Royal Holloway - Pure Mathematics Seminar


The PM-seminar takes place on Wednesday at 2pm in McCrea 219.
Here is a campus plan.


September 26: Steven Galbraith (Auckland)

"Supersingular isogeny graphs and applications"

Abstract: The graph of isogenies of supersingular elliptic curves has many
applications in computational number theory and public key
cryptography.  I will present some of these applications and I will also
discuss some open problems.


October 3: Waltraud Lederle (Zurich)

"Almost automorphism groups of trees and topological full groups"

Abstract: We will introduce the concepts mentioned in the title, explain why they
are interesting and show a connection between them. Thereby we will see examples
of simple locally compact groups without lattices; finitely generated, simple amenable
groups and the famous Higman-Thompson groups.


October 10: Mark Grant (Aberdeen)

"An equivariant Eilenberg-Ganea Theorem"
 
Abstract: There are (at least) 3 competing notions of "dimension" for discrete groups:
cohomological dimension, geometric dimension (the smallest dimension of a classifying
space), and Lusternik-Schnirelmann category (of a classifying space). Theorems of
Eilenberg-Ganea and Stallings and Swan from the 1950’s and 60's imply that these all
coincide, except for the possible existence of a group with cat=cd=2 and gd=3.
 
I will discuss equivariant generalisations of these theorems to the setting of groups with
operators. The statements involve Bredon cohomological dimension with respect to families
of subgroups, which I'll define during the talk.
 

October 17: Ian Leary (Southampton) !!at 4pm
in McCrea 219!!

"CAT(0) groups need not be biautomatic"

Abstract: Ashot Minasyan and I construct groups that establish the result in the title,
resolving a question that  has been around for almost 30 years.  I will start  by explaining
the phrases `CAT(0)' and `biautomatic'.  After that I will talk about our groups and why
they have the properties that we claim. 


October 18: Victor Moreno (Royal Holloway)  at 4pm in Munro Fox Lecture Theatre
(!!note change of day, time and venue!!)

"Classifying spaces for chains of families of subgroups"


October 24: No seminar!
 

October 31: Arno Fehm (Dresden)
!!at 2.30pm in McCrea 219!!

"Deciding solvability of polynomial equations over local fields"

The celebrated Hasse-Minkowski local-global principle relates the existence of zeros of
quadratic forms over the field of rational numbers, and more generally number fields ('global'),
to the existence of zeros over various completions ('local'), namely the real and complex numbers,
and the p-adics, where analytic methods can be applied. A similar local-global principle holds in
positive characteristic, where the 'local' fields are the fields of formal Laurent series over finite
fields. However, while it is classical that for each local field K of characteristic zero there is an
algorithm that determines whether a given system of polynomial equations has a common zero in
K, and even more generally whether a given first-order sentence in the language of rings holds in
K, for Laurent series fields over finite fields the existence of such algorithms is only partially
understood. In this talk I will report on what is known about this, which will lead us from number
theory and algebraic geometry to the model theory of valued fields.


November 7: Jessica Banks (Bristol)

"Knots (and surfaces)"

Abstract: We will consider some questions in classical knot theory, and see how surfaces
play a part. In particular, we will look at how knot theory compares with the physical
world, and how hard it is to untangle a knot.


November 14: Xin Li (Queen Mary)

"Semigroup C*-algebras"

Abstract: This talk is about semigroup C*-algebras, i.e., C*-algebras generated by left regular
representations of semigroups. After a general introduction, we will focus on classes of one-relator
monoids and Artin monoids of finite type. We present structural results and K-theory computations
for the corresponding semigroup C*-algebras. This is joint work with Tron Omland and Jack Spielberg.


November 21: Evgeny Khukhro (Lincoln)

"Almost Engel compact groups"

Abstract


November 28: Krystal Guo (Bruxelles)

"Transversals in covers of graphs"

Abstract: We study a polynomial with connections to correspondence colouring, a recent generalization
of list-colouring, and the Unique Games Conjecture. Given a graph G and an assignment of elements of
the symmetric group S_r to the edge of G, we define a cover graph: there are sets of r vertices corresponding
each vertex of G, called fibres, and for each edge uv, we add a perfect matching between the fibres
corresponding to u and v. A transversal subgraph of the cover is an induced subgraph which has exactly
 one vertex in each fibre. In this setting, we can associate correspondence colourings with transversal cocliques
and unique label covers with transversal copies of G.

We define a polynomial which enumerates the transversal subgraphs of G with k edges. We show that this
polynomial satisfies a contraction deletion formula and use this to study the evaluation of this polynomial
at -r-1. This is joint work with Chris Godsil and Gordon Royle.


December 5:
Vincent Jansen (Royal Holloway)

"Using mathematics to understand biology: on hotspots, homoclinics and horseshoes"
 
Abstract: I will start with a few words about the joint history of math and biology. I will touch on the
work of Fibonacci and Volterra. What I then will talk about in detail is a neat biological problem: the
paradoxical existence of recombination hotspots in the genome. I will start with a model for that
system based on two alleles, and I will explain how we analysed the behaviour. This will lead me
to the existence of a homoclinic cycle, and the analysis of the stability of the homoclinic cycle. As
a finale I will then take that same model but now for more alleles, explain how the homoclinic cycles
join up to form a homoclinic network in the vicinity of which we find chaotic dynamics (which is
where the horseshoes come in). After that I will interpret these results in terms of biology


December 12: Laura Ciobanu (Heriot-Watt)


"Conjugacy growth in groups, combinatorics and geometry"

Abstract: In this talk I will give an overview of what is known about conjugacy growth in infinite discrete
groups and the formal series associated with it. In particular, I will highlight the connections between the
rationality or lack of rationality of these series to analytic combinatorics and geometry.



Previous Pure Mathematics Seminars