2:30-3:30 pm

Room 3307, CUNY Graduate Center

365 Fifth Avenue at 34th Street

**September 21:** Giacomo Micheli (University of Oxford and EPFL, Lausanne), *Permutations and codes using a density method *

**Abstract: ** The construction of permutation functions over a finite field is a task
of great interest in applied areas such as cryptography and coding
theory. In this talk I describe a method which combines Chebotarev
density theorem with elementary group theory to produce permutation
rational functions over a finite field. The method is entirely
constructive and as a corollary we get the classification of permutation
polynomials up to degree 4 over any finite field of odd characteristic.
Time permitting, I briefly explain what is a locally recoverable code
(LRC) and describe another application of a similar method which allows
to build optimal LRCs by solving a Galois theoretical problem.

**September 28:** Thomas Koberda (University of Virginia), * Graph theory versus algebra of right-angled Artin groups*

**Abstract: ** Right-angled Artin groups, due to their tractable algorithmic properties, are a fruitful class of groups to study from the point of view of group-based cryptography. I will discuss some of the ways in which the combinatorics of the underlying graph is reflected on the algebraic structure of the right-angled Artin group, and some algebraic phenomena which are in some sense invisible from the point of view of the combinatorics of the graph. Some of this work is joint with R. Flores and D. Kahrobaei.

**October 26:** Alexander Treyer (Omsk State Technical University), * Universal input for knapsack problem for nilpotent groups *

**Abstract: ** Through equivalence between Diophantine problem over integers and knapsack problem (KP) over nilpotent groups, it was proven earlier that KP is undecidable over nilpotent groups. Also, this approach gives us a way to construct a universal input for knapsack type problems over nilpotent groups.

**November 2: ** "The elementary theory of groups and group rings" conference

**November 16: ** Alexander A. Mikhalev (Moscow State University), * Nonassociative algebraic structures in coding and cryptography *

**Abstract: ** We consider applications of nonassociative
algebraic structures to constructing codes and cryptoschemes.

**December 7: ** Manhattan Algebra Day

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