Pure Mathematics Seminars
All seminars will take place on Wednesday at 2 pm in Horton LT1, unless stated otherwise. Here is a campus plan.Tea will be served after the seminar at 3pm in Room 237 of the McCrea Building. All are welcome!
Spring Term 2018
January 10: No Seminar!
January 17: Brent Everitt (York) !!Cancelled!!
January 24: Sam Chow (York)
"A Galois counting problem"
Abstract. We count monic quartic polynomials with prescribed Galois group, by box height. Among other things, we obtain the order of magnitude for D_4 quartics, and show that non-S_4 quartics are dominated by reducibles. Weapons include determinant method estimates, the invariant theory of binary forms, the geometry of numbers, and diophantine approximation. Joint with Rainer Dietmann.
January 31: Christopher Frei (Manchester)
"Bounds for l-torsion in class groups"
Abstract: The arithmetic of a number field is determined in large parts by its class group. While it is a classical result of algebraic number theory that this group is always finite and abelian, precise information on its structure remains quite elusive. To emphasise how little we know, it is still unknown whether the class group is trivial for infinitely many number fields. In this talk, we introduce class groups and survey classical and recent results (conditional and unconditional) bounding the cardinality of their l-torsion subgroups, for a natural number l. In the remaining time, we discuss recent joint work with Martin Widmer on average bounds for this l-torsion in certain families of number fields.
February 7: Dan Segal (Oxford)
"Groups of finite upper rank"
Abstract: The upper rank of a group is the supremum of the Prufer ranks of its finite quotient groups. The upper p-rank, for a prime p, is defined analogously, using the Sylow p-subgroups of finite quotients. I’ll discuss to what extent the upper rank of a finitely generated group is controlled by its upper p-ranks.
February 14: Sofia Lindqvist (Oxford)
"Rado's criterion over k'th powers"
Abstract: An equation is said to be partition regular if for any finite colouring of the integers there is a monochromatic solution to the equation. In the case of linear homogeneous equations Rado showed that an equation is partition regular iff the coefficients satisfy something known as Rado's criterion. We extend this result to sums of k-th powers, provided the number of variables is sufficiently large in terms of k. This is joint work with Sam Chow and Sean Prendiville.
February 20 (Tuesday!): Extra seminar at !!2 pm in Windsor 1-02!!: Christian Elsholtz (Graz)
"Iterated divisor functions”
Abstract: The divisor function d(n) is large, when n is a product of many small primes. For example d(184.108.40.206)=16.The iterated divisor function d(d(n)) is quite large, whend(n) is such a product of small primes. But what is the *maximal* order of magnitude of d(d(n))? This question was raised by Ramanujan in 1915, and was later studied by Erdos, Katai and Ivic.
In joint work with Y. Buttkewitz, K Ford, J.C. Schlage-Puchta we determined the maximal order.
With M. Technau and N. Technau we generalized this result to a class of related multiplicative functions, which includes the case r_2(n), counting the number of representations as sums of two squares, also investigated by Ramanujan.
February 21: Amanda Cameron (Leipzig)
"An Ehrhart theory generalisation of the Tutte polynomial"
Abstract: The Tutte polynomial is one of the most important and well-known graph polynomials, and also features prominently in matroid theory. It is however not directly applicable to polymatroids, these being a natural generalisation of matroids. For instance, deletion-contraction properties do not hold. We construct a polynomial for polymatroids which behaves similarly to the Tutte polynomial of a matroid, and in fact contains the same information as the Tutte polynomial when we restrict to matroids. This is based on joint work with Alex Fink.
February 28: No seminar!
March 7: No seminar!
March 14: No seminar!
March 21: Eugene Shargorodsky (Kings College)
April 26: Victor Beresnevich (York)
April 30: Philip Dittmann (Oxford)
May 2: Matthew Tointon (Cambridge) !!at 2pm in Arts LT1!!
May 9: Brent Everitt (York)
"(Co)Homology of arrangements"
Abstract: An arrangement is a finite collection of linear hyperplanes in some vector space. In this talk we survey a number of different answers to the question, “what is the cohomology of an arrangement?”
May 16: Martin Liebeck (Imperial College)