09:10 to 10:00 Mohamed Barakat Chevalley’s Theorem on constructible images made constructive Chevalley proved that the image of an algebraic morphism between algebraic varieties is a constructible set. Examples are orbits of algebraic group actions. A constructible set in a topological space is a finite union of locally closed sets and a locally closed set is the difference of two closed subsets. Simple examples show that even if the source and target of the morphism are affine varieties the image may neither be affine nor quasi-affine. In this talk, I will present a Gröbner-basis-based algorithm that computes the constructible image of a morphism of affine spaces, along with some applications. INI 1 10:10 to 11:00 Alexander Hulpke Towards a nonsolvable Quotient Algorithm [This is joint work with Heiko Dietrich from Monash U.] Quotient algorithms have been a principal tool for the computational investigation of finitely presented groups as well as for constructing groups. We describe a method for a nonsolvable quotient algorithm, that extends a known finite quotient with a module. Generalizing ideas of the $p$-quotient algorithm, and building on results of Gaschuetz on the representation module, we construct, for a finite group $H$, an irreducible module $V$ in characteristic $p$, and a given number of generators $e$ a covering group of $H$, such that every $e$-generator extension of $H$ with $V$ must be a quotient thereof. This construction uses a mix of cohomology (building on rewriting systems) and wreath product methods. Evaluating relators of a finitely presented group in such a cover of a known quotient then yields a maximal quotient associated to the cover. I will describe theory and implementation of such an approach and discuss the scope of the method. INI 1 11:00 to 11:30 Morning Coffee 11:30 to 12:20 Bettina Eick Conjugacy problems in GL(n,Z) The talk describes a practical algorithm to solve the conjugacy and the centralizer problems in GL(n,Z) in full generality; that is, given two matrices A and B in GL(n,Q) these algorithms allow to check if A and B are conjugate in GL(n,Z) and, if so, then to determine a conjugating element, and they allow to compute generators for the centralizer of A in GL(n,Z).  The talk also discusses possible extensions of this algorithm to finitely generated abelian or nilpotent subgroups of GL(n,Z). The latter are open problems in computational group theory and they have interesting applications. INI 1 12:20 to 13:45 Lunch at Westminster College 13:45 to 14:35 Ulrich Thiel Minimal models of symplectic quotient singularities Namikawa associated to any conic symplectic singularity a hyperplane arrangement which is deeply intertwined with its geometry. For example, Bellamy proved that for a symplectic quotient singularity the cohomology of the complement of this arrangement encodes the number of minimal models of the singularity. For the symplectic singularity associated to a complex reflection group we were able to prove that the Namikawa arrangement coincides with the degenericity locus of the number of torus fixed points of the corresponding Calogero-Moser deformation. This has a series of remarkable consequences, especially it proves a conjecture by Bonnafé and Rouquier. Using representation theory and sophisticated computer algebraic methods, we could compute this arrangement explicitly for several exceptional complex reflection groups. The arrangements seem to be of a new kind, and many more are out there. This is joint work with Gwyn Bellamy (Glasgow) and Travis Schedler (London), and with Cédric Bonnafé (Montpellier). INI 1 14:45 to 15:35 Dane Flannery Classifying finite linear groups in prime degree We describe the complete, computational solution of an enduring problem in linear group theory. Specifically, we describe the classification of the finite irreducible monomial groups of prime degree (over the complex numbers). An exhaustive and self-contained solution of this problem has been obtained for all such solvable groups, and for all such groups of reasonably small degree (say, at most 23). We note obstacles that prevent a full solution of the problem for non-solvable groups in arbitrary prime degree. This is joint work with Zolt\'an B\'acskai and Eamonn O'Brien. INI 1 15:35 to 16:05 Afternoon Tea 16:05 to 16:35 Eilidh McKemmie Invariable generation of finite classical groups We say a group is invariably generated by a subset if it forms a generating set even if an adversary is allowed to replace any elements with their conjugates. Eberhard, Ford and Green built upon the work of many others and showed that, as $n \rightarrow \infty$, the probability that $S_n$ is invariably generated by a random set of elements is bounded away from zero if there are four random elements, but goes to zero if we pick three random elements. This result gives rise to a nice Monte Carlo algorithm for computing Galois groups of polynomials. We will extend this result for $S_n$ to the finite classical groups using the correspondence between classes of maximal tori of classical groups and conjugacy classes of their Weyl groups. INI 1 16:35 to 17:05 Mun See Chang Computing normalisers of highly intransitive permutation groups In general, there is no known polynomial-time algorithm for computing the normaliser $N_{S_n}(H)$ of a given group $H \leq S_n$. In this talk, we will consider the case when $H$ is a subdirect product of permutation isomorphic non-abelian simple groups. In contrast to the case with abelian simple groups, where only practical improvements have been made, here we show that $N_{S_n}(H)$ can be computed in polynomial time. INI 1 19:30 to 22:00 Formal Dinner at Corpus Christi (Hall)   LOCATION Corpus Christi Trumpington St, Cambridge CB2 1RH - map   DRESS CODE Smart casual.