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Measuring the entanglement complexity of 3-periodic networks through the untangling number

Autoren: Toky Andriamanalina, Sonia Mahmoudi, Myfanwy E. Evans (2025)

Periodic networks serve as models for the structural organisation of biological and chemical crystalline systems. Single or multiple networks can have different configurations in space, where entanglement may arise due to the way the (possibly curvilinear) edges weave around each other. This entanglement influences the functional, physical, and chemical properties of the materials modelled by the networks, which highlights the need to quantify its complexity. In this paper, we define the least tangled embeddings of 3-periodic networks that we call ground states, through the use of knot-theoretic crossing diagrams. The concept of a ground state permits the definition of a measure of entanglement complexity called the untangling number that quantifies the distance between a given 3-periodic structure and its least tangled version.


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Applied Geometry and Topology

Address

University of Potsdam
Institute of Mathematics
Campus Golm, Haus 9
Karl-Liebknecht-Str. 24-25
14476 Potsdam
Germany

Activities

21.05.2026, 14:00–16:30  –  FU Berlin, Room 101
Forschungsseminar Differentialgeometrie

Interuniversity Seminar in Geometric Analysis (FU Berlin)

Peter Topping and Isabel Fernández

The Interuniversity Seminar in Geometric Analysis (IGA) is a joint research seminar hosted between researchers from multiple institutes. The seminar takes place several times per semester and rotates... 

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22.05.2026, 13:00 - 16:00  –  Campus Griebnitzsee, House 6, Room H01
SFB-Kolloquium

9th Kálmán Lecture with Ruth Baker: "What is parameter identifiability, why do we need identifiable models, and what can identifiable models tell us about regulation of the cell cycle?"

Ruth Baker (Oxford University)

Ruth Baker from Oxford University will be the speaker of our 9th Kálmán Lecture on Fri 22 May. Ruth will give a one-hour talk after which we can spend some time discussing new DA developments over... 

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22.05.2026, 14:00  –  Auditorium Maximum im Haus 8, Am Neuen Palais
Ankündigung

Euler-Vorlesung 2026

Jessica Fintzen und Johannes Buchmann

Die Euler-Vorlesung in 2026 wird von Professorin Jessica Fintzen von der Universität Bonn gehalten. Den Kulturvortrag wird Professor Johannes Buchmann von der Technischen Universität Darmstadt geben.

... 

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27.05.2026, 10:15  –  2.09.1.22
Forschungsseminar: Gruppen und Operatoralgebren

Amenable open covers

Kevin Li (FU Berlin)

We want to cover a topological space by open subsets with amenable fundamental group. The minimal number of sets needed is called the "amenable category". Obstructions (lower bounds) are given by L2-B... 

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03.06.2026, 12:00  –  Campus Golm, Building 9, Room 1.22
Forschungsseminar Numerische Analysis

Solution of infinite Bayesian linear inverse Problems with Chebfun

Adrian Lorenz (Uni Potsdam)

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