| EPSRC Reference: |
EP/N025636/1 |
| Title: |
Positivity problems at the boundary between combinatorics and analysis |
| Principal Investigator: |
Sokal, Professor A |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Mathematics |
| Organisation: |
UCL |
| Scheme: |
EPSRC Fellowship |
| Starts: |
01 September 2016 |
Ends: |
31 August 2021 |
Value (£): |
836,383
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| EPSRC Research Topic Classifications: |
| Logic & Combinatorics |
Numerical Analysis |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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| Related Grants: |
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| Panel History: |
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Summary on Grant Application Form |
Combinatorics is the branch of mathematics concerned with counting finite
structures of various types (permutations, graphs, etc.); it has
applications in computer science, statistical physics, molecular biology,
and many other fields. Analysis, by contrast, is the branch of mathematics
concerned with continuous variation (i.e. functions of real or complex
numbers); it has applications in nearly all fields of science and engineering.
The proposed research lies at the interface between combinatorics and
analysis: it involves using combinatorial tools to study analytic problems,
and vice versa. More specifically, the proposed research comprises
three themes, all of which are aimed at exploring novel positivity properties
that arise at the interface between combinatorics and analysis.
The first theme involves studying situations in which inverse powers
of combinatorially important polynomials have Taylor expansions with
positive coefficients. The second theme involves studying situations
in which certain matrices formed from sequences of combinatorially
important polynomials have a property called "total positivity".
The third theme involves studying situations in which certain power
series formed from combinatorially important polynomials (for example,
the counting polynomials of connected graphs) have positive coefficients.
This latter property was discovered empirically by the PI in many
situations, but most of these have not yet been proven, and their deeper
meaning remains to be elucidated.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
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