Joan Claramunt Caros
Max-Planck-Institut für Mathematik in den Naturwissenschaften
Inselstr. 22
04103 Leipzig
Germany

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Joan Claramunt Caros

Research interests

My mathematical research is in the general areas of group theory, noncommutative algebra , operator algebras and the interplay between these. More concretely, my interests are on a question of Atiyah concerning l2-Betti numbers for groups, analysis of rank functions and algebraic structure of dynamical systems through the theory of graphs.

I have also extensive interests in the area of mathematical physics, more specifically in the axiomatization of quantum field theory.

Publications

  • Approximating the group algebra of the lamplighter by infinite matrix products, with P. Ara (UAB), Forum Math. 34 (2022), 851 - 891.
  • L2-Betti numbers arising from the lamplighter group, with P. Ara (UAB), J. Agebr. Comb. 54 (2021), 1201 - 1245.
  • Dynamical preparation of stripe states in spin-orbit coupled gases, with J. Cabedo (UAB), A. Celi (UAB), Phys. Rev. A 104 (2021), L031305.
  • Effective triangular ladders with staggered flux from spin-orbit coupling in 1D optical lattices, with J. Cabedo (UAB), J. Mompart (UAB), V. Ahufinger (UAB), A. Celi (UAB), Eur. J. Phys. D 74 (2020), 123.
  • Sylvester matrix rank functions on crossed products, with P. Ara (UAB), Ergod. Theory Dyn. Syst. 40 (2020), 2913 - 2946.
  • Coherent spin mixing via spin-orbit coupling in Bose gases, with J. Cabedo (UAB), A. Celi (UAB), Y. Zhang (SHU), V. Ahufinger (UAB), J. Mompart (UAB), Phys. Rev. A 100 (2019), 063633.
  • Uniqueness of the von Neumann continuous factor, with P. Ara (UAB), Canad. J. Math. 70 (2018), 961 - 982.
  • Preferred traces on C*-algebras of self-similar groupoids arising as fixed points, with A. Sims (UoW), J. Math. Annal. Appl. 466 (2018), 806 - 818.

Curriculum vitae

Since March 2023 I am a postdoctoral researcher in the Nonlinear Algebra Group at MPI MiS.

Education

  • 12.2015 - 12.2018: PhD in Mathematics, Universitat Autònoma de Barcelona (UAB), Bellaterra (Spain).
    Title: Sylvester matrix rank functions on crossed products and the Atiyah problem.
    Supervisor: Prof. Pere Ara Bertran.
  • 10.2014 - 09.2015: MSc in Pure Mathematics, Imperial College London, London (United Kingdom).
    Title MSc project: Topics in Galois Representations attached to Elliptic Curves.
    Supervisor MSc project: Prof. Kevin Buzzard.
  • 09.2009 - 07.2014: Bachelor of Sciences: double degree in Mathematics and Physics, Universitat Autònoma de Barcelona (UAB), Bellaterra (Spain).
    Title Degree project: Differential Galois Theory.
    Supervisor Degree project: Prof. Pere Ara Bertran.

Professional work history

  • 03.2023 - Present: Postdoctoral Researcher, Max Planck Institute for Mathematics in the Sciences, Leipzig (Germany).
  • 07.2022 - 02.2023: Scientific Assistant, Mathematisches Institut, Universität Leipzig, Leipzig (Germany).
  • 08.2020 - 06.2022: Senior Research Associate, Lancaster University, Lancaster (United Kingdom).
  • 02.2020 - 07.2020: Postdoctoral Researcher, Universidade Federal de Santa Catarina (UFSC), Florianópolis (Brazil).
  • 09.2019 - 01.2020: Postdoctoral Researcher, Universitat Autònoma de Barcelona (UAB), Bellaterra (Spain).
  • 12.2018 - 08.2019: Postdoctoral Researcher, Universitat Autònoma de Barcelona (UAB), Bellaterra (Spain).

Teaching

  • Academic course 2022/23:
    Teaching Assistant, Mathematisches Institut, Universität Leipzig, Leipzig (Germany).
    - Tutorials on `Mathematics for Physicists 1', 1st year of the International Physics Studies Programme (IPSP).
  • Academic course 2019/20:
    Teaching Lectures, Departament de Matemàtiques, Universitat Autònoma de Barcelona (UAB), Bellaterra (Spain).
    - Lectures on `Algebra', 1st year of the Computer Engineering Degree.
    Teaching Problem Sessions, Departament de Matemàtiques, Universitat Autònoma de Barcelona (UAB), Bellaterra (Spain).
    - Problem sessions on `Mathematics I', 1st year of the Chemistry Degree.
    Teaching Assistant, Departament de Matemàtiques, Universitat Autònoma de Barcelona (UAB), Bellaterra (Spain).
    - Assisting problem sessions (RePMat) about solving mathematical problems as a preparation for the Mathematical Olympiad in Catalunya.
  • Academic course 2018/19:
    Teaching Problem Sessions, Departament de Matemàtiques, Universitat Autònoma de Barcelona (UAB), Bellaterra (Spain).
    - Problem sessions on `Algebraic structures', 2nd year of the Mathematics Degree.
    - Problem Sessions on `Commutative algebra', 4th year of the Mathematics Degree.
    Teaching Assistant, Departament de Matemàtiques, Universitat Autònoma de Barcelona (UAB), Bellaterra (Spain).
    - Assisting lectures on `Modelling workshop', 2nd year of the Mathematics Degree.
    - Assisting problem sessions (RePMat) about solving mathematical problems as a preparation for the Mathematical Olympiad in Catalunya.
  • Academic course 2017/18:
    Teaching Problem Sessions, Departament de Matemàtiques, Universitat Autònoma de Barcelona (UAB), Bellaterra (Spain).
    - Problem sessions on `Algebraic structures', 2nd year of the Mathematics Degree.
    - Problem Sessions on `Commutative algebra', 4th year of the Mathematics Degree.
    Teaching Assistant, Departament de Matemàtiques, Universitat Autònoma de Barcelona (UAB), Bellaterra (Spain).
    - Assisting lectures on `Modelling workshop', 2nd year of the Mathematics Degree.
    - Assisting problem sessions (RePMat) about solving mathematical problems as a preparation for the Mathematical Olympiad in Catalunya.
  • Academic course 2016/17:
    Teaching Problem Sessions, Departament de Matemàtiques, Universitat Autònoma de Barcelona (UAB), Bellaterra (Spain).
    - Problem sessions on `Algebraic structures', 2nd year of the Mathematics Degree.
    - Problem Sessions on `Commutative algebra', 4th year of the Mathematics Degree.
    Teaching Assistant, Departament de Matemàtiques, Universitat Autònoma de Barcelona (UAB), Bellaterra (Spain).
    - Assisting problem sessions (RePMat) about solving mathematical problems as a preparation for the Mathematical Olympiad in Catalunya.

Research stays

  • 15.09.2022 - 28.02.2023: Guest researcher at the Max Planck Institute for Mathematics in the Sciences, Leipzig (Germany).
    Supervisor: Prof. Bernd Sturmfels.
    Topic: Algebra and Pure Mathematics.
  • 01.07.2018 - 31.07.2018: Research visit at the Universidade Federal de Santa Catarina (UFSC), Florianópolis (Brazil).
    Supervisor: Prof. Ruy Exel.
    Topic: Dynamical systems through separated graphs.
  • 01.09.2017 - 31.10.2017: Research visit at the University of Wollongong (UoW), Wollongong (Australia).
    Supervisor: Prof. Aidan Sims.
    Topic: KMS states on C*-algebras of self-similar groupoids.
  • 01.03.2017 - 21.07.2017: Research visit at the Centre de Recerca Matemàtica (CRM), Bellaterra (Spain).
    Short description: Visit during the programme "Operator Algebras: Dynamics and Interactions".
  • 24.10.2016 - 26.10.2016: Research visit at the Centre for Research in Mathematics (CRM), Western Sydney University (WSU), Sydney (Australia).
    Supervisor: Prof. Roozbeh Hazrat.
    Topic: L2-Betti numbers and the Atiyah problem.
  • 01.09.2016 - 31.10.2016: Research visit at the University of Wollongong (UoW), Wollongong (Australia).
    Supervisor: Prof. Aidan Sims.
    Topic: KMS states on C*-algebras of self-similar group actions.
  • 01.02.2016 - 12.02.2016: Research visit at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI) of the University of Vienna, Vienna (Austria).
    Short description: Visit during the programme "Measured group theory".
  • 01.10.2015 - 30.11.2015: Introduction to Research Grant, Instituto de Ciencias Matemáticas (ICMAT), Madrid (Spain).
    Supervisor: Prof. Fernando Lledó Macau.
    Topic: Amenability for groups and algebras.

Conferences & meetings

  • 05.09.2021 - 10.09.2021: Hybrid conference "Baby Steps Beyond the Horizon: Mathematics for Students", online, Będlewo (Poland).
  • 05.10.2020 - 09.10.2020: Hybrid conference "CIRM-SMF Program: Measured and Geometric Group Theory, Rigidity, Operator Algebras" at the Centre International de Recontres Mathématiques (CIRM), Marseille (France).
  • 05.08.2019 - 10.08.2019: Annual conference "Young Mathematicians in C*-algebras (YMC*A)" at the University of Copenhagen, Copenhagen (Denmark).
  • 26.06.2019 - 28.06.2019: Meeting "2nd BMS-BGSMath Junior Meeting 2019" at the Zuse Institute Berlin (ZIB), Berlin (Germany).
  • 13.08.2018 - 17.08.2018: Annual conference "Young Mathematicians in C*-algebras (YMC*A)" at the KU Leuven, Leuven (Belgium).
  • 26.07.2018 - 30.07.2018: ICM Operator Algebras Satellite Conference (ICMOA), 6th Florianópolis-Münster-Ottawa meeting dedicated to Ruy Exel's 60th birthday, at the Palace Praia Hotel, Florianópolis (Brazil).
  • 19.06.2017 - 23.06.2017: Barcelona Conference on C*-algebras: Structure, Classification and Dynamics, as part of the "Intensive Research Program Operator Algebras: Dynamics and Interactions, at the Centre de Recerca Matemàtica (CRM), Bellaterra (Spain).
  • 25.07.2016 - 29.07.2016: Annual conference "Young Mathematicians in C*-algebras (YMC*A)" at the Mathematical Institute of the University of Münster, Münster (Germany).
  • 29.07.2015 - 31.07.2015: Applied Geometric Algebra in Computer Science and Engineering (AGACSE) 2015 Conference at the Universitat Politècnica de Catalunya (UPC), Barcelona (Spain).

Courses, schools & workshops

  • 08.02.2023 - 09.02.2023: Workshop "Reflection groups" at the Otto-von-Guericke-Universität Magdeburg, Magdeburg (Germany).
  • 19.07.2021 - 23.07.2021: "LMS-INI-Bath Summer School on K-Theory and Representation Theory", online, Bath (United Kingdom).
  • 07.10.2019 - 23.01.2020: "BGSMath Course: Singular Integrals" at the Centre de Recerca Matemàtica (CRM), Bellaterra (Spain).
  • 19.09.2019 - 21.09.2019: Workshop "II Barcelona Weekend on Operator Algebras and Noncommutative Algebra" on the occasion of Pere Ara's 60th birthday, at the Centre de Recerca Matemàtica (CRM), Bellaterra (Spain).
  • 27.05.2019 - 31.05.2019: Advanced course on Geometry, Topology and Algebra at the Centre de Recerca Matemàtica (CRM), Bellaterra (Spain).
  • 06.05.2019 - 10.05.2019: School II: Applications to Quantum Information, as part of the "Thematic Research Programme: Operator Algebras, Groups and Applications to Quantum Information" at the Instituto de Ciencias Matemáticas (ICMAT), Madrid (Spain).
  • 24.04.2019 - 05.06.2019: "BGSMath Course: An Introduction to Wavelets and their Applications" at the Universitat de Barcelona (UB), Barcelona (Spain).
  • 11.03.2019 - 22.03.2019: School I and Workshop I: Operator algebras and Groups, as part of the "Thematic Research Programme: Operator Algebras, Groups and Applications to Quantum Information" at the Instituto de Ciencias Matemáticas (ICMAT), Madrid (Spain).
  • 16.11.2018 - 17.11.2018: Workshop "Barcelona Weekend on Operator Algebras" at the Centre de Recerca Matemàtica (CRM), Bellaterra (Spain).
  • 23.04.2018 - 26.04.2018: Advanced course "The theory of epic *-regular rings and its applications to the study of L2-Betti numbers", as part of the "Thematic Program: L2-Invariants and their analogues in positive characteristic" at the Instituto de Ciencias Matemáticas (ICMAT), Madrid (Spain).
  • 26.02.2018 - 09.03.2018: Introductory School as part of the "Thematic Program: L2-Invariants and their analogues in positive characteristic" at the Instituto de Ciencias Matemáticas (ICMAT), Madrid (Spain).
  • **.09.2017 - **.02.2018: Course "Groupoid C*-algebras" at the Ring Theory research group, Departament de Matemàtiques at Universitat Autònoma de Barcelona (UAB), Bellaterra (Spain).
  • 11.05.2017 - 18.05.2017: Lecture Series on von Neumann Algebras, as part of the "Intensive Research Program Operator Algebras: Dynamics and Interactions, at the Centre de Recerca Matemàtica (CRM), Bellaterra (Spain).
  • 20.03.2017 - 24.03.2017: Workshop on C*-Algebras and Dynamical Systems, as part of the "Intensive Research Program Operator Algebras: Dynamics and Interactions, at the Centre de Recerca Matemàtica (CRM), Bellaterra (Spain).
  • 13.03.2017 - 17.03.2017: Advanced Course "Operator Algebras: Groupoids, Crossed Products, and Rokhlin Dimension", as part of the "Intensive Research Program Operator Algebras: Dynamics and Interactions, at the Centre de Recerca Matemàtica (CRM), Bellaterra (Spain).
  • 06.03.2017 - 21.03.2017: Course "An invitation to C*-algebras", as part of the "Intensive Research Program Operator Algebras: Dynamics and Interactions, at the Centre de Recerca Matemàtica (CRM), Bellaterra (Spain).
  • 10.01.2017 - 26.01.2017: "BGSMath Course: Category Theory" at the Centre de Recerca Matemàtica (CRM), Bellaterra (Spain).
  • 22.02.2016 - **.05.2016: "BGSMath Course: A primer on K-theory and its applications" at the Centre de Recerca Matemàtica (CRM), Bellaterra (Spain).
  • 31.01.2016 - 14.02.2016: Winter School of the programme on "Measured Group Theory" at the Research Centre Erwin Schrödinger International Institute for Mathematics and Physics (ESI) of the University of Vienna, Vienna (Austria).
  • 02.11.2015 - 03.11.2015: Course "Derivations on Banach and C*-Algebras" at the Universidad Carlos III de Madrid (UC3M), Madrid (Spain).
  • 27.07.2015 - 28.07.2015: Applied Geometric Algebra in Computer Science and Engineering (AGACSE) 2015 Summer School at the Universitat Politècnica de Catalunya (UPC), Barcelona (Spain).
  • 18.07.2015 - 24.07.2015: French-German Summer School "Galois Theory and Number Theory" at the Universität Konstanz, Konstanz (Germany).

Organized scientific events

  • 09.2019: Workshop II Barcelona Weekend on Operator Algebras and Noncommutative Algebra, Centre de Recerca Matemàtica (CRM), Bellaterra (Spain).
  • 07.2017: Barcelona Conference on C*-algebras: Structure, Classification and Dynamics, Centre de Recerca Matemàtica (CRM), Bellaterra (Spain).
    Part of the Intensive Research Program Operator Algebras: Dynamics and Interactions.
  • 03.2017: Advanced Course on Operator Algebras: Groupoids, Crossed Products, and Rokhlin Dimension, Centre de Recerca Matemàtica (CRM), Bellaterra (Spain).
    Part of the Intensive Research Program Operator Algebras: Dynamics and Interactions.
  • 03.2017: Workshop on C*-algebras and Dynamical Systems, Centre de Recerca Matemàtica (CRM), Bellaterra (Spain).
    Part of the Intensive Research Program Operator Algebras: Dynamics and Interactions.

Seminars, talks & posters

  • 09.01.2023: Seminar talk "On group rings of virtually abelian groups" at the Ring Theory research group, Departament de Matemàtiques at Universitat Autònoma de Barcelona (UAB), Bellaterra (Spain).
  • 02.11.2022: Seminar talk "L2-Betti numbers, the Atiyah conjecture and related conjectures" at the Nonlinear Algebra group at Max Planck Institute for Mathematics in the Sciences (MPI MiS), Leipzig (Germany).
  • 20.12.2021: Seminar talk "The stability problem" at the Ring Theory research group, Departament de Matemàtiques at Universitat Autònoma de Barcelona (UAB), Bellaterra (Spain).
  • 02.11.2021: Seminar talk "L2-Betti numbers and the Atiyah conjecture" at the PG Forum at Lancaster University, Lancaster (United Kingdom).
  • 28.06.2019: Invited talk "L2-Betti numbers and the Atiyah conjecture" at the "2nd BMS-BGSMath Junior Meeting 2019" at the Zuse Institute Berlin (ZIB), Berlin (Germany).
  • 18.03.2019: Contributed talk "Uniqueness of the von Neumann continuous factor" at the Workshop I: Operator Algebras and Groups, as part of the "Thematic Research Programme: Operator Algebras, Groups and Applications to Quantum Information" at the Instituto de Ciencias Matemáticas (ICMAT), Madrid (Spain).
  • 01.03.2019: Seminar talk "The Banach-Tarski paradox and amenable groups" at the Seminari Molt Informal, Departament de Matemàtiques at Universitat Autònoma de Barcelona (UAB), Bellaterra (Spain).
  • 17.11.2018: Invited talk "Preferred traces on C*-algebras of self-similar groupoids arising as fixed points" at the Workshop "Barcelona Weekend on Operator Algebras" at the Centre de Recerca Matemàtica (CRM), Bellaterra (Spain).
  • 12.09.2018: Contributed talk "The algebra of the lamplighter and the Atiyah problem" at the joint meeting of the Czech, Slovenian, Austrian, Slovak and Catalan Mathematical Societies (CSASC 2018), Bratislava (Slovakia).
  • 26.07.2018 - 30.07.2018: Contributed poster "Sylvester matrix rank functions on Z-crossed product algebras" at the ICM Operator Algebras Satellite Conference (ICMOA) at the Palace Praia Hotel, Florianópolis (Brazil).
  • 09.07.2018: Seminar talk "Sylvester matrix rank functions on crossed product algebras" at the Operator Algebra Seminars, Departamento de Matemática at the Universidade Federal de Santa Catarina (UFSC), Florianópolis (Brazil).
  • 24.04.2018: Seminar talk "Sylvester Matrix Rank Functions on Crossed Product Algebras" at the Instituto de Ciencias Matemáticas (ICMAT), Madrid (Spain).
  • 19.10.2017: Seminar talk "Some advances on the Atiyah Problem" at the Operator Algebras and Noncommutative Geometry Seminar, Institute for Mathematics and Its Applications at the University of Wollongong (UoW), Wollongong (Australia).
  • 24.03.2017: Contributed talk "KMS states over group and graph algebras" at the workshop on C*-Algebras and Dynamical Systems, as part of the "Intensive Research Program Operator Algebras: Dynamics and Interactions, at the Centre de Recerca Matemàtica (CRM), Bellaterra (Spain).
  • 25.10.2016: Seminar talk "Atiyah Conjecture" at the Mathematics department, Centre for Research in Mathematics at the Wester Sydney University (WSU), Parramatta (Australia).
  • 09.11.2015: Seminar talk "Paradoxical decompositions in groups and algebras" at the Q-Math Seminar, Departamento de Matemáticas at the Universidad Carlos III de Madrid (UC3M), Madrid (Spain).
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