NZ Mathematics Research Institute - Summer School

'El Rancho', Waikanae, 6 - 11 January 2019

The Unreasonable Effectiveness of Random Matrix Theory : Achievements and Challenges since Hurwitz, Wishart and Wigner

The theory of random matrices lies at the crossroads of many sub-disciplines of mathematics - probability theory, mathematical statistics, representation theory, approximation theory, integrable systems theory - and has profound implications for an ever-widening horizon of diverse applications:

  • Antenna Networks and Wireless Communications
  • Ecological Systems: Biogeographic pattern of species nested-ness, ordered binary presence-absence matrices, distribution of mutation fitness effects across species,
  • Financial Modelling, cross correlations of financial data
  • Quantum Chaos, Semi-classical Approximations, Entanglement of Quantum States, Quantum transport in mesoscopic systems.
  • Data analysis and Statistical Learning
  • Stable signal recovery from incomplete and inaccurate measurements
  • Compressed sensing, best k-term approximation, n-widths
  • Modelling of the Riemann zeta function, L-functions
  • Asymetric Simple Exclusion Process, Interfacial growth processes, Kardar-Parisi-Zhang Class

This is a very dynamic area and is currently undergoing rapid and exciting developments.

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Background

The New Zealand Mathematics Research Institute (NZMRI) has ran an annual summer school since 1994. The summer schools bring around five or six international speakers together to address a particular theme in contemporary mathematics and a list of past themes can be found at NZMRI. Speakers each give four hours of lectures, usually in the mornings, to an audience (around 60 plus) of  upper-level undergraduates, postgraduates, academics and other research workers. The intention and clear focus is to start at the level of a final year honours/4th year undergraduate and progress in an explicit and detailed way to some current research problem in the allotted time.

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Venue and Activities

The schools are held during the second week of January at a beach-side resort with a quintessential New Zealand character.

In 2019 the venue will be the 'El Rancho' camp in Waikanae, on the Kapiti Coast which is located on the western side of the lower North Island. A variety of accommodation options are available at the Camp.

The afternoons are free for recreational and outdoor activities, some of which are organised for visitors and some adventurous options are also possible. Informal sessions/tutorials are held in the evenings which follow-up up on or explore away from the contents of the previous mornings talks. This might be lead or initiated by the organisers/speakers but is really up to the participants.

Funding

Students enrolled in New Zealand higher education institutions will be fully supported for accommodation and meals at the Camp. Provision for internal transportation costs to the Camp are usually made by the home institution.

However the New Zealand Mathematical Society has student travel awards for this purpose, visit http://nzmathsoc.org.nz/?assistance or contact Rua Murray.

After the needs of local students are met then we may be able to cover the Camp expenses for participating academics and research workers etc.

International visitors are most welcome. Please contact the organisers for further information.

(Image by Sunil Chhita 2015: Uniformly random domino tiling of a Double Aztec Diamond with the overlap parameter set of 2.)

Registration

Registration>

Kalman Summer Scholarships

Four or five Kalman Summer Scholarships are available to New Zealand university students attending this NZMRI summer meeting. For further information on the scholarship and application requirements.  Scholarship

Lecturers/Topics:
      • Professor Peter Forrester, University of Melbourne:
         General survey and background, RMT ensembles, Log-gases and potential theory.
      • Professor Iain Johnstone, Stanford University:
         Applications to statistics, Principal Components Analysis, sample covariance matrices - null and non-null, spiked population models.
      • Professor Jon Keating, Bristol University:
         Number theory, Zeta functions and conjectures derived from RMT.
      • Professor Craig Tracy, University of California Davis:
         Fredholm determinants, asymmetric exclusion processes (ASEP, TASEP) and Kardar-Parisi-Zhang growth models.
      • Professor Alice Guionnet, ENS Lyon:
         Universality of random matrices, central limit theorems, large deviations, and asymptotic methods.
Organisers:

The organising committee : Dr Nicholas Witte (Massey University), n.s.witte@massey.ac.nz, and Professor Stephen Marsland (Victoria University of Wellington), stephen.marsland@vuw.ac.nz.

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