## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

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Please note: The University of Waterloo is closed for all events until further notice.

Monday, March 3, 2014 — 4:00 PM EST

Let F be a field, G a group and V a finite dimensional representation of G defined over F. The ring of polynomial functions on V, denoted k[V] inherits a natural G-action. The subring of polynomials fixed pointwise by this action is the ring of invariants denoted F[V]G. Invariant Theory is the study of these rings and their generators and relations.

Classical Invariant Theory flourished in the late nineteenth century and was the dominant field of study in algebra at that time. Giants such as David Hilbert, Emmy Noether, Arthur Cayley and J.J. Sylvester and others were particularly interested in the case G = SL(2, C) and F = C.

In the last thirty years, there has been a great deal of work on modular invariant theory, i.e., the case where G is a finite group, F is some field of characteristic p > 0 and p divides |G|. Of particular interest and importance here is the case where G = Z/p.

I will describe how a theorem published in 1861 provides an unexpected bridge which connects the classical and modern problems. I will show how this connection can be used to prove that these two problems are in fact equivalent.

Refreshments will be served in MC 5046 at 3:30 p.m. Everyone is welcome to attend.

Location

MC - Mathematics & Computer Building

5158

200 University Avenue West

Waterloo, ON N2L 3G1

Canada

200 University Avenue West

Waterloo, ON N2L 3G1

Canada

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Indigenous Initiatives Office.