Quantum Matter, Information, Dynamics, and Computation

 

Quantum Matter, Information, Dynamics, and Computation Program

2027-2028

Quantum matter and quantum information increasingly meet on the same mathematical objects: many-body states, spectra, effective Hamiltonians, channels, measurement records, and dynamical phases. In materials, the challenge is to understand how topology, disorder, quasiperiodicity, interactions, and geometry shape observable states. In quantum dynamics, the challenge is to determine how information moves, is measured, is lost, and can be controlled. The 2027-2028 TIAMS program brings these frontiers into one academic year so that methods developed for structure in matter can interact with methods developed for structure in information and dynamics.

 

Fall 2027

Quantum Materials: Topology, Spectra, Disorder, and Emergent Structure

The fall semester program will focus on spectral and topological mechanisms in layered, incommensurate, disordered, and interacting systems. Problems include localization and criticality, effective models for twisted multilayers, states bound to boundaries or defects, and the influence of wave-function geometry on collective behavior. 

Fall 2027 Program

Spring 2028

Quantum Computation, Information, and Dynamics

The spring semester program will turn to monitored circuits, quantum channels, feedback-controlled many-body systems, mixed-state phases, error correction, and the operational meaning of order when measurement records or coherence are incomplete. Across the two semesters, common questions about robustness, approximation, topology, and information provide a natural bridge.

Spring 2028 Program

 

The year-long bridge

TIAMS will organize the year around sustained residence, overlapping visitors, seminars, working groups, and a small number of focused convenings. A graduate research school in the Fall is intended to give junior researchers enough spectral theory, Fourier analysis, effective quantum modeling, Fredholm theory, and index ideas to enter active problems. Spring tutorials will build a shared language for monitored dynamics, quantum channels, entanglement, control, and noise. The aim is to move repeatedly between models, calculations, and rigorous structure until participants can say which mechanisms persist, what assumptions matter, and which questions need new mathematics. Modern computation and visualization can help groups compare regimes and share evidence quickly, while the scientific judgments about approximation, mechanism, and proof remain with the researchers working directly on the models.

 

PROGRAM DETAILS

  • Which notions of topology and spectral structure remain meaningful in disordered, incommensurate, or interacting quantum systems?
  • What distinguishes stable critical phases, localization transitions, and finite-model effects in quasiperiodic and layered materials
  • How do measurement, feedback, and noise reshape dynamical phases and the flow of quantum information?
  • Which forms of mixed-state order are operationally detectable and connected to recoverable information or error correction?
  • Can common mathematical structures clarify when a proposed material or information-processing effect is robust across changes of model and scale?

  • Spectral theory and effective Hamiltonians
  • Topological and quasiperiodic quantum matter
  • Disorder, localization, and criticality
  • Wave-function geometry and collective behavior
  • Monitored quantum dynamics
  • Quantum channels, feedback, and control
  • Mixed-state order, entanglement, and error correction

  • Justin H. Wilson — TIAMS scientific lead; LSU
  • Stephen P. Shipman — TIAMS mathematical/scientific lead for Fall 2027; LSU
  • Michael I. Weinstein — external scientific leader for Fall 2027; Columbia University
  • Allan H. MacDonald (pending) — intended external scientific leader for the year/Fall program; The University of Texas at Austin
  • Piers Coleman (pending) — intended scientific adviser / international-network partner; Rutgers University

The year uses two linked residential semesters. Extended and month-scale visitors should overlap around working groups, while shorter targeted visits bring in expertise for specific calculations. Each semester begins with common-language activity, contains one major focused workshop plus a second smaller school/intensive where scientifically useful, and ends with a synthesis period. Seminars and working groups provide the continuity between convenings.

Preliminary Workshops, Schools, or Focused Meetings

Fall opening tutorials / graduate research school

Mathematical Foundations of Quantum Materials
Dates TBA

Fall focused workshop on spectral, topological, and emergent mechanisms

Dates TBA

Spring opening tutorials on quantum information and monitored dynamics

Dates TBA

Spring focused workshop on measurement, feedback, mixed states, and information

Dates TBA

Year-end synthesis / cross-semester research meeting

Dates TBA

Seminars and Working Groups

Likely working-group clusters include:

  • aperiodic spectra and localization
  • interfaces/defects and embedded states
  • wave-function geometry and collective order
  • monitored dynamics and control transitions
  • mixed-state topology and recoverable information

Groups should use common model systems and maintain short records of assumptions, calculations, numerical evidence, and open questions so ideas can move between semesters.

The program is designed for mathematical and theoretical physicists, condensed-matter theorists, spectral analysts, PDE researchers, topologists working on quantum systems, quantum-information scientists, researchers in quantum computation and control, and computational scientists studying many-body dynamics. Faculty, postdoctoral researchers, and graduate students are all invited. Researchers in neighboring fields—operator algebras, probability, numerical analysis, information theory, materials science, and computer science—should consider participating when their methods address the program's central models or questions. The program is especially well suited to researchers who want enough time to learn another community's language and then test that language on a shared Hamiltonian, channel, phase transition, or information measure.

  • Extended or semester-scale residence for scientific anchors and long-term collaborators.
  • One- to three-month research visits timed to overlap with active working groups.
  • Short targeted visits around a defined calculation, model, or focused meeting.
  • Workshop and graduate-school participation.
  • Ongoing seminar and working-group participation for LSU and visiting researchers.
  • Expression of interest through the TIAMS participation form.

Graduate students and postdocs will be invited into the same working groups as senior visitors. The Fall research school is designed to supply the operator, Fourier, effective-model, Fredholm, and index-theoretic background needed to contribute to active quantum-materials problems; Spring tutorials should play the same role for monitored dynamics, channels, entanglement, control, and noise.

Junior researchers should have repeated opportunities to present partial results and follow one problem through several stages of refinement. They should also be able to move between semesters when a question in topology, robustness, or information naturally crosses the year boundary.

Expected outcomes include rigorous results on spectra or localization, improved effective models, comparisons of topological or mixed-state invariants, controlled dynamical calculations, numerical studies tied to explicit hypotheses, open-problem documents, software or reproducible computational tools, and new collaborations connecting materials, dynamics, and information.

Researchers may express interest in one semester or the full academic year through the TIAMS Program Participation form.

Applicants should identify their research area, the working groups most relevant to them, preferred dates, and whether travel or housing support is requested.