Algebra and Cryptography Seminar, Spring 2019

Organizers: Delaram Kahrobaei, Vladimir Shpilrain, Robert Gilman, and Alexei Myasnikov

Fridays:

2:30-3:30 pm
Room 3307, CUNY Graduate Center
365 Fifth Avenue at 34th Street


February 22:


March 15 : Robert Laugwitz (Rutgers University), Hopfological algebra and categorifications of cyclotomic rings
Abstract: Hopfological algebra is an approach to categorification of small quantum groups suggested by Khovanov in 2005. Here, stable categories of modules over finite-dimensional Hopf algebras are used and replace the usual homological algebra of differentially graded algebras. Based on this approach, sl2-quantum groups were categorified for prime roots of unity by Khovanov-Qi and Elias-Qi through constructing p-differentials on nil-Hecke algebras.
Most of this talk will be an introduction to the algebraic structures involved in Hopfological algebra. Later parts will report on joint work with You Qi (Caltech) on the categorification of general rings of cyclotomic integers.


May 3: Niko Inassaridze (Mathematical Institute, Tbilisi), On one-way homomorphisms and some new cryptographic protocols
 


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