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Faculty of Science Mathematics & Statistics
Faculty of Science

Mathematics & Statistics

Model Theory Seminar - "Effective Pila--Wilkie bounds for Pfaffian surfaces", Margaret Thomas

From October 17, 2017 13:30 until October 17, 2017 14:30
At HH/410


Margaret Thomas
McMaster University
Department of Mathematics and Statistics

Title:   Effective Pila--Wilkie bounds for Pfaffian surfaces

Abstract:  The counting theorem of Pila and Wilkie has become celebrated as one of the most important developments in o-minimality in recent years, with far-reaching consequences in diophantine geometry. It provides a `subpolynomial' bound on the number of rational points of bounded `height' lying on the `transcendental parts' of sets definable in o-minimal expansions of the real field. The proof of this theorem does not, however, provide an effective bound, and the pursuit of examples for which one can obtain this remains very active, with a view to number-theoretic applications. I will discuss some recent progress made (in joint work with Gareth O. Jones) on obtaining this in the particular setting of surfaces implicitly defined from `Pfaffian' functions, in both restricted and unrestricted settings.

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McMaster University - Faculty of Science

Mailing Address

Department of Mathematics & Statistics
McMaster University

Hamilton Hall, Room 218
1280 Main Street West
Hamilton, Ontario, Canada
L8S 4K1

Contact Information

Office Hours:
8:30 a.m. - 12:00 p.m.
1:00 p.m. - 4:30 p.m.
Telephone Inquiries:
+1 (905) 525-9140 ext.27034
Undergrad Email Inquiries:
undergrad@math.mcmaster.ca

McMaster University - Faculty of Science

Mailing Address

Department of Mathematics & Statistics
McMaster University

Hamilton Hall, Room 218
1280 Main Street West
Hamilton, Ontario, Canada
L8S 4K1

Contact Information

Office Hours:
8:30 a.m. - 12:00 p.m.
1:00 p.m. - 4:30 p.m.
Telephone Inquiries:
+1 (905) 525-9140 ext.27034
Undergrad Email Inquiries:
undergrad@math.mcmaster.ca