All seminars will take place in the McCrea Building, Room 219, on Tuesdays at 2 pm, unless stated otherwise. Tea will be served after the seminar at 3pm in Room 237 of the McCrea Building. All are welcome!
Seminars for Spring Term 2012:
- 10th January: Jan-Christoph Schlage-Puchta (Ghent): Random actions of $p$-groups on the $p$-adic tree and subgroup growth of pro-$p$-group
- 17th January: Matthew Towers (Kent): Koszul duality and small quantum sl3
Abstract: Let $G$ be a $p$-group, $P_n$ the $p$-Sylow subgroup of the symmetric group $S_{p^n}$. Homomorphisms of $G$ into $P_n$ can be viewed as actions of $G$ on the $p$-adic tree of height $n$. We show how the behaviour of random actions is linked to the subgroup growth of $G$, and describe some phenomena for random actions. As application we show that the subgroup growth of large pro-$p$-groups is much more irregular than the subgroup growth of large discrete groups.
Abstract: Certain graded algebras have a remarkable relationship to their Ext algebras called Koszul duality. The small quantum groups, deformed versions of restricted enveloping algebras of semisimple Lie algebras, have long been conjectured to have this property. I will try to explain exactly what Koszul duality means and to illustrate it with the case of small quantum sl3.
- 24th January: Nikolay Nikolov (Imperial College): Words with few values in finite simple groups
Abstract: I will survey some recent results about word values in finite groups and the open problems that remain. I will also present a new result with M. Kassabov constructing words which take values only the 3-cycles and the identity in a given alternating group.
- 31th January: David Conlon (Oxford): Graph regularity and removal lemmas
Abstract: Szemerédi's regularity lemma states that every large graph may be partitioned into a small number of parts so that the bipartite graph between almost all pairs of parts is random-like. One of the most important applications of this theorem is the graph removal lemma, which roughly says that every graph with few copies of a fixed graph H can be made H-free by removing few edges. In this talk, we will discuss recent progress on bounds for these theorems and for several important variants. This is joint work with Jacob Fox. - 7th February: Amarpreet Rattan (Birkbeck): Star factorisations in the symmetric group
Abstract: I will be talking about certain factorisations in the symmetric group known as star factorisations. I will put these factorisations into the context of general transitive factorisations, as well as giving an overview of the results to date. I will end with some open questions. - 14th February: Eira Scourfield (RHUL): Divisors of a polynomial over the integers
Abstract: The motivation for the topic of this talk is a problem, still
unsolved, raised in a 1952 paper by Paul Erdos. Let f be a product of
irreducible polynomials with integer coefficients. Various authors have
investigated problems related to determining an asymptotic formula for the
number of divisors d<y=y(x) of f(n) summed over n<x, where d may be
restricted in some way and f itself may be irreducible. In particular we
discuss the cases when d is smooth or unrestricted or q-free or exact, where
d is exact if d|f(n) but dp is not a divisor of f(n) for any prime divisor p
of d, and d is smooth if its largest prime divisor is restricted in size. - 21th February: Lutz Warnke (Oxford)
- 28th February: Tim Jones (Bristol)
- 6th March: Peter Pappas (Oxford)
- 20th March: Tim Browning (Bristol)
Useful links:
Campus map (The McCrea Building is number 17)