Elite Network: Detail
Go back to overview

100 Years of Toeplitz-Hausdorff Theorem

When host­ing the 14th WONRA to cele­brate 100 Years of the Toeplitz-Hausdorff theo­rem, ExQM tried its best to leave both a scien­tific and cul­tural hall­mark in the tradi­tion of this inter­na­tional con­fer­ence. Be­yond the 50 inter­na­tional ex­perts in multi­linear alge­bra, ExQM invit­ed key­note speakers with a par­ticular link to quan­tum phys­ics, data com­pres­sion as well as to the histor­ical im­mer­sion of Toeplitz and Hausdorff.

International Exchange of Ideas and Results

The nu­meri­cal range plays a cru­cial role in spec­tral theory and in the search of ground-state ener­gies of quan­tum physi­cal sys­tems. In 1918/1919, by the cele­brated Toeplitz-Hausdorff theo­rem, it was shown to form a con­vex set.

In quan­tum-many-body sys­tems – the focus of inter­est in the Inter­na­tional Doc­torate Pro­gram „Exploring Quantum Matter“ – the im­portant ques­tion arises whether the spec­tra of the under­lying Ham­iltoni­ans are gapped. This deci­sion prob­lem was brought to Gö­del-form by Prof. Mi­chael Wolf (who is an ExQM PI) in a semi­nal paper in Na­ture. His talk on “Un­de­cida­bility of the Spec­tral Gap” was one high­light of the con­fer­ence.

First-year ExQM PhD stu­dent Fred­erik vom Ende pre­sented his results on in­fi­ni­te-dimension­al sys­tems and found him­self im­medi­ately well re­ceived in the com­muni­ty.

Upon invita­tion by ExQM, Prof. David Gross (Uni­versi­ty of Co­logne) lec­tured on low-rank re­con­struc­tion algo­rithms. They are im­portant not only in quan­tum phys­ics but also in eve­ry-day-life when it comes to image recon­struc­tion and signal pro­cess­ing.

Mathematicians in Germany 1933-45, a Cultural Round-Up

Prof. Thomas Huck­le (who also is an ExQM PI) gave an over­view on the fate of math­emati­cians in Ger­many 1933-45 (in­clud­ing the cele­brated Hausdorff and Toeplitz) with spe­cial hints to the then run­ning exhi­bition “Die Tech­nische Hochschule im Na­tion­al­sozi­alis­mus”. – An excur­sion to the collec­tion of the Blue Rider in Lehnbachhaus was a cul­tural round-up.

Text: International Doctorate Program "Exploring Quantum Matter“