COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Exact results for degree growth of lattice equations and their signature over finite fields

## Exact results for degree growth of lattice equations and their signature over finite fieldsAdd to your list(s) Download to your calendar using vCal - Roberts, J (University of New South Wales)
- Thursday 11 July 2013, 09:30-10:00
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact Mustapha Amrani. Discrete Integrable Systems In the first part of the talk, we study the growth of degrees (algebraic entropy) of certain multi-affine quad-rule lattice equations with corner boundary conditions. We work projectively with a free parameter in the boundary values, so that at each vertex, there are 2 polynomials in this parameter. We show the ambient growth of their degree is known exactly, via the asymptotics of the Delannoy double sequence. Then we give a conjectured growth for the degrees of the greatest common divisor that is cancelled at each vertex. Taken together, these provide us with a constant coefficient linear partial difference equation that determines the growth in the reduced degrees at each vertex. For a whole class of equations, including most of the ABS list, this proves polynomial growth of degree. For other equations where the cancellation at each vertex is not high enough, we prove exponential growth. In the second part of the talk, we study integrable lattice equations and their perturbations over finite fields. We discuss some tests that can distinguish between integrable equations and their non-integrable perturbations, and their limitations. Some integrable candidates found using these tests can then be shown to have vanishing entropy via the results of the first part of the talk. Both parts of the talk are joint work with Dinh Tran (UNSW). This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
- Featured lists
- INI info aggregator
- Isaac Newton Institute Seminar Series
- School of Physical Sciences
- Seminar Room 1, Newton Institute
- bld31
Note that ex-directory lists are not shown. |
## Other listsEPRG Energy and Environment Seminar Series Think Green Team Presentations Tracing Human Ancestry, using DNA How to write a successful grant application Babbage Seminar Series Graduate Development Lecture Series## Other talksTo be confirmed Stakeholder perceptions across scales of governance: areas of controversy and consensus related to the Indonesian peatland fires Cosmological Probes of Light Relics Liberalizing Contracts: Nineteenth Century promises through literature, law and history Simulating wave propagation in elastic systems using the Finite-Difference-Time-Domain method Comparative perspectives on social inequalities in life and death: an interdisciplinary conference The Digital Doctor: Hope, Hype, and Harm at the Dawn of Medicine’s Computer Age Investigating the Functional Anatomy of Motion Processing Pathways in the Human Brain The Anne McLaren Lecture: CRISPR-Cas Gene Editing: Biology, Technology and Ethics Structural basis for human mitochondrial DNA replication, repair and antiviral drug toxicity Amino acid sensing: the elF2a signalling in the control of biological functions Electoral intrigue, ethnic politics and the vibrancy of the Kenyan public sphere |