Alissa Crans (Loyola Marymount University, USA)
Knots and links with finite n-quandles

Abstract: A quandle is a set equipped with two binary operations satisfying axioms that capture the essential properties of the operations of conjugation in a group and algebraically encode the three Reidemeister moves from classical knot theory.  Thus, quandles are a fruitful source of applications to knots and knotted surfaces; in particular they provide a complete invariant of knots. An n-quandle is a quandle that, roughly speaking, satisfies the additional axiom that applying the quandle operation n times with the same element is trivial. We will consider the collection of knots and links having finite n-quandles, describe many of these quandles, and identify their automorphism, inner automorphism, and transvection groups.

Vladimir Dotsenko (Trinity College Dublin, Ireland and CINVESTAV, Mexico)
Pre-Lie algebras and F-manifolds

I will talk about an algebraic structure that underpins the notion of an F-manifold introduced by Hertling and Manin a bit less than 20 years ago. The operad encoding this algebraic structure is outside of the scope of conventionally used methods of the operad theory; for that reason it was not really studied. I shall explain how this operad is related to the celebrated operad of pre-Lie algebras, also known as the rooted trees operad, the operad of right-symmetric algebras, the operad of Koszul-Vinberg algebras, etc. The main slogan is that the algebras of F-manifolds are the same to pre-Lie algebras as Poisson algebras to associative algebras.

Michael Duff (Imperial College London and University of Oxford, UK)
A magic pyramid of supergravities

Abstract: By formulating N = 1, 2, 4, 8, Yang-Mills in D = 3 with a single Lagrangian and single set of transformation rules, but with fields valued respectively in R, C, H, O, it was shown that tensoring left and right multiplets yields a Freudenthal magic square of D = 3 supergravities. When tied in with the more familiar R, C, H, O description of super Yang-Mills in D = 3, 4, 6, 10 this results in a magic pyramid of supergravities: the known 4x4 magic square at the base in D=3, a 3x3 square in D=4, a 2x2 square in D=6 and TypeII supergravity at the apex in D=10.

Jaromy Kuhl (University of West Florida, USA)
Completing partial latin squares

Abstract: A partial latin square (PLS) can be completed if there is a latin square of the same order containing it. In this talk we will discuss sufficient conditions under which completions of PLSs exist. One such condition is the following: let r, c, s be elements of {1,2,...,n} and P be a partial latin square of order n in which each nonempty cell lies in row r, column c, or contains symbol s. Except for a few small counterexamples, we show that if row r, column c, and symbol s can be completed in P, then a completion of P exists. We will then end the talk by briefly discussing a few notable open problems.

Andrew Linshaw (University of Denver, USA)
Introduction to vertex algebras and a classification problem

Vertex algebras are a class of non-commutative, non-associative algebras that arose out of conformal field theory in the 1980s, and were axiomatized by Borcherds in his proof of the Moonshine Conjecture. They have applications in many areas of mathematics including representation theory, combinatorics, finite group theory, number theory, and algebraic geometry. I will give an introduction to the subject and will discuss some recent progress on a certain classification problem.

Susanne Pumplün (University of Nottingham, UK)
Nonassociative algebras obtained from skew polynomial rings and their applications

Abstract: Starting from a skew polynomial ring, we define a class of unital nonassociative algebras introduced by Petit in 1966, but still basically unknown. These algebras are canonical generalizations of (associative) central simple algebras. Classical results from Amitsur, Albert and Jacobson on central simple algebras can thus be generalized to a nonassociative setting. They can be used for instance in space-time block coding, to build linear skew-cyclic codes, or can be employed in lattice constructions generalizing Construction A. 

Andrei Zavarnitsine (Sobolev Institute of Mathematics, Russia)
On Moufang loops and related groups

Abstract: We will discuss some results, problems, and research directions in the theory of Moufang loops. Among others, the following topics will be mentioned: groups with triality, multiplication formulas, Moufang action, abelian-by-simple loops, triality modules, free Moufang loops, inverse-free identities.