AADIOS (2020) 2021


Algebraic and Algorithmic Aspects of Differential and Integral Operators Session

ACA 2021



Moulay Barkatou (University of Limoges, XLIM DMI, Limoges, France)
Thomas Cluzeau (University of Limoges, CNRS, XLIM DMI, Limoges, France)
Clemens Raab (Johannes Kepler University Linz, Austria)
Georg Regensburger (Johannes Kepler University Linz, Austria)


The algebraic/symbolic treatment of differential equations is a flourishing field, branching out in a variety of subfields committed to different approaches. In this session, we want to give special emphasis to the operator perspective of both the underlying differential operators and various associated integral operators (e.g. as Green’s operators for initial/boundary value problems).

In particular, we invite contributions in line with the following topics:

  • Symbolic Computation for Operator Algebras
  • Factorization of Differential/Integral Operators
  • Linear Boundary Problems and Green’s Operators
  • Initial Value Problems for Differential Equations
  • Symbolic Integration and Differential Galois Theory
  • Symbolic Operator Calculi
  • Algorithmic D-Module Theory
  • Rota-Baxter Algebra
  • Differential Algebra
  • Discrete Analogs of the above
  • Software Aspects of the above

If you are interested in joining the session, please contact us.

Previous ACA sessions were held at

Hagenberg 2008, Montréal 2009, Vlora 2010, Houston 2011,
Sofia 2012
, Malaga 2013, New York 2014, Kalamata 2015,
Kassel 2016
, Santiago de Compostela 2018, Montréal 2019.

We have published an MCS Special Issue based on the 2008-10 sessions and a Springer LNCS Postproceedings Volume based on the 2011-12 sessions.

We have co-edited a Special Issue with Alexey Ovchinnikov on Computational Aspects of Differential/Difference Algebra and Integral Operators for the journal Advances in Applied Mathematics based on ACA 2014 and 15.



Saturday, 24 July, CEST 15:30-20:30

15:30: Vladimir Bavula
16:00: Ngo Quoc Hoan
16:30: Manfred Buchacher
17:00: Cyrille Chenavier
17:30: Thierry Combot

18:00: Break

18:30: Thomas Dreyfus
19:00: Li Guo
19:30: Marc Härkönen
20:00: Mark van Hoeij

Tuesday, 27 July, CEST 15:30-20:00

15:30: Shaoshi Chen
16:00: Hao Du
16:30: Yi Zhang
17:00: Clemens Hofstadler

17:30: Break

18:00: Alexander Levin
18:30: Emma Previato
19:00: Sonia Rueda
19:30: Thibaut Verron


Speakers and Talks


Vladimir Bavula
The global and weak global dimensions of algebras of integro-differential operators

Manfred Buchacher
The Kernel-Method and Automated Positive Part Extraction

Shaoshi Chen
Holonomic Polynomial Sequences I: Degree Growth

Cyrille Chenavier
Strategies for linear rewriting systems: link with parallel rewriting and involutive divisions

Thierry Combot
Symbolic integration on planar differential foliation

Thomas Dreyfus
Differential algebraic generating series of walks in the quarter plane

Hao Du
Two Complete Reduction Systems for Integration

Li Guo
Rota’s Program on Algebraic Operators

Marc Härkönen
Linear PDE with constant coefficients

Mark van Hoeij
Factoring Difference Operators in Maple 2021

Clemens Hofstadler
Automatizing proofs of properties of operators

Ngo Quoc Hoan
Towards a Theory of Domains for Harmonic Functions and its Symbolic Counterpart

Alexander Levin
Multivariate Bernstein-type Polynomials of Finitely Generated D-Modules

Emma Previato
Commutative rings of Differential Operators

Sonia L. Rueda
Factoring Third Order Ordinary Differential Operators over Spectral Curves

Thibaut Verron
Integral bases of P-recursive operators

Yi Zhang
On sequences associated to the invariant theory of rank two simple Lie algebras