Logic seminar: Neer Bhardwaj
| Dates: | 19 March 2025 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Adults, Alumni, Current University students |
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Title: Effective and approximate Pila-Wilkie type counting with complex-analytic sets
Abstract: The Pila-Wilkie point counting theorem has had striking applications to arithmetic geometry, functional transcendence, and Hodge theory. This statement cannot be made effective in general, but various effective versions of the theorem exist for zero sets of functions satisfying certain forms of differential equations.
In joint work with Binyamini, we establish an effective point-counting statement of Pila-Wilkie type for the zero-set of any computable complex-analytic function over a ball. For our proof, we develop an approximate counting result to cover rational points close to being a solution of a family of complex-analytic functions in a ball. This second theorem is unique among results of Pila-Wilkie type in that it applies uniformly to any family of functions.
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Frank Adams 1
Alan Turing Building
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