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Faculty of Science Mathematics & Statistics
Faculty of Science

Mathematics & Statistics

Evelyn nelson lecture 2012-2013

Non-archimedean Approximations by Special Points

Let x_1,x_2,... be a sequence of n-tuples of roots of unity and suppose X is the vanishing locus of a polynomial in n variables and rational coefficients. For a prime number p, Tate and Voloch proved that if the p-adic distance between x_k and X tends to 0 then all but finitely many sequence members lie on X. Buium and Scanlon later generalized this result. The distribution of those x_k that lie on X is governed by the classical (and resolved) Manin-Mumford Conjecture. I will explain this conjecture and also the related (and open) Andre-Oort Conjecture towards which there has been much progress in the last years due to work of Klingler, Pila, Ullmo, Yafaev, Zannier and others. I will then present a variant of Tate and Voloch's discreteness result which was motivated by the Andre-Oort Conjecture.

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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