University of Oslo Mathematics PhD: Quantum Groups, Tensor Categories or Quantum Codes

University of Oslo Mathematics PhD: Quantum Groups, Tensor Categories or Quantum Codes

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Which algebraic or categorical structures can establish a precise result about quantum information, fault tolerance or noise? This doctorate is aimed at a Mathematics graduate, or a Physics graduate with substantial mathematical preparation, who wants proof-based research in operator algebras, quantum groups and quantum information. The operator-algebra community and QSTAR network provide an intellectual setting; the thesis must still define its own mathematical contribution. Industry relevance does not establish a useful quantum computer, a practical decoder improvement or a commercial product. UiO Operator Algebra research group SINTEF QSTAR official opening

The UiO vacancy notice for role 310655 gives 15 November 2026 as its deadline but no precise cutoff time. Apply through the role-specific official recruitment system. Current vacancy availability and successful submission through the role-specific system remain unconfirmed; confirm both before relying on the stated deadline. The fellowship lasts three years; a fourth year with 25% other career-promoting work may be considered, depending on qualifications and departmental needs. Start is as soon as possible and no later than 1 April 2027; applicants still completing a Master's have until 31 March 2027 to finish the final examination. The advertised annual gross salary is NOK 550,800–595,000, with a separate 2% pension contribution. Do not budget for a guaranteed fourth year.

The decisive fit question is which of the two alternative theoretical projects would be selected. One concerns tensor categories/quantum groups and topological computation; the other concerns algebraic quantum-code construction and quantum channels as noise models. A short scientific discussion with Nadia S. Larsen or Makoto Yamashita should establish that choice before a candidate promises a specific thesis direction. The university's official vacancies gateway is navigation, not a substitute for the complete detailed role 310655 conditions.

Research Problem and Actual Doctoral Work

Quantum information must remain useful despite noise. This post asks how mathematical structure can help describe fault tolerance and error correction, rather than treating these as only engineering problems. The formal challenge is to connect algebraic or categorical constructions with a precisely defined information-theoretic question. An elegant invariant does not by itself establish a code's rate, distance, decoding cost or device-level noise tolerance. That distinction matters when defining a realistic three-year thesis. UiO official vacancy 310655; Jaklitsch and Yamashita: braided monoidal structure of tube algebra representations Larsen and Vdovina: higher-dimensional digraphs and spectral theory

Advertised alternative	Actual mathematical work	What remains to be selected
Quantum groups and tensor categories	Study their possible application to fault-tolerant computation through topological quantum computation; develop broader connections with quantum information beyond fault tolerance	Specific categories, quantum groups, mathematical statements and the link to computational models
Algebraic codes and quantum channels	Use group theory, representation theory and operator algebras to construct new quantum-code families with improved performance or novel features; study channel families to quantify noise	Code/channel families, performance quantities, comparison criteria and the balance between the two tasks
The advert assigns one of these projects, not both as a compulsory combined thesis. It also expects collaboration with operator-algebra and quantum-information researchers, investigation of tensor-category/quantum-group applications to topological computation, and connections between quantum information and noncommutative geometry through channels. Mathematics, quantum chemistry and theoretical physics are represented in the wider environment. It does not specify an experimental laboratory programme or require building quantum hardware. UiO official vacancy 310655.

Evidence-backed interpretation: the early work is likely to include mastering definitions and existing results, building tractable examples, proving structural statements and checking where an apparent correspondence fails. The recent tube-algebra paper shows why a stronger equivalence matters: recovering a linear category is less informative than recovering tensor product, braiding and twist. The graph paper shows another recurring issue: finite combinatorial data must satisfy compatibility conditions before producing the desired higher-rank object. These are examples of the team's methods, not an announced first-year syllabus. Jaklitsch and Yamashita: braided monoidal structure of tube algebra representations Larsen and Vdovina: higher-dimensional digraphs and spectral theory

Three possible discussion points follow from that evidence. First, identify exactly which assumptions permit a categorical construction and which extension would be new. Second, for codes or channels, agree on a noise/performance quantity before claiming improvement. Third, retain a mathematically valuable fallback theorem or counterexample if the hoped-for quantum application does not follow. These are analyst suggestions, not additional admission conditions or promised deliverables. The vacancy specifies no fixed channel family, hardware access, software allocation or minimum publication count. UiO official vacancy 310655; Farsi et al.: spectral triples for noncommutative solenoids and Wiener lemma

University, Mathematics and Doctoral Training

UiO is both the advertised employer and the degree-awarding university. The host is the Department of Mathematics at Blindern within the Faculty of Mathematics and Natural Sciences (MN), with the Operator Algebra group in Section 6. QSTAR is a collaboration framework; participation by NTNU, OsloMet, SINTEF, Simula, Copenhagen and RISE does not establish a joint degree or employment by every partner. The department describes almost 50 permanent academic staff across mathematics, mechanics and statistics. UiO Department of Mathematics UiO official vacancy 310655.

For institutional context, QS World University Rankings 2027 places UiO at joint 131 overall; its 2026 value was joint 119. This is an overall institutional measure, not a mathematics or quantum-error-correction ranking. More directly relevant evidence is the active operator-algebra community, its regular C*-seminar alternating with QOMBINE, and recent events connecting quantum error correction with operator algebras. These support an active research environment without measuring supervision quality or completion outcomes. QS University of Oslo: 2027 institutional ranking UiO Operator Algebra research group

The MN faculty operates one PhD programme across its subject areas. Its specific educational component is 30–40 credits, including 5 credits in research ethics/philosophy/scientific methodology and 10 credits of advanced assessed academic/research courses in Part A; Part B supplies 15–25 credits. The generic UiO page's 30-credit description should not replace that faculty rule. Approved coursework, research, an English thesis, trial lecture and public defence form the degree path. MN Faculty supplementary doctoral regulations UiO before applying for a PhD

For employees in a faculty PhD fellow position, the rules provide automatic admission from commencement, subsequently formalised through the doctoral agreement. The agreement goes to the department within two months, then to the faculty within three months; the latter deadline excludes July. This is different from applying for an externally funded study place. A 4–10 page project description belongs to that formalisation process; the vacancy's application asks for a cover letter of at most two A4 pages, so do not invent a compulsory 4–10 page initial proposal. MN Faculty supplementary doctoral regulations UiO official vacancy 310655.

There must be at least two actively involved supervisors. A third-semester review takes place 12–15 months after starting and includes discussion of supervision with and without supervisors present; annual candidate/supervisor reporting is also required. The faculty's outcomes emphasise independent research, method assessment, integrity, communication and career planning. The two named contacts do not establish the formal supervision pair or division of responsibility. Confirm the supervisor pair, course availability and meeting frequency; individual completion and placement outcomes are not established by the cited material. MN Faculty supplementary doctoral regulations MN doctoral learning outcomes

Research Contacts, Papers and Working Environment

Nadia S. Larsen is a professor and the operator group's named contact, with recent work on higher-rank graphs, C*-algebras and noncommutative geometry. Makoto Yamashita is an associate professor whose official interests include operator algebras, quantum groups and noncommutative geometry; his course history includes representation theory, operator algebras, topology and quantum computing. Both are the vacancy's scientific contacts. Their names do not determine which is the formal main supervisor or how responsibility is divided. Nadia S. Larsen official profile Makoto Yamashita official profile

Three recent relevant mathematical papers

Jaklitsch and Yamashita, tube-algebra representations. The cited version is the November 2025 preprint; UiO's bibliography records a 2026 journal article. It constructs tensor product, braiding and twist directly for representations of a tube algebra. The main comparison theorem recovers the braided Drinfeld centre of the ind-category, with a ribbon equivalence on dualisable objects. This is closely aligned with the first advertised branch and demonstrates how graphical calculus is used to prove structural compatibility. Jaklitsch and Yamashita: braided monoidal structure of tube algebra representations Makoto Yamashita official profile

The hypotheses include a spherical semisimple multitensor category. The result does not supply a practical error threshold, universal gate set or hardware implementation. The two authors share the published contribution; no reliable individual task allocation was found. The discussion is limited to the preprint's introduction, relevant definitions, construction overview and main theorem; it is not an independent audit of every proof. The doctoral relevance is deep categorical training, with the application bridge still requiring its own argument. Jaklitsch and Yamashita: braided monoidal structure of tube algebra representations

Larsen and Vdovina, 2024, higher-dimensional digraphs. Finite coloured-graph data and cube complexes produce new families of higher-rank graphs and associated Cuntz–Krieger algebras. The paper establishes infinite Ramanujan families for each k≥2 and presents a 25-vertex rank 3 example. The contribution is a tractable construction and spectral framework joining geometric group theory, combinatorics and operator algebras. Larsen and Vdovina: higher-dimensional digraphs and spectral theory

That shows a relevant mathematical toolkit for building structured examples. It is not a quantum-code performance theorem: a graph spectral gap alone does not establish code distance, rate or decoder performance. Any such connection would be further research. Larsen and Vdovina are joint authors; the cited record does not assign individual proof contributions. The 2024 journal publication derives from an earlier preprint, so it should not be presented as a newly published 2026 result. Larsen and Vdovina: higher-dimensional digraphs and spectral theory

Farsi, Landry, Larsen and Packer, 2024, spectral triples. The authors construct finitely summable spectral triples on noncommutative solenoids and obtain quantum compact metric structures and inductive-limit descriptions. A noncommutative Wiener lemma supplies a dense smooth subalgebra stable under holomorphic functional calculus for the stated nilpotent-group setting. This is concrete evidence of noncommutative geometry and functional analysis in the local research orbit. Farsi et al.: spectral triples for noncommutative solenoids and Wiener lemma

Its relationship to the second branch is methodological, not a completed theorem about noisy quantum channels. The assumptions and choice of length functions matter; a question about convergence in Latrémolière's propinquity remains open in the text. The article does not report a channel capacity or error-correction improvement, and the cited record does not establish individual author roles. These boundaries are useful: a successful applicant should distinguish a transferable mathematical method from an application already proved. Farsi et al.: spectral triples for noncommutative solenoids and Wiener lemma

QSTAR's official opening article was published 2 June 2026 and dates the event to 28 May 2026. It describes SINTEF leadership, Nordic collaboration and links with companies/public organisations, alongside seminars and international mobility. The centre homepage frames error correction, algorithms, software, quantum chemistry and optimisation as priorities. This broadens intellectual contacts but does not guarantee an internship, secondment, industrial job, travel allocation or access to every partner's facilities. SINTEF QSTAR official opening QSTAR Centre for Quantum Computing and Applications

Funding, Fees and Oslo Living Costs

The vacancy lists NOK 550,800–595,000 gross/year, which corresponds arithmetically to roughly NOK 45,900–49,583/month gross. This is division by 12, not a payslip: holiday-pay timing, salary placement and tax treatment require payroll confirmation. 2% pension is approximately NOK 11,016–11,900/year at those annual amounts, and income tax is separate. SPK explains conditional pension, disability, dependant and occupational-injury benefits. A mortgage benefit is not an automatic mortgage approval. UiO official vacancy 310655; SPK public employee membership Norwegian Tax Administration: to Norway

UiO explicitly says PhD candidates pay no tuition fee. Do not apply ordinary non-EU taught-degree invoices to this employed doctorate. MN rules also provide programme-course study rights without semester/copy fees, subject to the relevant rules for external courses. The cited materials do not itemize conference, visit, research-computing, relocation or residence-permit costs. The centre's five-year Research Council of Norway grant does not extend this individual's three-year contract. UiO before applying for a PhD MN Faculty supplementary doctoral regulations UiO official vacancy 310655.

UiO's April 2026 Oslo student budget totals NOK 15,250/month: housing 7500, food 3500, transport 700, study costs 1000, leisure 700, communications 400, health 250 and other fixed costs 1200. It is based on Eurostudent 8, not a quoted employee apartment or a guaranteed current personal budget. A salaried PhD must check employee transport/welfare eligibility instead of assuming ordinary student discounts. Neither this figure nor the gross salary establishes net savings. UiO Oslo budget and living costs

A more relevant, but limited, housing route is available through the department for international PhD candidates/researchers arriving from abroad: under 40, for single occupancy, and a three-month to one-year stay, with limited capacity. The page lists NOK 4,464–10,417, with a 20% surcharge, arithmetically about NOK 5,357–12,500. That price line does not explicitly state its billing period; obtain a dated quote confirming the period and included utilities before using it as a monthly budget. Departmental guarantee removes the deposit in this scheme, not in all private rentals. Applications go through the department rather than directly to SiO. Furnished rooms do not include bedding or kitchen utensils; studios are not guaranteed. Couples, older applicants and housing after the first year need another plan. UiO housing for international doctoral candidates and young researchers

Eligibility, Chinese Qualifications and Application

The required qualification is a Mathematics or Physics Master's/equivalent. A completed foreign MSc-level qualification must correspond to at least four years in the Norwegian system; this does not make a standalone four-year Bachelor's sufficient. Physics applicants need substantial mathematics. Relevant experience in operator algebras, representation theory or quantum information theory is required. The normal grades are Bachelor courses C or better, Master's courses B or better, thesis B or better, with individual assessment of equivalence. The faculty allows a justified departmental/supervisor case below the norm; that is not a self-declared exemption. UiO official vacancy 310655; MN Faculty supplementary doctoral regulations

C*-algebras, noncommutative geometry, representation theory/quantum groups, quantum field theory or quantum information are desired areas of sound documented knowledge. Scandinavian-language fluency is also desired, rather than mandatory. Suggested preparation is to demonstrate a proof, an example/counterexample or a thesis argument relevant to one branch, and explain individual contributions. This suggestion should not be converted into a requirement for every listed subject or a previous quantum publication. UiO official vacancy 310655; Jaklitsch and Yamashita: braided monoidal structure of tube algebra representations Larsen and Vdovina: higher-dimensional digraphs and spectral theory

For English, the MN rule lists TOEFL iBT 90 including test-centre/home edition, IELTS Academic or IELTS Online 6.5, PTE Academic 62, or Cambridge CAE/CPE. The page does not specify additional component minima or a validity period; confirm current test versions and certificate requirements. Exemptions cover applicants from EU/EEA/EFTA, a completed university year in Australia/Canada/Ireland/New Zealand/Singapore/UK/US, an IB diploma, or an English-taught Bachelor's/Master's in Nordic countries or the Netherlands. A Chinese English-medium degree alone is not a listed exemption. Approved evidence must be supplied before the appointed candidate can start. MN Faculty supplementary doctoral regulations UiO official vacancy 310655.

The MN external-admission guidance contains country-specific original-document rules: for China, CDGDC or CHESICC verification can substitute for original diplomas sent directly by the institution, with accompanying educational records. Because that page is explicitly for external funding, confirm the exact verification form/timing for this employed appointment with HR/MN. Do not impose its external-funding payment rules on role 310655. The advert itself requires degree/transcript copies, official grading-system explanation and English/Scandinavian documentation. The advert does not state a blanket exclusion based on Chinese nationality. MN external admission guidance: original degree documents UiO official vacancy 310655.

China-based applicants should separately coordinate the applicable employee residence route. UDI's skilled-worker guidance requires a concrete qualifying offer, education and normal pay/conditions; employer confirmation is required for relevant applications from abroad. Recruitment, academic qualification and residence permission are distinct decisions. This is not an automatic permit or permanent-residence promise, and the ordinary student work-hour rule should not be transferred to this salaried position. UDI skilled worker guidance: Chinese citizen

The initial application includes a cover letter of at most two A4 pages on motivation/scientific work/research interests, CV, original-degree/transcript copies, English documentation, selected publication/work list and 2–3 referee contacts with relationship, email and phone. Recommendation letters are not submitted now and may be requested later. Use Vitnemålsportalen where results are available; otherwise upload records. All documents must be English or Scandinavian. The strongest candidates are interviewed. Only one UiO PhD Research Fellowship period can be held; the public applicant list normally includes names, and a justified exemption request may be refused. UiO also has employee research-results transfer agreements. UiO official vacancy 310655.

Career Context

The strongest direct preparation is for academic mathematical research and specialised quantum-theory work. Rigorous proof, operator methods, structured problem solving and communication are transferable; moving into industrial algorithms/software may require additional programming and applied modelling beyond the advertised mathematics. The July 2025 European Commission quantum strategy prioritises skills and mobility while acknowledging fragmentation and difficulty turning innovation into markets. It supports field relevance, not a Norwegian hiring forecast or this group's placement rate. European Commission Quantum Europe Strategy MN doctoral learning outcomes

Next Actions and Questions to Verify

Before applying: check degree/exam timing, C/B/B equivalence, relevant research experience and English evidence; confirm the Chinese-document route and choose a preferred scientific branch. Submit the exact package by 15 November. Scientific contacts are Nadia S. Larsen, nadiasl@math.uio.no, and Makoto Yamashita, makotoy@math.uio.no; recruitment contact is Ole Rustad, ole.rustad@mn.uio.no, +4741385202. UiO official vacancy 310655.

At interview: ask which first-year theorem problems/code or channel families are planned; what counts as a meaningful outcome if the application bridge fails; who supervises and meets regularly; which specialised courses and seminars are available; and what QSTAR visits/computing support is budgeted. Clarify whether the fourth year is available and its duties rather than assuming it. UiO official vacancy 310655; MN Faculty supplementary doctoral regulations QSTAR Centre for Quantum Computing and Applications

Before accepting: obtain the three-year contract, exact salary placement, project expense responsibilities, formal doctoral/supervision agreement timeline and any fourth-year commitment in writing. Confirm residence approval and a housing offer/longer-term alternative, with sufficient initial cash for moving and private deposits where applicable. The important unresolved issue is the match between a concrete mathematical thesis and the candidate's preparation, not a generic claim that quantum computing is growing. UiO housing for international doctoral candidates and young researchers UDI skilled worker guidance: Chinese citizen MN Faculty supplementary doctoral regulations

Evidence and Sources

The recruitment record is dated 24 October 2026. A 25 October access attempt reached the login page, but it does not establish current vacancy availability or successful post-login submission; the stated 15 November deadline has no precise cutoff time. The cited version of the tube-algebra paper is the November 2025 preprint, while UiO's bibliography lists a 2026 journal article. The three paper discussions retain their stated scope: selected sections and results, not complete proof audits.

University, mathematics and training

• UiO official vacancies gateway
• UiO Department of Mathematics
• UiO Operator Algebra research group
• UiO before applying for a PhD
• MN Faculty supplementary doctoral regulations
• MN doctoral learning outcomes
• MN external admission guidance: original degree documents
• QS University of Oslo: 2027 institutional ranking

Research contacts, papers and QSTAR

• Nadia S. Larsen official profile
• Makoto Yamashita official profile
• Jaklitsch and Yamashita: braided monoidal structure of tube algebra representations
• Larsen and Vdovina: higher-dimensional digraphs and spectral theory
• Farsi et al.: spectral triples for noncommutative solenoids and Wiener lemma
• QSTAR Centre for Quantum Computing and Applications
• SINTEF QSTAR official opening

Funding, cost and career context

• UiO Oslo budget and living costs
• UiO housing for international doctoral candidates and young researchers
• SPK public employee membership
• Norwegian Tax Administration: to Norway
• UDI skilled worker guidance: Chinese citizen
• European Commission Quantum Europe Strategy