Set Theory and Logic by Tom Forster. Prime Numbers by Ben Green. Additive Number Theory by Ben Green. Introduction to Probability by Mike Tehranchi.

Applied Multivariate Analysis by Pat Altham. Quantum Field Theory by David Tong.

## Andrzej Schinzel, professor

Statistical Field Theory by Ron Horgan. Black Holes by Paul Townsend. Computer-aided Geometric Design by Malcolm Sabin. Approximation Theory by Alexei Shadrin. George Weatherill has a collection of lecture notes, some typed by himself. Mathematicians of Pembroke have a list of links to lecture notes.

Principles of Dynamics by Colm Whelan. Stochastic Networks by Alan Bain. Methods of Mathematical Physics by Mark Trodden. Arnold of the IMA, Minneapolis. Heath-Brown of Oxford. Abstract: In the s Magnus conjectured that two one-relator groups and are isomorphic if and only if they "obviously" are. Although counter-examples were found in the s, there exist important sub-classes of one-relator groups where the conjecture does hold.

Indeed, the conjecture holds for almost all one-relator groups! I will unpack the word "obviously" in the previous paragraph, and I will explain the known counter-examples to the conjecture. All these counter-examples are non-hyperbolic. I will end the talk by giving a hyperbolic counter-example, as well as some positive results.

They play the same role that the group algebras of the symmetric groups do for the representation theory of the general linear groups in the classical Schur-Weyl duality. The main point is to show that it categorifies a certain Fock space for a coideal subalgebra inside a quantum group. As an application we obtain a connection between decomposition numbers in Brauer centralizer algebras and Kazdhan-Lusztig polynomials of type D. If time allows we will also mention the relevance of this construction to the representation theory of Lie superalgebras.

Abstract: R-matrices arising from quantum affine algebras may be used to define the transfer matrix of a closed quantum spin chain.

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The 'prime directive' of the field of quantum integrable systems is to find the eigenvectors and eigenvalues of this transfer matrix. A short exact sequence for infinite-dimensional modules then leads to a functional relation for simultaneous eigenvalues of the transfer matrix and Q-operator.

These functional relations may then be solved exactly. In this talk I will summarise this approach and then extend it to 'open' quantum systems. The transfer matrix of an open system involves both the quantum affine algebra R-matrix and a solution of Cherednik's reflection equation associated with a coideal subalgebra.

I will give a new construction of the Q-operator for such open systems and derive functional relations. This is joint work with Bart Vlaar. Abstract: We show that behind any Lie-Rinehart algebra, and in particular behind any singular foliation or behind any affine variety, there is a canonical homotopy class of Lie-infinity algebroid also called "dg-manifolds" or "Q-manifolds".

## Units in Abelian Group Algebras Over Direct Products of Indecomposable Rings

We are able to give an explicit construction. Also, we shall try to explain the algebraic and geometrical meanings of this higher structure. Joint works with Sylvain Lavau and Thomas Strobl. Abstract: Given a Fano variety X, Dubrovin's conjecture relates semisimplicity of the big quantum cohomology ring of X to the existence of a full exceptional collection in the derived category of coherent sheaves on X.

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One of the goals of our joint work with C. Pech, R. Gonzales, and N. Perrin is to establish Dubrovin's conjecture for the varieties in the title. In this talk, I will focus on the derived category side of the conjecture, and try to explain a connection to categorical joins that have recently been introduced by A. Kuznetsov and A. Abstract: From certain triangle functors, called non-negative functors, between the bounded derived categories of abelian categories with enough projective objects, we introduce their stable functors which are certain additive functors between the stable categories of the abelian categories.

The construction generalizes a previous work by Hu and Xi. We show that the stable functors of non-negative functors have nice exactness property and are compatible with composition of functors. This allows us to compare conveniently the homological properties of objects linked by the stable functors. Particularly, we prove that the stable functor of a derived equivalence between two arbitrary rings provides an explicit triangle equivalence between the stable categories of Gorenstein projective modules.

This generalizes a result of Y. This is joint work with Wei Hu. For a prime ideal I in C, we study the largest subring of B in which the right ideal IB becomes a two-sided ideal - the idealiser subring. In this talk we will introduce the idealizer and describe some interesting results about how the noetherianity of these subrings is closely linked to the orbit of I under the G-action. We will also give examples to show how this works in practice. Abstract: In this talk I will articulate and contextualize the following sequence of results. This result is extracted from a larger program -- entirely joint with John Francis, some parts joint with Nick Rozenblyum -- which proves the cobordism hypothesis.

We work in the setting of the coherent-constructible correspondence, a sheaf-theoretic model of toric mirror symmetry. This is joint work with David Treumann and Eric Zaslow. Abstract: The theory of cluster algebras gives a concrete and explicit way to quantize character varieties for a group G and a surface S. In order to do this, one must show that character varieties admit natural cluster structures. It turns out to be enough to carry this out in the case of a disc with marked points.

The key step will be to show that cluster variables can be realized in terms of tensor invariants of G. Abstract: Associative Clifford algebras have long been in use in the algebaic theory of quadratic forms, as well as in geometry and physics. Attempts to formualate the Rost invariant for quadratic forms led to the definition of the alternative Clifford algebra by Musgrave.

### Journal and other Refereed Publications

We describe the structure of the alternative Clifford algebra of a ternary quadratic form, and present some other preliminary results and open problems. This talk is based on join work with Uzi Vishne.

Abstract: Laplace-Runge-Lenz vector represents hidden symmetry of Coulomb problem equivalently, hydrogen atom , which is so 4. I am going to discuss its generalisation for the Dunkl settings in which a Coxeter group is present. The corresponding model is related to Calogero-Moser system, and the arising symmetry algebra is related to the Dunkl angular moment subalgebra of the rational Cherednik algebra.