The mathematics colloquium is held twice a term.
During term time seminars are held by the different research groups in the School of Mathematics.
Events this week:
Analysis Seminar: Singular integral operators of layer potential type
- Irina Mitrea (Temple University)
- Tuesday 15 October 2019, 14:00
- Lecture Theatre B, Watson Building
- Tea and coffee will be provided after the talk at the common room
One of the most efficient approaches to solving boundary value problems for elliptic partial differential equations is the method of boundary layer potentials. In this talk I will survey some of the recent progress made in understanding the nature of integral operators of boundary layer type in optimal geometrical settings.
Geometry and Mathematical Physics seminar: Quivers and supersymmetric QFTs
- Cyril Closset, University of Oxford
- Tuesday 15 October 2019, 14:30
Time and room changed
Quivers appears in string theory as a convenient way of summarising the spectrum of open-string BPS states at “orbifold” points. Similarly, in QFT , quiver methods are useful either to characterize the field theory itself, or to characterize its spectrum of BPS states. After a general introduction, I will focus on quivers that appear in the context of five-dimensional supersymmetric field theories, including new results about the Coulomb branch of 5d SCF Ts.
Algebra Seminar: The maximal dimensions of simple modules over restricted Lie algebras
- Lewis Topley, Birmingham
- Tuesday 15 October 2019, 16:00
- Watson Building, Lecture Room C
Restricted Lie algebras were introduced by Jacobson in the 1940’s and ever since the first investigations into their representation theory, it has been understood that the simple modules of a given such algebra have bounded dimensions. In 1971 Kac and Weisfeiler made a striking conjecture (KW1) giving a precise formula for the maximal dimension M(g) of a restricted Lie algebra g.
In this talk I will give a general overview of this theory, and then I will describe a joint work with Ben Martin and David Stewart in which we apply the Leftschetz principle, along with classical techniques from Lie theory, to prove the KW1 conjecture for all restricted Lie subalgebras of the general linear algebra gl_n, provided the characteristic of the field is large compared to n.
Optimisation and Numerical Analysis Seminars: Topology optimization of discrete structures by semidefinite programming
- Marek Tyburec (Czech Technical University, Prague)
- Wednesday 16 October 2019, 12:00
- Strathcona, SR5
This contribution investigates applications of semidefinite programming (SDP) techniques to two problems of structural topology optimization. We consider first the problem of designing optimum truss reinforcement of a thin-walled composite laminate to withstand manufacturing and operational loads and to suppress elastic wall instabilities. For this problem, the instabilities can be described using free-vibration eigenmodes, allowing thus for a convex SDP representation. To accelerate the solution of these types of problems, we utilize the static condensation/(generalized) Schur complement lemma, which additionally provides us with an upper bound on the maximum admissible fundamental eigenfrequency, and a lower bound on the minimum admissible compliance of the manufacturing load case. Finally, we manufacture the composite beam prototype with a 3D-printed internal structure, perform experimental validation, and conclude that the structural response agrees well with the model predictions. As the second problem, we consider the topology optimization of frame structures. In this case, the SDP formulation is no longer convex in general. However, because the SDP constraints are polynomial matrix inequalities, we adopt the moment-sums-of-squares hierarchy for their solution. It turns out that each relaxation of this hierarchy generates both lower and upper bounds on the optimal design, which provides us not only with a measure of the solution quality but also an inexpensive sufficient condition of global optimality. For all the tested problems, finite convergence was observed.
Combinatorics and Probability Seminar: Path and cycle decompositions of dense graphs
- Bertille Granet (University of Birmingham)
- Thursday 17 October 2019, 14:00
- Watson LTB
- Tea, coffee and biscuits will be provided after the talk at the common room
We make progress on three long standing conjectures from the 1960s about path and cycle decompositions of graphs. Gallai conjectured that any connected graph on n vertices can be decomposed into at most ⌊n/2⌋ paths, while a conjecture of Hajós states that any Eulerian graph on n vertices can be decomposed into at most ⌈(n-1)/2⌉ cycles. The Erdős-Gallai conjecture states that any graph on n vertices can be decomposed into O(n) cycles and edges.
We show that if G is a sufficiently large graph on n vertices with linear minimum degree, then the following hold.(i) G can be decomposed into n/2+o(n) paths.(ii) If G is Eulerian, then it can be decomposed into n/2+o(n) cycles.(iii) G can be decomposed into 3n/2+o(n) cycles and edges.All bounds in (i)-(iii) are asymptotically best possible.
This is joint work with António Girão, Daniela Kühn, and Deryk Osthus.
Find out more
There is a complete list of talks in the School of Mathematics that can be accessed on talks@bham.