Discrete Mathematics

  • Postbus 513, MF

    5600MB Eindhoven

    Nederland

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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Onderzoeksoutput 1973 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 tijdschriftTijdschriftartikelAcademicpeer review

Open Access
Bestand
Coloring
Colouring
Discrepancy
Set Systems
Efficient Algorithms

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/CongresprocedureConferentiebijdrageAcademicpeer review

Entanglement
Towers
Error-correcting Codes
Redundancy
Algebraic-geometry Codes

A reaction attack against cryptosystems based on LRPC codes

Samardjiska, S., Santini, P., Persichetti, E. & Banegas, G., 2019, Progress in Cryptology -- LATINCRYPT 2019. Schwabe, P. & Thériault, N. (redactie). Cham: Springer International Publishing Switzerland, blz. 197-216 20 blz. (Lecture Notes in Computer Science; vol. 11774)

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

Cryptography
Decoding
Standardization

Prijzen

Algorithms for coping with uncertainty and intractability

Nikhil Bansal (Ontvanger), 2013

Prijs: ERCConsolidatorWetenschappelijk

Combinatorial optimization
Approximation algorithms
Computer science
Uncertainty
Optimum design

Best investigative reporting

Jacob Appelbaum (Ontvanger), 2014

Prijs: AndersWerk, activiteit of publicatie gerelateerde prijzen (lifetime, best paper, poster etc.)Wetenschappelijk

Best Paper Award at IH&MMSec 2015

Thijs Laarhoven (Ontvanger), 19 jun 2015

Prijs: AndersWerk, activiteit of publicatie gerelateerde prijzen (lifetime, best paper, poster etc.)Wetenschappelijk

Bestand

Activiteiten 2014 2019

  • 11 Aangemelde presentatie
  • 5 Genodigd spreker
  • 1 Workshop, seminar, cursus of expositie

Strong IP Formulations Need Large Coefficients

Christopher Hojny (Spreker)
6 sep 2019

Activiteit: Types gesprekken of presentatiesAangemelde presentatieWetenschappelijk

Symmetry Handling in Binary Programs: Combining Symretopes and Orbital Fixing

Christopher Hojny (Spreker)
1 jul 2019

Activiteit: Types gesprekken of presentatiesGenodigd sprekerWetenschappelijk

Strong IP Formulations Need Large Coefficients

Christopher Hojny (Spreker)
27 mrt 2019

Activiteit: Types gesprekken of presentatiesGenodigd sprekerWetenschappelijk

Pers/media

Fast, Furious and Insecure: Passive Keyless Entry and Start in Modern Supercars

Tomer Ashur

10/09/1827/08/19

2 items van media-aandacht

Pers / media: Onderzoek

Dutch report finds cybersecurity not keeping up with growing number of attacks

Tanja Lange

24/04/18

1 item van media-aandacht

Pers / media: Vakinhoudelijk commentaar

Scripties/masterproeven

A characterization of the special linear and unitary Lie algebra via its extremal geometry

Auteur: Oostendorp, M., 31 aug 2018

Begeleider: Cuypers, F. (Afstudeerdocent 1)

Scriptie/masterproef: Master

Bestand

Achieving differential privacy in secure multiparty computation

Auteur: Thissen, K., 15 mei 2019

Begeleider: Schoenmakers, B. (Afstudeerdocent 1), Koster, R. (. (Externe persoon) (Externe coach) & van Liesdonk, P. (Externe coach)

Scriptie/masterproef: Master

Bestand

A group-theoretical analysis of solvability, solutions and solution strategies of permutation puzzles

Auteur: Rijpert, D. T., 15 aug 2019

Begeleider: Cuypers, H. (Afstudeerdocent 1)

Scriptie/masterproef: Bachelor

Bestand