Prof.

APPEL Andrea

Professore di II fascia
Settore scientifico disciplinare
Algebra
  • Presentation
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  • Research

I am Associate Professor in Algebra at the University of Parma. My research lies in representation theory and mathematical physics, with a particular focus on quantum groups, quantum symmetric pairs, Yangians, Kac-Moody algebras, and related structures in integrable systems and gauge theory.

I received my PhD in Mathematics from Northeastern University in 2013, under the supervision of Valerio Toledano Laredo, after completing my MSc and BSc in Mathematics at Sapienza University of Rome, under the supervision of Corrado De Concini. Before joining Parma, I held academic positions at the University of Edinburgh, the University of Southern California, and the Hebrew University of Jerusalem.

My work has appeared in leading journals including Inventiones Mathematicae, the Journal of the European Mathematical Society, Advances in Mathematics, Selecta Mathematica, International Mathematics Research Notices, and Communications in Mathematical Physics. I have been principal investigator or coordinator of several research grants, including INdAM, PRIN, and University of Parma projects, and I am actively involved in the organization of international conferences and research activities in algebra, representation theory and mathematical physics.

I am accepting Ph.D. students. Potential candidates are encouraged to contact me.

Selected Publications

  • The R-matrix of the affine Yangian (with S. Gautam and C. Wendlandt)
    Journal of the European Mathematical Society (2026). Accepted for publication.
    [arXiv:2309.02377, 57pp.].
  • Trigonometric K-matrices for finite-dimensional representations of quantum affine algebras (with B. Vlaar)
    Journal of the European Mathematical Society (2025), 41pp. Published online first.
    [DOI] [arXiv:2203.16503]
  • Tensor K-matrices for quantum symmetric pairs (with B. Vlaar)
    Communications in Mathematical Physics 406 (2025), 57pp.
    [DOI] [arXiv:2402.16676]
  • Monodromy of the Casimir connection of a Kac-Moody algebra (with V. Toledano Laredo)
    Inventiones Mathematicae 236 (2024), 124pp.
    [DOI] [arXiv:1512.03041]
  • Generalized Schur-Weyl duality for quantum affine symmetric pairs and orientifold KLR algebras (with T. Przeździecki)
    Advances in Mathematics 435 (2023), 52pp.
    [DOI][arXiv:2204.04123]
  • On a conjecture of Khoroshkin and Tolstoj (with S. Gautam and C. Wendlandt)
    International Mathematics Research Notices IMRN 2023 n.24 (2023) 17pp.
    [DOI] [arXiv:2206.14857] [OWP]
  • Coxeter categories and quantum groups (with V. Toledano Laredo)
    Selecta Mathematica (N.S.) 25 (2019), 97pp.
    [DOI] [arXiv:1610.09741]
  • Uniqueness of Coxeter structures on Kac-Moody algebras (with V. Toledano Laredo)
    Advances in Mathematics 347 (2019), 104pp.
    [DOI] [arXiv:1508.01945]
  • A 2-categorical extension of Etingof-Kazhdan quantisation (with V. Toledano Laredo)
    Selecta Mathematica (N.S.) 24 (2018), 87pp.
    [DOI] [arXiv:1610.09744]

Selected Research Grants

2024–2026
PRIN – Progetto di Ricerca di Rilevante Interesse Nazionale Algebraic Aspects of 2dQFT with reflection symmetr
PRIN ID: 2022HMBTTL - CUP: D53C24003390001
Role: co-Principal Investigator and Local Coordinator of the Research Unit at the University of Parma. Scope: Research Funds. Amount: €125,162.00

2024–2026
Progetto di Ricerca INdAM 2024 – Linea 2 Consolidator Grants Bispectrality and Boundary Phenomena in Quantum Groups CUP: E53C23001740001.
Role: Principal Investigator. Scope: Research Funds. Amount: €30,000.00

2020
Programma per giovani ricercatori Rita Levi Montalcini 2018 (D.M. 511 – 24/8/2020)
Role: Principal Investigator. Scope: Salary and Research Funds. Amount: €180,481.44 + €43,000.00. Notes: grant declined.

Research Interests
Representation Theory, Mathematical Physics

Current Employment
2023–present: Associate Professor in Algebra, Università di Parma, Italy

Previous Appointments
2020–2022: Assistant Professor, Università di Parma, Italy
2017–2020: Research Fellow, University of Edinburgh, UK
2014–2017: Assistant Professor, University of Southern California, Los Angeles, USA
2013: Research Fellow, Hebrew University of Jerusalem, Israel

Education
2013: PhD in Mathematics, Northeastern University, Boston, USA
Advisor: Prof. V. Toledano Laredo

2008: MSc in Mathematics, Sapienza Università di Roma, Italy
Advisor: Prof. C. De Concini

2006: BSc in Mathematics, Sapienza Università di Roma, Italy
Advisor: Prof. M.J. de Resmini

ASN
Abilitazione Scientifica Nazionale alle funzioni di professore universitario di Prima Fascia nel Settore Concorsuale 01/A2 – Geometria e Algebra. Validità: 24/10/2023 – 24/10/2034.

Active Research Group Affiliations
INdAM, Istituto Nazionale di Alta Matematica
Research Group GNSAGA – Gruppo Nazionale Strutture Algebriche, Geometriche ed Applicazioni

INFN, Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Parma
Research Group GAST – Gauge and String Theory

CaLISTA, COST Action 2022–2026
CA21109 – Cartan geometry, Lie, Integrable Systems, quantum group Theories for Applications

Publications and Preprints

  • The R-matrix of the affine Yangian (with S. Gautam and C. Wendlandt)
    Journal of the European Mathematical Society (2026). Accepted for publication.
    [arXiv:2309.02377, 57pp.].
  • Trigonometric K-matrices for finite-dimensional representations of quantum affine algebras (with B. Vlaar)
    Journal of the European Mathematical Society (2025), 41pp. Published online first.
    [DOI] [arXiv:2203.16503]
  • Boundary Transfer Matrices arising from Quantum Symmetric Pairs (with B. Vlaar)
    Indagationes Mathematicae 36 (2025), 33pp.
    Special Issue dedicated to Tom Koornwinder.
    [DOI] [arXiv:2410.21654]
  • Tensor K-matrices for quantum symmetric pairs (with B. Vlaar)
    Communications in Mathematical Physics 406 (2025), 57pp.
    [DOI] [arXiv:2402.16676]
  • Monodromy of the Casimir connection of a Kac-Moody algebra (with V. Toledano Laredo)
    Inventiones Mathematicae 236 (2024), 124pp.
    [DOI] [arXiv:1512.03041]
  • Pure braid group actions on category O modules (with V. Toledano Laredo)
    Pure and Applied Mathematics Quarterly 20.1 (2024), 51pp.
    Special Issue dedicated to Corrado De Concini.
    [DOI][arXiv:2208.05331]
  • Generalized Schur-Weyl duality for quantum affine symmetric pairs and orientifold KLR algebras (with T. Przeździecki)
    Advances in Mathematics 435 (2023), 52pp.
    [DOI][arXiv:2204.04123]
  • On a conjecture of Khoroshkin and Tolstoj (with S. Gautam and C. Wendlandt)
    International Mathematics Research Notices IMRN 2023 n.24 (2023) 17pp.
    [DOI] [arXiv:2206.14857] [OWP]
  • Universal K-matrices for quantum Kac-Moody algebras (with B. Vlaar)
    Representation Theory 26 (2022), 61pp.
    [DOI] [arXiv:2007.09218]
  • Continuum Kac-Moody algebras (with F. Sala and O. Schiffman)
    Moscow Mathematical Journal 22 (2022), 48pp.
    [DOI] [ arXiv:1812.08528]
  • Quantization of continuum Kac-Moody algebras (with F. Sala)
    Pure and Applied Mathematics Quarterly 16 (2020), 55pp.
    Special Issue dedicated to Kyoji Saito.
    [DOI][arXiv:1903.01413]
  • An explicit isomorphism between quantum and classical sl(n) (with S. Gautam)
    Transformation Groups 25 (2020), 36pp.
    [DOI] [arXiv:1712.03601]
  • Coxeter categories and quantum groups (with V. Toledano Laredo)
    Selecta Mathematica (N.S.) 25 (2019), 97pp.
    [DOI] [arXiv:1610.09741]
  • Uniqueness of Coxeter structures on Kac-Moody algebras (with V. Toledano Laredo)
    Advances in Mathematics 347 (2019), 104pp.
    [DOI] [arXiv:1508.01945]
  • A 2-categorical extension of Etingof-Kazhdan quantisation (with V. Toledano Laredo)
    Selecta Mathematica (N.S.) 24 (2018), 87pp.
    [DOI] [arXiv:1610.09744]
  • A DG-extension of symmetric functions arising from higher representation theory (with I. Egilmez, M. Hogancamp, A. Lauda)
    Journal of Combinatorial Algebra 2 (2018), 45pp.
    [DOI] [arXiv:1704.00713]

Lecture Notes

  • The interplay of R-matrices and quantum groups
    Advances in Group Theory and Applications (2025) 20, 60pp.
    [DOI]

PhD Thesis

• Monodromy theorems in the affine setting, PhD Thesis hdl.handle.net/2047/d20003201

Research Grants

2024–2026
PRIN – Progetto di Ricerca di Rilevante Interesse Nazionale Algebraic Aspects of 2dQFT with reflection symmetr
PRIN ID: 2022HMBTTL - CUP: D53C24003390001
Role: co-Principal Investigator and Local Coordinator of the Research Unit at the University of Parma. Scope: Research Funds. Amount: €125,162.00

2024–2026
Progetto di Ricerca INdAM 2024 – Linea 2 Consolidator Grants Bispectrality and Boundary Phenomena in Quantum Groups CUP: E53C23001740001.
Role: Principal Investigator. Scope: Research Funds. Amount: €30,000.00

2024–2025
Progetto d’Ateneo Università di Parma Bispectrality and Boundary Phenomena in Quantum Groups
Bando di Ateneo per la Ricerca 2024 Linea D. Role: Principal Investigator. Scope: Research Funds. Amount: €23,891.00

2023–2024
Progetto d’Ateneo Università di Parma Quantum groups at root of unity and integrable systems with boundary
Bando di Ateneo per la Ricerca 2022 Linea B (Young Researchers), partially funded by Fondazione Cariparma
Role: Principal Investigator. Scope: Research Funds. Amount: €8,500.00

2021–2022
Progetto d’Ateneo Università di Parma Reflection Symmetries arising from quantum loop algebras
Bando di Ateneo per la Ricerca 2020 Linea B (Young Researchers), partially funded by Fondazione Cariparma
Role: Principal Investigator. Scope: Research Funds. Amount: €8,500.00

2020
Programma per giovani ricercatori Rita Levi Montalcini 2018 (D.M. 511 – 24/8/2020)
Role: Principal Investigator. Scope: Salary and Research Funds. Amount: €180,481.44 + €43,000.00. Notes: grant declined

2015–2017
AMS–Simons Travel Grant, AMS–Simons Foundation
Role: Principal Investigator. Scope: Research Funds. Amount: $4,000

Tuesday 11:00-12:00 (upon request).

Anno accademico di erogazione: 2025/2026

Anno accademico di erogazione: 2024/2025

Anno accademico di erogazione: 2023/2024

Anno accademico di erogazione: 2022/2023

Anno accademico di erogazione: 2021/2022

Anno accademico di erogazione: 2020/2021

Anno accademico di erogazione: 2019/2020

Professor/Teacher

  • First cycle degree (DM 270) MATHEMATICS A.Y. 2026/2027
  • First cycle degree (DM 270) MATHEMATICS A.Y. 2024/2025
  • First cycle degree (DM 270) MATHEMATICS A.Y. 2023/2024
  • First cycle degree (DM 270) MATHEMATICS A.Y. 2022/2023

Lines of research

My research is in Representation Theory and Mathematical Physics. My interests include Lie algebras and Kac-Moody algebras, quantum groups, Yangians and quantum loop algebras, classical and quantum integrable systems, Coxeter and Artin groups, combinatorics, and categorification.

Publications

Orcid

0000-0002-6446-9305

Contacts

Phone number
906563
Office location

Deparment of Mathematics, Physics, and Computer Science

Mathematics Building - Office 2.043

Parco Area delle Scienze 53/A 

43124 Parma (PR) ITA

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