Organisatieprofiel

Introductie / missie

The three chairs within DM maintain the three main research areas: the more applied coding theory and cryptology; the combinatorial optimization which goes into problems in operational management; and the more fundamental discrete algebra and geometry.

Highlighted phrase

The section DM is interested in all mathematical problems of a discrete nature.

Over de organisatie

The section DM has three chairs:

The chair for Coding Theory and Cryptology (CC) performs research in theoretical and applied areas of both topics:

Coding Theory is the mathematical theory of encoding information in such a way that it becomes resistant to transmission errors. The main topics are the study of the properties of various codes (cyclic codes, BCH-codes, MDS-codes, algebraic-geometric codes) and the construction of efficient decoding algorithms for these codes.

Cryptology is the mathematical theory of protecting information against unauthorized access (privacy), determining if a message has been altered by a third party (integrity), adding a signature to an electronic document and verifying the identity.

The Combinatorial Optimization (CO) group focuses on the analysis and solution of discrete algorithmic problems that are computationally difficult (NP-hard). A generic formulation of such problems is: given a number of boundary conditions and constraints, find a solution that minimizes the cost or maximizes the profit.

Phenomena throughout mathematics and the natural sciences have discrete algebraic aspects, often along with analytical counterparts. While the latter are typically modelled using real numbers, differential equations, and numerical computations, describing the discrete-algebraic aspects involves objects like nite elds, graphs, polynomials, groups, algebras, and symbolic computations. The Discrete Algebra and Geometry (DAG) group at the TU/e develops the mathematics needed for such a description.

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Profielen

Jacob R. Appelbaum

j.appelbaum@tue.nl

Faculteit Wiskunde & Informatica, Discrete Mathematics - Promovendus
Faculteit Wiskunde & Informatica, Discrete Mathematics W&I - Promovendus

Persoon: Prom. : Promovendus

Tomer Ashur

t.ashur@tue.nl

Faculteit Wiskunde & Informatica, Discrete Mathematics - Universitair Docent

Persoon: UD : Universitair Docent

Nikhil Bansal

n.bansal@tue.nl

Faculteit Wiskunde & Informatica, Combinatorial Optimization
Faculteit Wiskunde & Informatica, Discrete Mathematics W&I - Hoogleraar
Faculteit Wiskunde & Informatica, Discrete Mathematics - Hoogleraar

Persoon: HGL : Hoogleraar

Onderzoeksoutput 1970 2019

An algorithm for komlós conjecture matching Banaszczyk's bound

Bansal, N., Dadush, D. & Garg, S., 30 apr 2019, In : SIAM Journal on Computing. 48, 2, blz. 534-553 20 blz.

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

Open Access

Bestand

Coloring

Colouring

Discrepancy

Set Systems

Efficient Algorithms

A new class of irreducible pentanomials for polynomial-based multipliers in binary fields

Banegas, G., Custódio, R. & Panario, D., 1 nov 2019, In : Journal of Cryptographic Engineering. 9, 4, blz. 359–373

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

Open Access

Bestand

Polynomials

Time delay

Costs

Application of complementary dual AG codes to entanglement-assisted quantum codes

Pereira, F. R. F., Pellikaan, R., La Guardia, G. G. & De Assis, F. M., 1 jul 2019, 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings. Piscataway: Institute of Electrical and Electronics Engineers, blz. 2559-2563 5 blz. 8849685

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

Entanglement

Towers

Error-correcting Codes

Redundancy

Algebraic-geometry Codes