**Date & Time:** Tuesday, July 22, 2008, 15:00-16:00.

**Venue:** Ramanujan Hall

**Title:** On the Redundancy of Higher Transvectants

**Speaker:** Jaydeep Chipalkatti, University of Manitoba

**Abstract:** Transvectants were introduced into algebra by the German school of invariant theorists in the nineteenth century. Given binary forms *A*
and *B* of degrees *m,n* respectively,their *r*^{th} transvectant *T _{r}* =

*(A,B)*is a new binary form of degree

_{r}*m+n-2r*. In modern terminology, this construction encodes the multiplicative decomposition of representations for the algebraic group

*SL(2)*.

In this talk, I will explain the basic definitions and the role
of transvectants in invariant theory. Our main theorem classifies all
quadratic syzygies amongst the *T _{r}*. As
a corollary, one can recover the higher transvectants

*T*etc from

_{2}, T_{3}, ...*T*and

_{0}*T*alone. No substantial knowledge of algebraic geometry, or invariant theory will be presupposed.

_{1}All of this is joint work with Abdelmalek Abdesselam from the University of Virginia.