ICMS 2020 Session: Computational Algebraic Analysis
ICMS 2020 Session: Computational Algebraic Analysis
ICMS 2020:
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Aim and Scope
The theory of Dmodules enables an investigation of homogeneous partial linear
differential equations with polynomial coefficients by algebraic methods.
Many (special) functions arising in a mathematician's or physicist's daily
life can be understood by their annihilating ideal in the Weyl algebra. The
class of holonomic functions is a prominent, widelyused example for this
approach. Applications include maximum likelihood estimates in statistics,
volume computations of compact semialgebraic sets, high precision evaluation
of holonomic functions, and local optimization methods. There is a variety of
computer algebra systems that allow computations in noncommutative rings of
linear partial differential operators. The aim of this session is to give an
overview of the broad range of applications, to introduce the participants to
existing software, and to discuss recent developments in this field.
Topics (including, but not limited to)
 Bernstein–Sato theory
 Creative telescoping algorithms
 Highprecision numerical evaluation of holonomic functions
 Holonomic gradient method and holonomic gradient descent
 Holonomic sequences
 Symbolic integration and summation
 Volume computation of compact semialgebraic sets
Submission Guidelines
For details, see the official guidelines.
The most important points are:

If you wish to give a talk at ICMS, you need to submit a title and short
abstract to the session organizers (until February 23 at latest –
the earlier the better).

Those speakers which have been accepted to the session may submit an
extended abstract to the LNCS proceedings volume (4–8 pages, due
March 16). Please use this
EasyChair link
for the submission.

The PC decision on the extended abstracts will be communicated on April 27,
and the cameraready papers are due on May 9, 2020.
Talks/Abstracts
(in alphabetical order)

Francisco Jesús Castro Jiménez
(Universidad de Sevilla, Spain):
On the bfunction associated with some irregular GKZhypergeometric ideals
A result of M. Saito, B. Sturmfels and N. Takayama gives a
closed formula for the generic bfunction associated with a real weight
vector and a regular GKZhypergeometric ideal in the complex Weyl algebra
of order n. In this talk we propose an analogous formula in the
irregular case, also valid for nongeneric bfunctions, when the
hypergeometric ideal is associated with a smooth monomial curve in the
three dimensional affine space. This talk is based on a joint work with
Helena Cobo.

Paul Görlach
(Technische Universität Chemnitz, Germany):
The holonomic gradient method in statistics
The evaluation and optimization of holonomic functions can be aided by a
systematic usage of its annihilating differential operators, known as the
holonomic gradient method. In statistics, its importance revolves around
the computation of normalizing constants and maximum likelihood
estimates. We survey recent developments in this area with a focus on
existing implementations.

András Cristian Lőrincz
(HumboldtUniversität zu Berlin, Germany):
Algebraic Analysis of Rotation Data
In this talk we present tools from algebraic analysis for statistical
inference in the Fisher model for the rotation group. Based on the
holonomic gradient method, we develop algorithms for maximum likelihood
estimation and apply them for data from the applied sciences. On the
theoretical side, we generalize the underlying equivariant Dmodules from
SO(3) to arbitrary Lie groups. This is joint work with Michael F. Adamer,
AnnaLaura Sattelberger, and Bernd Sturmfels.

Viktor Levandovskyy
(RWTH Aachen University, Germany):
Dmodules and algorithmic algebraic analysis with Singular
We review the needs of modern algebraic analysis in the realm of
algorithms and their implementations. Some highlights from the rich
experience of developing, implementing and applying such algorithms will
be presented. A whole suite of functionalities, implemented in
Singular:Plural, will be described.

SaieiJaeyeong MatsubaraHeo
(Kobe University, Japan):
Computing cohomology intersection numbers of GKZ systems
In the theory of special functions, a particular kind of multidimensional
integral appears frequently. It is called the Euler integral. In order to
understand the topological nature of the integral, twisted de Rham
cohomology theory plays an important role. In this talk, we propose an
algorithm of computing an invariant "cohomology intersection number". The
algorithm is based on the fact that the Euler integral satisfies a GKZ
system and utilizes algorithms to find rational solutions of differential
equations. We also provide software to perform this algorithm. This talk
is based on a joint work with Nobuki Takayama.

AnnaLaura Sattelberger
(MaxPlanckInstitut für Mathematik in den Naturwissenschaften, Leipzig, Germany):
Computational Algebraic Analysis
This talk is meant to be an introductory talk to the session on
Computational Algebraic Analysis. We briefly describe the general
mathematical setup, give a first overview of the broad range of
applications and existing software, and discuss recent developments in
this field.

Bernd Sturmfels
(University of California at Berkeley, U.S., and MaxPlanckInstitut
für Mathematik in den Naturwissenschaften, Leipzig, Germany):
Primary Ideals and their Differential Equations
An ideal in a polynomial ring encodes a system of linear partial
differential equations with constant coefficients. Primary decomposition
organizes the solutions to the PDE. Recent work with Yairon CidRuiz and
Roser Homs furnishes a structure theory for primary ideals in this
context. After a brief historical introduction, from Gröbner to
Ehrenpreis and Palamodov, we present connections to Dmodules and software
in Macaulay2.