February 6, Graduate Center, room 4102: Joint meeting of NY Applied Algebra Colloquium, Model Theory, Algebra and Cryptography, and New York Group Theory seminars
February 27, Graduate Center: Jean-Francois Biasse (University of Waterloo), On quantum-safe cryptosystems based on (ideal) lattice assumptions
Abstract: In this talk, I will present some cryptosystems based on the hardness of lattice problems. These schemes are the most popular proposals for quantum-safe cryptography. We will focus specifically on the case of ideal lattices, and present recent results on the resolution of the so-called "Principal Ideal Problem" and their impact on the security of quantum resistant schemes based on ideal lattices.
March 13, Graduate Center: Albert Garreta-Fontelles (Stevens Institute of Technology), Undecidability of systems of equations in a large class of nilpotent groups
Abstract: We will provide a criterion for systems of quadratic equations to be undecidable in nilpotent groups, and then we will give some examples of groups satisfying this criterion. These include free nilpotent groups.
This is joint work with Alexei Miasnikov.
March 27, Graduate Center: Matvei Kotov (Stevens Institute of Technology), Analysis of a polycyclic-group-based commutator key establishment protocol
April 17, Graduate Center: David Garber (Holon Institute of Technology), On Left regular bands and real conic-line arrangements
Abstract: An arrangement of curves in the real plane divides it into a collection of faces. In the case of line arrangements, there exists an associative product which gives this collection a structure of a left regular band. A natural question is whether the same is possible for other arrangements. In this talk, we try to answer this question for the simplest generalization of line arrangements, that is, conic--line arrangements. Investigating the different algebraic structures induced by the face poset of a conic--line arrangement, we present two possible generalizations for the product and its associated structures: an alternative left regular band and an associative aperiodic semigroup. We will give some applications for these generalizations. We also study the structure of sub left regular bands induced by these arrangements. Moreover, we present some chamber counting results for conic--line arrangements.
Based on a joint work with Michael Friedman.
April 24, Graduate Center: Conference on "Infinite Group Theory: From the Past to the Future"
May 15, Graduate Center: Ramon Flores (Universidad Autónoma de Madrid), Preservation of nilpotence for groups and spaces
Abstract: In this talk we will study the effect of idempotent functors over classifying spaces of nilpotent groups (in particular finite-p-groups) and also over nilpotent Postnikov stages. In particular, we prove that augmented idempotent functors preserve nilpotence in this context. This result generalizes to the homotopy category recent work of Blomgren et al. in the category of groups, and offers an interesting counterpart to the co-augmented case, in which the question of the preservation of nilpotence is a quite famous conjecture. The methods include Bousfield Key-Lemma and a modification of the classical Bousfield-Kan tower.
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