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\textsc{Algebra}
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\textsc{Colloquium}
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\textit{SAGBI bases}
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Dr. Zinovy Reichstein\par
University of British Columbia
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\textbf{Abstract:} One of the most important concepts in computational
algebra is that of a Groebner basis for an ideal in a polynomial ring
Pn = k[x1, . . . , xn]. (Here k is a field.) There are fast algorithms for
finding Groebner bases and for computing with them. These algorithms
have numerous application; in particular, they are at the core of many
computer algebra systems.
A SAGBI basis is an analogous notion for a subring R of Pn or of
the Laurent polynomial ring Ln = k[x�1
1 , . . . , x�1
n ]. In particular, one
can perform computations in R quickly and efficiently, with a given
SAGBI basis. The problem is that, unlike Groebner bases, SAGBI
bases do not always exist. Finding necessary and sufficient conditions
for the existence of a SAGBI basis, is an important open question in
computational algebra.
In this talk I will explain what SAGBI bases are, how they are used
in carrying out algebraic computations and under what circumstances
they are known to exist.
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Thursday, November 8, 2007, 4:00 pm\par
Mathematics and Science Center: W201
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Refreshments will be served at 3:30pm in the Department Lounge
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\textsc{Mathematics and Computer Science}\par
\textsc{Emory University}
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