Non-commutative geometry is an increasingly-studied field by researchers and graduate students in mathematics and mathematical physics to shed new light on the traditional commutative case. Berenstein (U. of Oregon) and Retakh (Rutgers U.) compile selected papers from talks presented at a special session of the Annual Meeting of the American Mathematical Society held in January 2012 in Boston. Presenters discuss current research on various aspects of noncommutative birational geometry and related topics, focusing primarily on the structure and representations of quantum groups and algebras, braided algebras, rational series in free groups, Poisson brackets on free algebras, and related problems in combinatories. Includes a list of participants, abstracts, proofs, diagrams, and references. Annotation ©2013 Book News, Inc., Portland, OR (booknews.com)
Table of Contents:
The number of right ideals of given codimension over a finite field by R.
Bacher and C. Reutenauer
Cocycle twists and extensions of braided doubles by Y. Bazlov and A.
Berenstein
Quantum Chevalley groups by A. Berenstein and J. Greenstein
The reciprocal of $\Sigma_{n\geq 0}a^nb^n$ for non-commuting $a$ and $b_1$,
Catalan numbers and non-commutative quadratic equations by A. Berenstein, V.
Retakh, C. Reutenauer, and D. Zeilberger
Semi-invariants for gentle algebras by A. Carroll and J. Weyman
Monodromy of the trigonometric Casimir connection for $\mathfrak{sl}_2$ by S.
Gautam and V. T. Laredo
Rational series in the free group and the Connes operator by A. Lauve and C.
Reutenauer
On natural maps from strata of quiver Grassmannians to ordinary Grassmannians
by K. Lee and L. Li Properties of a minimal non-Koszul $A(\Gamma)$ by D.
Nacin
Double Poisson brackets on free associative algebras by A. Odesskii, V.
Rubtsov, and V. Sokolov
Generalizing the notion of rank to noncommutative quadratic forms by M.
Vancliff and P. P. Veerapen
Arkady Berenstein, University of Oregon, Eugene, OR, USA.
Vladimir Retakh, Rutgers University, Piscataway, NJ, USA.
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