Complex analysis: techniques, applications and computations
CAT
2 September 2019 to 19 December 2019
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Programme theme
Would you like to know more about the CAT programme's eye-catching lead image (above)? Click here for a full mathematical explanation.
Complex analysis is unusual in that it pervades so many apparently disparate areas of mathematics, including analysis, algebra, geometry, algebraic geometry, differential geometry, numerical analysis, spectral theory, integrable systems and the theory of partial differential equations. In recent years, significant advances have been made in some fundamental aspects of the subject, among them the so-called unified transform method of Fokas with its relation to the spectral theory and integrable systems, the development and refinement of numerical methods for Riemann-Hilbert problems with connections to orthogonal polynomials, random matrices and special function theory, and conformal mapping with the discovery of a new constructive framework for deriving mappings for domains of arbitrary connectivity. Recent years have also witnessed a surge of activity in related free-boundary problems, largely driven by applications in mathematical and statistical physics, biology and medicine: examples include Laplacian growth, diffusion-limited aggregation, stochastic Loewner evolution, cancerous tumour modelling. Complex variables in numerical analysis is also a topic of burgeoning interest and activity. Complex-domain methods play an important role in the studies of finite-time singularity formation in various PDE problems. These investigations represent an area of increasing overlap between scientific computing and PDE analysis. Many of the newly developed tools of complex analysis also pose computational challenges which need to be addressed before these approaches can be used in real-world applications.
This programme is aimed at enhancing these new basic techniques, while assessing their scope and usefulness, and at bringing together key researchers working at the frontiers of these new developments to help steer future endeavours. It takes an integrated view of complex variable theory, computations and applications, and should be accessible to a wide range of attendees from a diverse spectrum of backgrounds. Its goal is to bring together researchers from the mathematics, physics and engineering communities, whose research shares a common theme of using complex analysis to attack real-world problems. In addition to exploring new applications of complex variable theory, the programme will focus on drawing out the unexpected connections between different branches of complex analysis that have been emerging. A key objective of the programme is to engage stakeholders from diverse application areas to learn about, discuss and develop these new methods and applications of complex analysis.
The programme's activities will be built around three main interaction vehicles: (1) workshops; (2) masterclasses; (3) ongoing themes and collaborations, linked to various events during each week of the programme. The three workshops are "The complex analysis toolbox: new techniques and perspectives", "Complex analysis in mathematical physics and applications", and "Computational complex analysis."
Click here to download the programme's final scientific report
CAT programme: interview with organisers Andre Weideman, Linda Cummings and Stefan Llewellyn Smith
Preprints
Workshops
The complex analysis toolbox: new techniques and perspectives
9 September 2019 to 13 September 2019
Complex analysis in mathematical physics and applications
28 October 2019 to 1 November 2019
Computational complex analysis
9 December 2019 to 13 December 2019
Complex analysis: techniques, applications and computations - perspectives in 2023
24 July 2023 to 28 July 2023
Seminars
| Tuesday 17th September 2019 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Andre Weideman Stellenbosch University |
Room 2 | 
|
| Thursday 19th September 2019 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Marcus Webb University of Manchester |
Room 2 |
|
| Tuesday 24th September 2019 | |||
|---|---|---|---|
| 11:00 to 12:00 |
Elias Wegert Technische Universität Bergakademie Freiberg |
Room 2 |
|
| 14:00 to 15:00 |
Elias Wegert Technische Universität Bergakademie Freiberg |
Room 2 |
|
| Thursday 26th September 2019 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Lesley Ward University of South Australia |
Room 1 |
|
| Tuesday 1st October 2019 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Pavel Lushnikov University of New Mexico; Landau Institute for Theoretical Physics |
Room 2 |
|
| Thursday 3rd October 2019 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Loredana Lanzani Syracuse University |
Room 2 | |
| Tuesday 8th October 2019 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Helena Stage University of Manchester |
Room 2 |
|
| Thursday 10th October 2019 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Irina Markina Universitetet i Bergen |
Room 2 |
|
| Thursday 17th October 2019 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Matthew Turner University of Surrey |
Room 2 |
|
| Thursday 24th October 2019 | |||
|---|---|---|---|
| 10:30 to 12:00 |
Saleh Tanveer Ohio State University |
Room 2 | |
| 14:00 to 15:30 |
Alexander Its Indiana University-Purdue University Indianapolis |
Room 2 |
|
| 16:00 to 17:00 |
Irina Mitrea Temple University |
Room 2 | |
| Friday 25th October 2019 | |||
|---|---|---|---|
| 10:30 to 12:00 |
Saleh Tanveer Ohio State University |
Room 2 |
|
| 14:00 to 15:30 |
Alexander Its Indiana University-Purdue University Indianapolis |
Room 2 |
|
| Thursday 7th November 2019 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Nick Moore Florida State University |
Room 2 |
|
| Tuesday 12th November 2019 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Robert Corless University of Western Ontario |
Room 2 |
|
| Thursday 14th November 2019 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Mark Ablowitz University of Colorado; University of Colorado Boulder |
Room 1 |
|
| Friday 15th November 2019 | |||
|---|---|---|---|
| 11:00 to 12:00 |
Thanasis Fokas University of Cambridge |
Room 2 |
|
| 14:00 to 15:00 |
Thanasis Fokas University of Cambridge |
Room 2 |
|
| Tuesday 19th November 2019 | |||
|---|---|---|---|
| 04:00 to 05:00 |
Jonathan Chapman University of Oxford |
Room 2 |
|
| Thursday 21st November 2019 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Peter Clarkson University of Kent |
Room 2 |
|
| Tuesday 26th November 2019 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Scott McCue Queensland University of Technology |
Room 2 |
|
| Wednesday 27th November 2019 | |||
|---|---|---|---|
| 11:00 to 12:00 |
Yuri Antipov Louisiana State University |
Room 2 |
|
| Tuesday 3rd December 2019 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Sonia Mogilevskaya University of Minnesota |
Room 2 |
|
| Thursday 5th December 2019 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Mark Blyth University of East Anglia |
Room 2 |
|
| Tuesday 17th December 2019 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Giovani Vasconcelos Universidade Federal do Paraná |
Room 2 | |
Organisers
- Darren Crowdy Imperial College London
- Linda Cummings New Jersey Institute of Technology
- Stefan Llewellyn Smith UC San Diego
- Bartosz Protas McMaster University
- Andre Weideman Stellenbosch University
Speakers
- Mark Ablowitz University of Colorado; University of Colorado Boulder
- Yuri Antipov Louisiana State University
- Mark Blyth University of East Anglia
- Jonathan Chapman University of Oxford
- Peter Clarkson University of Kent
- Robert Corless University of Western Ontario
- Thanasis Fokas University of Cambridge
- Alexander Its Indiana University-Purdue University Indianapolis
- Loredana Lanzani Syracuse University
- Pavel Lushnikov University of New Mexico; Landau Institute for Theoretical Physics
- Irina Markina Universitetet i Bergen
- Scott McCue Queensland University of Technology
- Irina Mitrea Temple University
- Sonia Mogilevskaya University of Minnesota
- Nick Moore Florida State University
- Helena Stage University of Manchester
- Saleh Tanveer Ohio State University
- Matthew Turner University of Exeter
- Giovani Vasconcelos Universidade Federal do Paraná
- Lesley Ward University of South Australia
- Marcus Webb University of Manchester
- Elias Wegert Technische Universität Bergakademie Freiberg
- Andre Weideman Stellenbosch University
Participants
- Mark Ablowitz University of Colorado; University of Colorado Boulder
- Mungo Aitken University of Cambridge
- Yuri Antipov Louisiana State University
- Peter Baddoo Imperial College London
- Martine Ben Amar CNRS - Ecole Normale Superieure Paris; Université Pierre et Marie Curie Paris
- Mark Blyth University of East Anglia
- Folkmar Bornemann Technische Universität München
- Bruno Carneiro da Cunha Universidade Federal de Pernambuco
- John Chapman Keele University
- Jonathan Chapman University of Oxford
- Peter Clarkson University of Kent
- Matthew Colbrook University of Cambridge
- Robert Corless University of Western Ontario
- Darren Crowdy Imperial College London
- Linda Cummings New Jersey Institute of Technology
- Bernard Deconinck University of Washington
- Tom DeLillo Wichita State University
- Marco Fasondini University of Kent
- Thanasis Fokas University of Cambridge
- Christopher Green Macquarie University
- Christopher Howls University of Southampton
- Daan Huybrechs KU Leuven
- Alexander Its Indiana University-Purdue University Indianapolis
- Ted Johnson University College London
- Thomas Kecker University of Portsmouth
- John King University of Nottingham
- Anastasia Kisil University of Manchester
- Vikas Krishnamurthy University of Vienna
- Loredana Lanzani Syracuse University
- Bill Lionheart University of Manchester
- Stefan Llewellyn Smith UC San Diego
- Elena Luca University of California, San Diego
- Pavel Lushnikov University of New Mexico; Landau Institute for Theoretical Physics
- Georg Maierhofer University of Cambridge
- Irina Markina Universitetet i Bergen
- Scott McCue Queensland University of Technology
- Robb McDonald University College London
- Irina Mitrea Temple University
- Sonia Mogilevskaya University of Minnesota
- Nick Moore Florida State University
- Shari Moskow Drexel University
- Mohamed Nasser Qatar University
- Sheehan Olver Imperial College London
- Beatrice Pelloni Heriot-Watt University
- Bartosz Protas McMaster University
- Mihai Putinar University of California, Santa Barbara; Newcastle University
- Takashi Sakajo Kyoto University
- Koya Sakakibara Kyoto University; RIKEN
- Michael Siegel New Jersey Institute of Technology
- Dave Smith National University of Singapore
- Euan Spence University of Bath
- Saleh Tanveer Ohio State University
- Nick Trefethen University of Oxford
- Thomas Trogdon University of Washington
- Matthew Turner University of Surrey
- Maria Christina van der Weele University of Cambridge
- Giovani Vasconcelos Universidade Federal do Paraná
- Lesley Ward University of South Australia
- Elias Wegert Technische Universität Bergakademie Freiberg
- Andre Weideman Stellenbosch University
- Anna Zemlyanova Kansas State University
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