Chvartatskyi
  
• Boundary value problems of the theory of viscoelasticity for Kelvin– Voigt materials. PAMM, Proc. Appl. Math. Mech. 10 (2010), 307–308
  M. M. Svanadze
  (See online at https://doi.org/10.1002/pamm.201010146)
• Boutet de Monvel’s calculus and groupoids I. J. Noncommut. Geom. 4 (2010), 313–329
  J. Aastrup, S. Melo, B. Monthubert, E. Schrohe
  (See online at https://doi.org/10.4171/JNCG/57)
• Continuous spectrum of automorphism groups and the infraparticle problem. Comm. Math. Phys. 300 (2010), 273
  W. Dybalski
  (See online at https://doi.org/10.1007/s00220-010-1091-y)
• Equivalence of the (generalised) Hadamard and microlocal spectrum condition for (generalised) free fields in curved spacetime. Commun. Math. Phys. 295 (2010), 485–501
  Ko Sanders
  (See online at https://doi.org/10.1007/s00220-009-0900-7)
• Explicit solution of the boundary value problems of the theory of elasticity for solids with double porosity. PAMM, Proc. Appl. Math. Mech. 10 (2010), 337–338
  Tsagareli, M.M. Svanadze
  (See online at https://doi.org/10.1002/pamm.201010161)
• Large time limit and the L2 local index theorem. Oberwolfach Rep. 28 (2010), Workshop Analysis and Geometric Singularities 10.4171
  S. Azzali
  
• Local Thermal Equilibrium in Quantum Field Theory on Flat and Curved Spacetimes. Class. Quant. Grav. 27 (2010), 235002
  C. Solveen
  (See online at https://doi.org/10.1088/0264-9381/27/23/235002)
• Non-integral central extensions of loop groups. Contemp. Math. 519 (2010), 203–214
  Ch. Wockel
  (See online at https://doi.org/10.1090/conm/519/10243)
• Solution of boundary problems of poro-elastostatics for elastic circular ring with double porosity. Bulletin of Yerevan State University of Architecture and Construction 15/2 (2010), 171–177. (In Russian)
  I. Tsagareli, M. M. Svanadze
  
• Some Aspects on Coarse Homotopy Theory. Georg-August-Universität Göttingen (2010)
  B. Norouzizadeh
  (See online at https://dx.doi.org/10.53846/goediss-3482)
• The locally covariant Dirac field. Rev. Math. Phys. 22 (2010), 381–430
  Ko Sanders
  (See online at https://doi.org/10.1142/S0129055X10003990)
• Asymptotic completeness in a class of massless relativistic quantum field theories. Comm. Math. Phys. 305 (2011), 427
  W. Dybalski, Y. Tanimoto
  (See online at https://doi.org/10.1007/s00220-010-1173-x)
• Boundary value problems of steady vibrations in the theory of thermoviscoelasticity for Kelvin–Voigt materials. Proc. 9th Int. Congress on Thermal stresses, TS2011. 5–9 June, 2011, Budapest, Hungary
  M. M. Svanadze
  
• Categorified central extensions, étale Lie 2-groups and Lie’s Third Theorem for locally exponential Lie algebras. Adv. Math. 228 (2011) 2218-2257
  Ch. Wockel
  (See online at https://doi.org/10.1016/j.aim.2011.07.003)
• Chern classes for differential SU-cobordism. Georg-August-Universität Göttingen (2011)
  I. Schröder
  
• Exactly solvable Schrödinger operators. Ann. Henri Poincaré 12 (2011), 397–418
  J. Dereziński; M. Wrochna
  (See online at https://doi.org/10.1007/s00023-011-0077-4)
• Explicit solutions of the boundary value problems of the theory of thermoelasticity with microtemperatures for elastic circle. PAMM, Proc. Appl. Math. Mech. 11 (2011)
  I. Tsagareli, M. M. Svanadze
  (See online at https://doi.org/10.1002/pamm.201110338)
• L2-rho form for normal coverings of fibre bundles. Int. J. Math. 22 (2011)
  S. Azzali
  (See online at https://doi.org/10.1142/S0129167X11007161)
• Local Commutators and Deformations in Conformal Chiral Quantum Field Theories. Int. J. Modern Physics A 26 (2011), 3357–3383
  A. Kukhtina, K.-H. Rehren
  (See online at https://doi.org/10.1142/S0217751X11053985)
• Local Extensions of Completely Rational Conformal Quantum Field Theories. Georg-August-Universität Göttingen (2011)
  A. Kukhtina
  (See online at https://dx.doi.org/10.53846/goediss-2915)
• Local Extensions of Completely Rational Conformal Quantum Field Theories. Georg-August-Universität Göttingen (2011)
  A. Kukhtina
  (See online at https://dx.doi.org/10.53846/goediss-2915)
• Noncommutative manifolds and Seiberg-Witten equations. Georg-August-Universität Göttingen (2011)
  V. Alekseev
  (See online at https://dx.doi.org/10.53846/goediss-2499)
• On invariants and scalar chiral correlation functions in N = 1 superconformal field theories. Int. J. Mod. Phys. A 26 (2011), 2007–2025
  H. Knuth
  (See online at https://doi.org/10.1142/S0217751X11053031)
• On semi-classical states of quantum gravity and noncommutative geometry. Comm. Math. Phys. 302 (2011), 675–696
  J. Aastrup, J. Grimstrup, R. Nest, M. Paschke
  (See online at https://doi.org/10.1007/s00220-010-1181-x)
• On Turing machines, groupoids, and Atiyha problem. Georg-August- Universität Göttingen (2011)
  L. Grabowski
  (See online at https://dx.doi.org/10.53846/goediss-2479)
• Periodic Cyclic Cohomology for Smooth Generalized Crossed Products. Université Paris Diderot - Paris 7 (2011)
  O. Gabriel
  
• Principal 2-bundles and their gauge 2-groups. Forum Math. 23 (2011), 565–610
  Ch. Wockel
  (See online at https://doi.org/10.1515/form.2011.020)
• Quantum Gravity coupled to Matter via Noncommutative Geometry. Classical Quantum Gravity 28 (2011), 075014, 10 pp.
  J. Aastrup, J. Grimstrup, M. Paschke
  (See online at https://doi.org/10.1088/0264-9381/28/7/075014)
• Spectral flow, index and the signature operator. J. of Topology and Analysis 3 (2011), 37–67
  S. Azzali, C. Wahl
  (See online at https://doi.org/10.1142/S1793525311000477)
• Superconnections and index theory. J. Geometry and Physics 61 (2011), 1601–1624
  A. Kahle
  (See online at https://doi.org/10.1016/j.geomphys.2011.04.004)
• The Index Bundle for Gap-Continuous Families, Morse-Type Index Theorems and Bifurcation. Georg-August-Universität Göttingen (2011)
  N. Waterstraat
  (See online at https://dx.doi.org/10.53846/goediss-2552)
• Universal Coefficient Theorems in Equivariant KK-theory. Georg-August-Universität Göttingen (2011)
  M. Köhler
  (See online at https://dx.doi.org/10.53846/goediss-2561)
• A Bicategory Approach to Differential Cohomology, (2012)
  M. Upmeier
  (See online at https://doi.org/10.48550/arXiv.1211.6832)
• A CharacterizationTheorem for Local Operators in Factorizing Scattering Models. Georg-August-Universität Göttingen (2012)
  D. Cadamuro
  (See online at https://dx.doi.org/10.53846/goediss-2946)
• A K-theoretic proof of the Morse Index Theorem in semi-Riemannian Geometry. Proc. Amer. Math. Soc., 140, 2012, 337-349
  N. Waterstraat
  (See online at https://doi.org/10.1090/S0002-9939-2011-10874-8)
• Amenability and vanishing of L2-Betti numbers: an operator algebraic approach. J. Funct. Anal., 263(4):1103–1128, 2012
  Vadim Alekseev and David Kyed
  (See online at https://doi.org/10.1016/j.jfa.2012.05.016)
• Composition theorems for paired Lagrangian distributions. Georg-August- Universität Göttingen (2012)
  N. Nguyen
  (See online at https://dx.doi.org/10.53846/goediss-2547)
• Distribution of rational points on algebraic varieties. Courant Institute of Mathematical Sciences, New York University (2012)
  T. Sho
  
• Explicit GL(2) trac formulas and uniform, mixed Weyl laws. Georg-August- Universität Göttingen (2012)
  M. Palm
  (See online at https://dx.doi.org/10.53846/goediss-2555)
• Higher Lefschetz invariants for foliated manifolds. Georg-August-Universität Göttingen (2012)
  A. Fermi
  (See online at https://dx.doi.org/10.53846/goediss-2579)
• Homeomorphisms between limbs of the Mandelbrot set. Proc. Amer. Math. Soc. 140 (2012), 1947-1956
  D. Dudko, D. Schleicher
  (See online at https://doi.org/10.1007/BF02921981)
• Homomorphisms of quantum groups, Münster J. of Math. 5 (2012), 1-24
  R. Meyer; S. Roy; S. L. Woronowicz
  
• Index Theory and Positive Scalar Curvature. Georg-August-Universität Göttingen (2012)
  D. Pape
  (See online at https://dx.doi.org/10.53846/goediss-2541)
• Integrable QFT and Longo-Witten endomorphisms. Ann. Henri. Poincaré. 16 (2) (2012) 569–608
  M. Bischoff; Y. Tanimoto
  (See online at https://doi.org/10.1007/s00023-014-0337-1)
• Local Equilibrium States in Quantum Field Theory in Curved Spacetime. Georg-August-Universität Göttingen (2012)
  C. Solveen
  (See online at https://dx.doi.org/10.53846/goediss-2969)
• Local Thermal Equilibrium and KMS states in Curved Spacetime. Class. Quant. Grav. 29 (2012), 245015
  C. Solveen
  (See online at https://doi.org/10.1088/0264-9381/29/24/245015)
• Quantum Field Theory in static external potentials and Hadamard states. Ann. Henri Poincaré 13 (2012), 1841–1871
  M. Wrochna
  (See online at https://doi.org/10.1007/s00023-012-0173-0)
• Superconformal Invariants and Correlation Functions. Georg-August-Universität Göttingen (2012)
  H. Knuth
  (See online at https://dx.doi.org/10.53846/goediss-2947)
• The Decoration Theorem of the Mandelbrot Set and Applications in Holomorphic Dynamics. Jacobs University Bremen (2012)
  D. Dudko
  
• The Geometry of the Milnor Number. Georg-August-Universität Göttingen (2012)
  A. Szawlowski
  (See online at https://dx.doi.org/10.53846/goediss-2523)
• Categorification and applications in topology and representation theory. Georg-August-Universität Göttingen (2013)
  D. Tubbenhauer
  (See online at https://dx.doi.org/10.53846/goediss-4019)
• Conformal Properties of Generalized Dirac Operator. Georg-August-Universität Göttingen (2013)
  V.Thakre
  (See online at https://dx.doi.org/10.53846/goediss-3957)
• K-theory, cyclic cohomology and pairings for quantum Heisenberg manifolds. J. Noncom. Geom. 7 2013 301-333
  O. Gabriel
  (See online at https://doi.org/10.4171/JNCG/118)
• Morita “Equivalences” of Equivariant Torus Spectral Triples, Lett Math Phys (2013) 103: 131
  J. J. Venselaar
  (See online at https://doi.org/10.1007/s11005-012-0584-3)
• On a variational principle in thermodynamics. Continuum Mech. Thermodyn. (2013) 25: 779
  J. Merker; M. Krüger
  (See online at https://doi.org/10.1007/s00161-012-0277-2)
• On–shell extension of distributions. Ann. Henri Poincaré (2013)
  D. Bahns; M. Wrochna
  (See online at https://doi.org/10.1007/s00023-013-0288-y)
• Singularities of two-point functions in Quantum Field Theory. Georg- August-Universität Göttingen (2013)
  M. Wrochna
  (See online at https://dx.doi.org/10.53846/goediss-4017)
• Six-term exact sequences for smooth generalized crossed products. J. Noncommut. Geom. 7 (2013), no. 2, 499–524
  O. Gabriel, M. Grensing
  (See online at https://doi.org/10.4171/JNCG/124)
• The equality of the homogeneous and the Gabor wave front set, (2013)
  R. Schulz and P. Wahlberg
  (See online at https://doi.org/10.48550/arXiv.1304.7608)
• The global wave front set of tempered oscillatory integrals with inhomogeneous phase functions. J. Fourier Anal. Appl. 19 (2013), no. 5, 1093–1121
  S. Coriasco; R. Schulz
  (See online at https://doi.org/10.1007/s00041-013-9283-4)
• Unruh Effect and the Concept of Temperature. Class. Quant. Grav. 30 (2013), 085011
  D. Buchholz; C. Solveen
  (See online at https://doi.org/10.1088/0264-9381/30/8/085011)
• “An operator expansion for integrable quantum field theories”, J. Phys. A: Math. Theor. 46, 095401 (2013)
  H. Bostelmann, D. Cadamuro
  (See online at https://doi.org/10.1088/1751-8113/46/9/095401)
• “Quantum Energy Inequality for the Massive Ising Model”, Physical Review D 88: 025019 (2013)
  H. Bostelmann, D. Cadamuro, C. J. Fewster
  (See online at https://doi.org/10.1103/PhysRevD.88.025019)
• Algebraic Structure and Integration in Generalized Differential Cohomology. Georg-August-Universität Göttingen (2014)
  M. Upmeier
  (See online at https://dx.doi.org/10.53846/goediss-4321)
• Amenable groups and a geometric view on unitarisibility. Universität Leipzig (2014)
  P. Schlicht
  
• Borel-Weil-Bott Theorem via Equivariant McKean-Singer Formula
  S.Hong
  (See online at https://doi.org/10.48550/arXiv.1412.3879)
• Construction of Hadamard states by pseudo–differential calculus. Comm. Math. Phys. 325 (2) (2014), 713–755
  C. Gérard; M. Wrochna
  (See online at https://doi.org/10.1007/s00220-013-1824-9)
• C∗-quantum groups with projection. Georg-August-Universität Göttingen (2014)
  S. Roy
  (See online at https://dx.doi.org/10.53846/goediss-4485)
• Existence of solutions of quasilinear elliptic equations on manifolds with conic points. Georg-August-Universität Göttingen (2014)
  T.. Nguyen
  (See online at https://dx.doi.org/10.53846/goediss-4507)
• Fixed points of compact quantum groups actions on Cuntz algebras. Ann. Henri Poincaré 15 (2014), no. 5, 1013–1036
  O. Gabriel
  (See online at https://doi.org/10.1007/s00023-013-0265-5)
• Higher Groupoid Actions, Bibundles, and Differentiation. Georg-August-Universität Göttingen (2014)
  D. Li
  (See online at https://dx.doi.org/10.53846/goediss-4622)
• Invariant states of quantum birth and death chains
  D. Bücher
  (See online at https://doi.org/10.48550/arXiv.1408.6162)
• Microlocal Analysis of Tempered Distributions. Georg-August-Universität Göttingen (2014)
  R. Schulz
  (See online at https://dx.doi.org/10.53846/goediss-4690)
• Microlocal properties of bisingular operators. J. Pseudo-Differ. Oper. Appl. 5 (2014), no. 1, 43–67
  M. Borsero; R. Schulz
  (See online at https://doi.org/10.1007/s11868-013-0083-z)
• Modular structure of chiral Fermi fields in conformal quantum field theory. Georg-August-Universität Göttingen (2014)
  G. Tedesco
  (See online at https://dx.doi.org/10.53846/goediss-4686)
• Non-classical problems for viscoelastic solids with microstructure. Georg- August-Universität Göttingen and Ivane Javakhishvili Tbilisi State University (2014)
  M. Svanadze
  (See online at https://dx.doi.org/10.53846/goediss-5290)
• On Turing dynamical systems and the Atiyah problem. Invent. Math., 198(1):27-69, 2014
  Ł. Grabowski
  (See online at https://doi.org/10.1007/s00222-013-0497-5)
• Quantum group-twisted tensor products of C∗-algebras, Internat. J. of Math. 25 (2014), no.2 1450019, 37
  R. Meyer; S. Roy; S. Woronowicz
  (See online at https://doi.org/10.1142/S0129167X14500190)
• SG-Lagrangian submanifolds and their parametrization, (2014)
  S. Coriasco and R. Schulz
  (See online at https://doi.org/10.48550/arXiv.1406.1888)
• sl3-web bases, intermediate crystal bases and categorification. J. Algebraic Combin. 40 (2014), no. 4, 1001–1076
  D. Tubbenhauer
  (See online at https://doi.org/10.1007/s10801-014-0518-5)
• The sl3-web algebra. Math. Z. 277 (2014), no. 1-2, 401–479
  Mackaay, M.; Pan, W.; D. Tubbenhauer
  (See online at https://doi.org/10.1007/s00209-013-1262-6)
• Topological construction of C∗-correspondences for groupoid C∗-algebras. Georg-August-Universität Göttingen (2014)
  R. Holkar
  (See online at https://dx.doi.org/10.53846/goediss-5257)
• Virtual Khovanov homology using cobordisms. J. Knot Theory Ramifications 23 (2014), no. 9, 1450046, 91 pp.
  D. Tubbenhauer
  (See online at https://doi.org/10.1142/S0218216514500461)
• 4-sphere with non central radius and its instanton sheaf
  Lucio S. Cirio, C. Pagani
  (See online at https://doi.org/10.1007/s11005-014-0739-5)
• A classification of localizing subcategories by relative homological algebra. Georg-August-Universität Göttingen (2015)
  G.. Nadareishvili
  (See online at https://dx.doi.org/10.53846/goediss-5429)
• A colimit construction for groupoids. Georg-August-Universität Göttingen (2015)
  S. Albandik
  (See online at https://dx.doi.org/10.53846/goediss-5785)
• Algebraic Structure and Integration Maps in Cocycle Models for Differential Cohomology. Algebr. Geom. Topol. 15 (2015), 65–83
  M. Upmeier
  (See online at https://dx.doi.org/10.2140/agt.2015.15.65)
• Analytic singularities near radial points. Georg-August-Universität Göttingen (2015)
  J. Zheng
  (See online at https://dx.doi.org/10.53846/goediss-4976)
• Characterization of 2D rational local conformal nets and its boundary conditions: the maximal case. Documenta Math. 20 (2015) 1137– 1184
  M. Bischoff; Y. Kawahigashi; R. Longo
  (See online at https://doi.org/10.48550/arXiv.1410.8848)
• Characterization of local observables in integrable quantum field theories', (2015)
  H. Bostelmann, D. Cadamuro
  (See online at https://doi.org/10.1007/s00220-015-2294-z)
• Darboux Transformations for (2+1)-Dimensional Extensions of the KP Hierarchy. SIGMA. 11 (2015), 028-1–028-20
  O. I. Chvartatskyi, Yu. M. Sydorenko
  (See online at https://doi.org/10.3842/SIGMA.2015.028)
• Duflo Isomorphism and Chern-Weil Theory
  S. Hong
  (See online at https://doi.org/10.48550/arXiv.1502.07342)
• Geometric twisted K-homology, T-duality isomorphism and T-duality for circle actions. Georg-August-Universität Göttingen (2015)
  B. Liu
  (See online at https://dx.doi.org/10.53846/goediss-5352)
• Haagerup property for Drinfeld doubles, Math. Proc. R. Ir. Acad. 115A (2015), no. 2, 9
  S. Roy
  (See online at https://doi.org/10.25537/dm.2020v25.2553-2582)
• Harish-Chandra’s volume formula via Weyl’s Law and Euler-Maclaurin formula. Differ. Geom. Appl. 38 (2015) 58-68
  S. Hong
  (See online at https://doi.org/10.1016/j.difgeo.2014.11.006)
• Microlocal analysis of quasianalytic Gelfand-Shilov type ultradistributions, (2015)
  M. Cappiello and R. Schulz
  (See online at https://doi.org/10.1080/17476933.2015.1106481)
• Product systems over Ore monoids. Doc. Math. 20 (2015), 1331–1402
  R. Meyer, S. Albandik
  (See online at https://doi.org/10.48550/arXiv.1502.07768)
• Quotients of spectra of almost factorial domains and Mori dream spaces
  M. Maslovaric
  (See online at https://doi.org/10.48550/arXiv.1508.00539)
• Tensor categories of endomorphisms of von Neumann algebras (with applications to Quantum Field Theory). Springer- Briefs in Math. Phys. 3 (2015) 1–94
  M. Bischoff; Y. Kawahigashi; R. Longo; K.-H. Rehren
  (See online at https://doi.org/10.1007/978-3-319-14301-9)
• The Drinfeld double for C∗-algebraic quantum groups, J. Operator Theory 74 (2015), no. 2, 485–515
  S. Roy
  (See online at https://doi.org/10.7900/jot.2014sep04.2053)
• The Geometry of Quantum Lens Spaces: Real Spectral Triples and Bundle Structure. Math Phys Anal Geom 18:9 (2015)
  A. Sitarz.; J. J. Venselaar
  (See online at https://doi.org/10.1007/s11040-015-9179-4)
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