New Graduates in Computer Algebra

New Ph.D.'s are vital to any research area and we are pleased to present a repository of new graduates and their thesis abstracts.  We encourage all recent Ph.D. graduates (and their supervisors), who have defended in the past year, to submit their abstracts for publication here through this web form.

These abstracts will also be published in an upcoming edition of the SIGSAM Communications in Computer Algebra. We hope you agree that this is a great way to bring attention to the young researchers in our field, and see the new directions of their research.

Sunday, October 9, 2011
Dr. Angelos Mantzaflaris, University of Nice and GALAAD INRIA Sophia-Antipolis. Advisor: Bernard Mourrain Defense date: October 3, 2011
Wednesday, October 13, 2010
A mechanism is statically balanced if, for any motion, it does not exert forces on the base. Moreover, if it does not exert torques on the base, the mechanism is said to be dynamically balanced. In 1969, Berkof and Lowen showed that in some cases, it is possible to balance mechanisms without adding additional components, simply by choosing the design parameters (i.e. length, mass, centre of mass, inertia) in an appropriate way. For the simplest linkages, some solutions were found but no complete characterization was given. The aim of the thesis is to present a new systematic approach to obtain such complete classifications for 1 degree of freedom linkages. The method is based on the use of complex variables to model the kinematics of the mechanism. The static and dynamic balancing constraints are written as algebraic equations over complex variables and joint angular velocities. After elimination of the joint angular velocity variables, the problem is formulated as a problem of factorisation of Laurent polynomials. Using computer algebra, necessary and sufficient conditions can be derived. Using this approach, a classification of all possible statically and dynamically balanced planar four-bar mechanisms is given. Sufficient and necessary conditions for static balancing of spherical linkages is also described and a formal proof of the non-existence of dynamically balanced spherical linkage is given. Finally, conditions for the static balancing of Bennett linkages are described.
Monday, July 12, 2010
Dr. Flavia Stan
Research Institute for Symbolic Computation (RISC)
Monday, February 1, 2010
The holonomic systems approach was proposed in the early 1990s by Doron Zeilberger. It laid a foundation for the algorithmic treatment of holonomic function identities. Fr'ed'eric Chyzak later extended this framework by introducing the closely related notion of $partial$-finite functions and by placing their manipulation on solid algorithmic grounds. For practical purposes it is convenient to take advantage of both concepts which is not too much of a restriction: The class of functions that are holonomic and $partial$-finite contains many elementary functions (such as rational functions, algebraic functions, logarithms, exponentials, sine function, etc.) as well as a multitude of special functions (like classical orthogonal polynomials, elliptic integrals, Airy, Bessel, and Kelvin functions, etc.). In short, it is composed of functions that can be characterized by sufficiently many partial differential and difference equations, both linear and with polynomial coefficients. An important ingredient is the ability to execute closure properties algorithmically, for example addition, multiplication, and certain substitutions. But the central technique is called creative telescoping which allows to deal with summation and integration problems in a completely automatized fashion. Part of this thesis is our Mathematica package HolonomicFunctions in which the above mentioned algorithms are implemented, including more basic functionality such as noncommutative operator algebras, the computation of Gr"obner bases in them, and finding rational solutions of parameterized systems of linear differential or difference equations. Besides standard applications like proving special function identities, the focus of this thesis is on three advanced applications that are interesting in their own right as well as for their computational challenge. First, we contributed to translating Takayama's algorithm into a new context, in order to apply it to an until then open problem, the proof of Ira Gessel's lattice path conjecture. The computations that completed the proof were of a nontrivial size and have been performed with our software. Secondly, investigating basis functions in finite element methods, we were able to extend the existing algorithms in a way that allowed us to derive various relations which generated a considerable speed-up in the subsequent numerical simulations, in this case of the propagation of electromagnetic waves. The third application concerns a computer proof of the enumeration formula for totally symmetric plane partitions, also known as Stembridge's theorem. To make the underlying computations feasible we employed a new approach for finding creative telescoping operators.
Monday, July 14, 2008
Department of Computer Science, Universidad de La Rioja, Spain
Title: Homologa Efectiva y Sucesiones Espectrales
Monday, July 14, 2008
Research Institute for Symbolic Computation (RISC) Johannes Kepler University, Linz, Austria
Title: Symbolic-Algebraic Methods for Linear Partial Differential Operators
Monday, July 14, 2008
Computer Science Department, University of Western Ontario, London, Ontario, Canada
Title: Fast Algorithms, Modular Methods, Parallel Approaches and Software Engineering for Solving Polynomial Systems Symbolically
Monday, July 14, 2008
Applied Mathematics Department University of Western Ontario London,Ontario, Canada.
Title: Symbolic Computation Techniques for Solving Large Expression Problems from Mathematics and Engineering
Monday, July 14, 2008
Department of Informatics and Telecommunications, National Kapodistrian University of Athens, Greece.
Title: Algebraic Computations and Applications to Geometry.
Monday, July 14, 2008
Department of Applied Mathematics, University of Western Ontario, Canada Title:

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