# Mathematical Sciences Research Institute

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# Seminar

Commutative Algebra and Algebraic Geometry (Eisenbud Seminar) April 30, 2013 (03:45PM PDT - 06:00PM PDT)
Location: UC Berkeley
Speaker(s) Persi Diaconis (Stanford University), David Eisenbud (MSRI - Mathematical Sciences Research Institute)
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Commutative Algebra and Algebraic Geometry Seminar

Tuesdays, 3:45-6:00

939 Evans Hall

Organized by David Eisenbud

More information at http://hosted.msri.org/alg/ 3:45 PM Quantitative Cocycles Speaker: Persi Diaconis Abstract: Choosing sections for natural maps is a basic mathematical activity. In joint work with Soundarajan and Shao we study the problem of choosing "nice" sections. Here is a typical theorem: Let $G$ be a finite group, $H$ a normal subgroup. Let $X$ be coset representatives for $H$ in $G$. suppose the proportion of $x,y$ in $X$ with $xy \in X$ is more than $1-1/60$. Then the extension splits. There are many variations, many open problems and applications to basic arithmetic and computer science. 5:00 PM Clifford Algebras and the Ranks of Modules in Free Resolutions Speaker: David Eisenbud Abstract: A conjecture of Horrocks, and independently of Buchsbaum and myself, asserts that the sum of the ranks of the modules in the free resolution of a module annihilated by a regular sequence of length c is at least $2^{c}$. I'll describe a related new conjecture by Irena Peeva and myself and show how we proved a special case, in our work on complete intersections, using results on Clfford algebras and enveloping algebras.