Forthcoming Seminars

Tue, 08/01 14:00	Jinwon Choi (University of Illinois at Urbana Champaign)	Algebraic and Symplectic Geometry Seminar	L3
	On the moduli spaces of stable pairs on the projective plane
	We study the birational relationship between the moduli spaces of $\alpha$ -stable pairs and the moduli space $M(d,1)$ of stable sheaves on ${\bf P}^2$ with Hilbert polynomial $dm+1$ . We explicitly relate them by birational morphisms when $d=4$ and $5$ , and we describe the blow-up centers geometrically. As a byproduct, we obtain the Poincare polynomials of the moduli space of stable sheaves, or equivalently the refined BPS index. This is joint work with Kiryong Chung.

Tue, 08/01 15:45	Jinwon Choi (University of Illinois at Urbana Champaign)	Algebraic and Symplectic Geometry Seminar	L3
	Refined stable pair invariants on local Calabi-Yau threefolds
	A refinement of the Pandharipande-Thomas stable pair invariants for local toric Calabi-Yau threefolds is defined by what we call the virtual Bialynicki-Birula decomposition. We propose a product formula for the generating function for the refined stable pair invariants extending the motivic product formula of Morrison, Mozgovoy, Nagao, and Szendroi for local ${\bf P}^1$ . I will also describe how the proposed product formula is related to the wall crossing in my first talk. This is joint work with Sheldon Katz and Albrecht Klemm.

Thu, 10/01 14:00	Professor Stephen Wright (University of Wisconsin-Madison)	Computational Mathematics and Applications	Gibson Grd floor SR
	Packing Ellipsoids with Overlap
	Problems of packing shapes with maximal density, sometimes into a container of restricted size, are classical in discrete mathematics. We describe here the problem of packing a given set of ellipsoids of different sizes into a finite container, in a way that allows overlap but that minimizes the maximum overlap between adjacent ellipsoids. We describe a bilevel optimization algorithm for finding local solutions of this problem, both the general case and the simpler special case in which the ellipsoids are spheres. Tools from conic optimization, especially semidefinite programming, are key to the algorithm. Finally, we describe the motivating application - chromosome arrangement in cell nuclei - and compare the computational results obtained with this approach to experimental observations. This talk represents joint work with Caroline Uhler (IST Austria).

Fri, 11/01 11:30	Various	OCCAM Special Seminar	OCCAM Common Room (RI2.28)
	OCCAM Group Meeting
	Kiran Singh - Multi-body dynamics in elastocapillary systems Graham Morris - Investigating a catalytic mechanism using voltammetry Thomas Woolley - Cellular blebs: pressure-driven axisymmetric, membrane protrusions

Mon, 14/01 12:00	Magdalena Larfors (Oxford)	String Theory Seminar	L3
	Non-commuting closed strings on non-geometric backgrounds
	Strings are extended objects, and this means that they can be compactified not only on Riemannian manifolds, but also on more exotic spaces with generalized transition functions. An example of this is the T-fold, where T-duality is used to glue the Neveu-Schwarz fields of the background. Collectively, these exotic set-ups are known as non-geometric string compactifications, and in this talk I will discuss two of their aspects. First, I will present a field redefinition in the Neveu-Schwarz sector that allows a ten-dimensional, effective description of certain non-geometric backgrounds. This redefinition is inspired by Generalized Geometry and Double Field Theory. Second, I will show that closed strings become non-commuting when non-geometric fluxes are turned on. This will be done through the analysis of a three-torus with H-flux and its T-dual configurations.

Mon, 14/01 14:15	Peter Topping (Warwick)	Geometry and Analysis Seminar	L3
	The Teichmueller harmonic map flow

Mon, 14/01 15:45	Vincent Guirardel (Toulouse)	Topology Seminar
	Automorphisms of relatively hyperbolic groups and McCool groups
	We define a McCool group of G as the group of outer automorphisms of G acting as a conjugation on a given family of subgroups. We will explain that these groups appear naturally in the description of many natural groups of automorphisms. On the other hand, McCool groups of a toral relatively hyperbolic group have strong finiteness properties: they have a finite index subgroup with a finite classifying space. Moreover, they satisfy a chain condition that has several other applications. This is a joint work with Gilbert Levitt.

Mon, 14/01 16:00	Thomas Reuss (Oxford)	Junior Number Theory Seminar	SR1
	An Introduction to the Square Sieve

Mon, 14/01 17:00	Jonathan Bevan (University of Surrey)	Partial Differential Equations Seminar	Gibson 1st Floor SR
	N-covering stationary points and constrained variational problems
	In this talk we show how degree N maps of the form $u_{N}(z) = \frac{z^{N}}{\|z\|^{N-1}}$ arise naturally as stationary points of functionals like the Dirichlet energy. We go on to show that the $u_{N}$ are minimizers of related variational problems, including one whose associated Euler-Lagrange equation bears a striking resemblance to a system studied by N. Meyers in the 60s, and another where the constraint $\det \nabla u = 1$ a.e. plays a prominent role.

Tue, 15/01 12:00	Mir Faizal	Quantum Field Theory Seminar	L3
	Supersymmetric loop space
	We will first review the construction of N =1 supersymmetric Yang-Mills theory in three dimensions. Then we will construct a superloop space formulation for this super-Yang-Mills theory in three dimensions.Thus, we will obtain expressions for loop connection and loop curvature in this superloop space. We will also show that curvature will vanish, unless there is a monopole in the spacetime. We will also construct a quantity which will give the monopole charge in this formalism. Finally, we will show how these results hold even in case of deformed superspace.

Tue, 15/01 14:15	David Mulholland (University of Reading))	Geophysical and Nonlinear Fluid Dynamics Seminar	Dobson Room, AOPP
	Baroclinic waves and dust storms in martian winter

Tue, 15/01 15:45	Kevin McGerty (Oxford)	Algebraic and Symplectic Geometry Seminar	L3
	Introduction to deformation quantization

Tue, 15/01 17:00	Peter Kropholler (Southamapton)	Algebra Seminar	L2
	Homological dimension of soluble groups and some new complement and supplement theorems.
	The homological dimension of a group can be computed over any coefficient ring $K$. It has long been known that if a soluble group has finite homological dimension over $K$ then it has finite Hirsch length and the Hirsch length is an upper bound for the homological dimension. We conjecture that equality holds: i.e. the homological dimension over $K$ is equal to the Hirsch length whenever the former is finite. At first glance this conjecture looks innocent enough. The conjecture is known when $K$ is taken to be the integers or the field of rational numbers. But there is a gap in the literature regarding finite field coefficients. We'll take a look at some of the history of this problem and then show how some new near complement and near supplement theorems for minimax groups can be used to establish the conjecture in special cases. I will conclude by speculating what may be required to solve the conjecture outright.

Tue, 15/01 17:00	Chris Heunen (Oxford)	Functional Analysis Seminar	L3
	Diagonalizing matrices over AW*-algebras

Wed, 16/01 10:30	Alejandra Garrido -- Queen's Lecture C	Algebra Kinderseminar	Queen's College
	On the structure of branch groups

Wed, 16/01 16:00	Robert Kropholler (University of Oxford)	Junior Geometric Group Theory Seminar	SR2
	Relations between some topological and group theoretic conjectures
	I will be looking at some conjectures and theorems closely related to the h-cobordism theorem and will try to show some connections between them and some group theoretic conjectures.

Thu, 17/01
12:00

Parth Soneji (OxPDE)

OxPDE Lunchtime Seminar

Gibson 1st Floor SR

Relaxation in BV via polyhedral approximation

We first provide a brief overview of some of the key properties of the space $\textrm{BV}(\Omega;\mathbb{R}^{N})$ of functions of Bounded Variation, and the motivation for its use in the Calculus of Variations. Now consider the variational integral

$F(u;\Omega):=\int_{\Omega}f(Du(x))\,\textrm{d} x\,\textrm{,}$

where $\Omega\subset\mathbb{R}^{n}$ is open and bounded, and $f\colon\mathbb{R}^{N\times n}\rightarrow\mathbb{R}$ is a continuous function satisfying the growth condition $0\leq f(\xi)\leq L(1+|\xi|^{r})$ for some exponent $r$ . When $u\in\textrm{BV}(\Omega;\mathbb{R}^{N})$ , we extend the definition of $F(u;\Omega)$ by introducing the functional

$\mathscr{F}(u,\Omega):= \inf_{(u_{j})}\bigg\{ \liminf_{j\rightarrow\infty}\int_{\Omega}f(Du_{j})\,\textrm{d} x\, \left| \!\!\begin{array}{r} (u_{j})\subset W_{\textrm{loc}}^{1,r}(\Omega, \mathbb{R}^{N}) \\ u_{j} \stackrel{\ast}{\rightharpoonup} u\,\,\textrm{in }\textrm{BV}(\Omega, \mathbb{R}^{N}) \end{array} \right. \bigg\} \,\textrm{.}$

For $r\in [1,\frac{n}{n-1})$ , we prove that $\mathscr{F}$ satisfies the lower bound

$\mathscr{F}(u,\Omega) \geq \int_{\Omega} f(\nabla u (x))\,\textrm{d} x + \int_{\Omega}f_{\infty} \bigg(\frac{D^{s}u}{|D^{s}u|}\bigg)\,|D^{s}u|\,\textrm{,}$

provided $f$ is quasiconvex, and the recession function $f_{\infty}$ ( $:= \overline{\lim}_{t\rightarrow\infty}f(t\xi )/t$ ) is assumed to be finite in certain rank-one directions. This result is a natural extension of work by Ambrosio and Dal Maso, which deals with the case $r=1$ ; it involves combining work of Kristensen, Braides and Coscia with some new techniques, including a polyhedral approximation result and a blow-up argument that exploits fine properties of BV functions.

Thu, 17/01 13:00		Mathematical Finance Internal Seminar
	NO SEMINAR THIS WEEK
	No Seminar this week

Thu, 17/01 14:00	Professor Massimiliano Pontil (University College London)	Computational Mathematics and Applications	Gibson Grd floor SR
	Multi-task Learning and Structured Sparsity
	We discuss the problem of estimating a structured matrix with a large number of elements. A key motivation for this problem occurs in multi-task learning. In this case, the columns of the matrix correspond to the parameters of different regression or classification tasks, and there is structure due to relations between the tasks. We present a general method to learn the tasks' parameters as well as their structure. Our approach is based on solving a convex optimization problem, involving a data term and a penalty term. We highlight different types of penalty terms which are of practical and theoretical importance. They implement structural relations between the tasks and achieve a sparse representations of parameters. We address computational issues as well as the predictive performance of the method. Finally we discuss how these ideas can be extended to learn non-linear task functions by means of reproducing kernels.

Thu, 17/01 14:00	Matthias Krebs (University of East Anglia)	Representation Theory Seminar	L3
	Auslander-Reiten-quivers in functorially finite resolving subcategories
	It has been shown that the Auslander-Reiten-quiver of an indecomposable algebra contains a finite component if and only if A is representation finite. Moreover, selfinjective algebras are representation finite if and only if the tree types of the stable components are given by Dynkin Diagrams. I will present similar results for the Auslander-Reiten-quiver of a functorially finite resolving subcategory Ω. We will see that Brauer-Thrall 1 and Brauer-Thrall 1.5 can be proved for these categories with only little extra effort. Furthermore, a connection between sectional paths in A-mod and irreducible morphisms in Ω will be given. Finally, I will show how all finite Auslander-Reiten-quivers of A-mod or Ω are related to Dynkin Diagrams with a notion similar to the tree type that coincides in a finite stable component.