ALGEBRAIC MODELING OF TOPOLOGICAL AND COMPUTATIONAL STRUCTURES AND APPLICATIONS

Abstract: 

This research proposal concerns the study of topological and computational structures using algebraic techniques, mainly braid groups and representations of theirs. Braids can be viewed either as algebraic or as topological objects and play a crucial role in low-dimensional topology, homotopy groups, reflection groups and C*-algebras, statistical mechanics, cryptography, Galois theory.

The proposal consists of three research projects (RP):

  1. «Algebraic modeling of topological structures» (knots, 3-manifolds and classical homotopy groups)
  2. «Algebraic modeling of applications»
  3. «Algebraic modeling of computational structures»

RP1 concerns the study of various types of braids and knots and of 3-manifolds via the Yokonuma-Hecke algebras. The computation of the Homflypt skein module for lens spaces using rational surgery and B-type Hecke algebras, and the construction of quotient algebras of mixed braid groups. These problems aim at a unifying algebraic scheme for the study of different knot categories and knots in 3-manifolds. Finally, it concerns the linearity problem of poly-free groups and its connection with homotopy groups of spheres using braid groups.

RP2 concerns the extension of linking number to open chains in periodic boundary conditions and the modeling of polymer melts via surface braids. The simulation of ionic liquids and mixtures of theirs, which will allow the optimal design of industrial units and procedures for the capture and segregation of carbon. Finally, the modeling of 3-dimensional topological surgery through a dynamical system.

RP3 concerns the algebraic modeling of computational structures and applications. Our methods include algebraic specifications for algorithm verification, braid verification, algebraic theories for imaging and elliptic curves. Applications include the modeling of communication protocols, video compression and transmission, coding theory, cryptography and medical imaging.

 

ALMODTOPCOM / MIS 380154
 

Project info

Acronym:
ALMODTOPCOM
Scientific Coordinator:
Lambropoulou Sofia
Research Team 2 Leader:
Theodorou Doros
Research Team 3 Leader:
Kontogeorgis Aristides

Stats

I.D.:
699
Mis:
380154
Duration (months):
48
Budget:
600 000.00
Diavgeia:
ΑΔΑ: Β4139-Β4Δ

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