I will discuss a notoriously hard problem in group theory known as the flat closing conjecture. This states that a group with a finite classifying space is either hyperbolic or contains a Baumslag-Solitar Subgroup. I will give some strategies to try and create a counterexample to this conjecture.
Quantum computers derive their computational power from the ability to manipulate superposition states of quantum registers. The generic quantum attack against a symmetric encryption scheme with key length n using Grover's algorithm has O(2^(n/2)) time complexity. For this kind of attack, an adversary only needs classical access to an encryption oracle. In this talk I discuss adversaries with quantum superposition access to encryption and decryption oracles. First I review and extend work by Kuwakado and Morii showing that a quantum computer with superposition access to an encryption oracle can break the Even-Mansour block cipher with key length n using only O(n) queries. Then, improving on recent work by Boneh and Zhandry, I discuss indistinguishability notions in chosen plaintext and chosen ciphertext attacks by a quantum adversary with superposition oracle access and give constructions that achieve these security notions.
Following an idea of Bridgeland, we study the operator on the K-group of algebraic stacks, which takes a stack to its inertia stack. We prove that the inertia operator is diagonalizable when restricted to nice enough stacks, including those with algebra stabilizers. We use these results to prove a structure theorem for the motivic Hall algebra of a projective variety, and give a more conceptual definition of virtually indecomposable stack function. This is joint work with Pooya Ronagh.
We discuss a new setting of algorithmic problems in random graphs, studying the minimum number of queries one needs to ask about the adjacency between pairs of vertices of $G(n,p)$ in order to typically find a subgraph possessing a certain structure. More specifically, given a monotone property of graphs $P$, we consider $G(n,p)$ where $p$ is above the threshold probability for $P$ and look for adaptive algorithms which query significantly less than all pairs of vertices in order to reveal that the property $P$ holds with high probability. In this talk we focus particularly on the properties of containing a Hamilton cycle and containing paths of linear size. The talk is based on joint work with Asaf Ferber, Michael Krivelevich and Benny Sudakov.
Our work (which is joint with Simon Smith) began as a study of the structure of infinite permutation groups $G$ in which point stabilisers are finite and all infinite normal subgroups are transitive. That led to two variations. One is the generalisation in which point stabilisers are merely assumed to satisfy min-{\sc N}, the minimal condition on normal subgroups. The groups $G$ are then of two kinds. Either they have a maximal finite normal subgroup, modulo which they have either one or two minimal non-trivial normal subgroups, or they have a regular normal subgroup $M$ which is a divisible abelian $p$-group of finite rank. In the latter case the point stabilisers are finite and act irreducibly on the socle of~$M$. This leads to our second variation, which is a study of the finite linear groups that can arise.
The talk will describe a new "Brute Force Optimizer" whose objective is to provide a very versatile derivative-free Matlab package for bound-constrained optimization, with the distinctive feature that it can be trained to improve its own performance on classes of problems specified by the user (rather than on a single-but-wide problem class chosen by the algorithm developer). In addition, BFO can be used to optimize the performance of other algorithms and provides facilities for mixed-integer and multilevel problems, including constrained equilibrium calculations.
Starting from Hilbert's 10th problem, I will explain how to characterise the set of integers by non-solubility of a set of polynomial equations and discuss related challenges. The methods needed are almost entirely elementary; ingredients from algebraic number theory will be explained as we go along. No knowledge of first-order logic is necessary.
Starting from Hilbert's 10th problem, I will explain how to characterise the set of integers by non-solubility of a set of polynomial equations and discuss related challenges. The methods needed are almost entirely elementary; ingredients from algebraic number theory will be explained as we go along. No knowledge of first-order logic is necessary.
We study the adaptive finite element approximation of the Dirichlet problem $-\Delta u = f$ with zero boundary values using newest vertex bisection. Our approach is based on the minimization of the corresponding Dirichlet energy. We show that the maximums strategy attains every energy level with a number of degrees of freedom, which is proportional to the optimal number. As a consequence we achieve instance optimality of the error. This is a joint work with Christian Kreuzer (Bochum) and Rob Stevenson (Amsterdam).
Abstract: A diffusion process on a Riemannian manifold whose generator is one half of the Laplacian is called a Brownian motion. The mean local time of Brownian motion on a hypersurface will be considered, as will the situation in which a Brownian motion is conditioned to arrive in a fixed submanifold at a fixed positive time. Doing so provides motivation for the remainder of the talk, in which a probabilistic formula for the integral of the heat kernel over a submanifold is proved and used to deduce lower bounds, an asymptotic relation and derivative estimates applicable to the conditioned process.
We study symplectic invariants of the open symplectic manifolds X
obtained by plumbing cotangent bundles of spheres according to a
plumbing tree. We prove that certain models for the Fukaya category F(X)
of closed exact Lagrangians in X and the wrapped Fukaya category W(X)
are related by Koszul duality. As an application, we give explicit
computations of symplectic cohomology essentially for all trees. This is
joint work with Tolga Etg\"u.
Abstract: The martingale optimal transport aims to optimally transfer a probability measure to another along the class of martingales. This problem is mainly motivated by the robust superhedging of exotic derivatives in financial mathematics, which turns out to be the corresponding Kantorovich dual. In this paper we consider the continuous-time martingale transport on the Skorokhod space of cadlag paths. Similar to the classical setting of optimal transport, we introduce different dual problems and establish the corresponding dualities by a crucial use of the S-topology and the dynamic programming principle. This is a joint work with Gaoyue Guo and Nizar Touzi.
By regarding gravity as the convolution of left and right Yang-Mills theories together with a spectator scalar field in the bi-adjoint representation, we derive in linearised approximation the gravitational symmetries of general covariance, p-form gauge invariance, local Lorentz invariance and local supersymmetry from the flat space Yang-Mills symmetries of local gauge invariance and global super-Poincare. As a concrete example we focus on the new-minimal (12+12) off-shell version of simple four-dimensional supergravity obtained by tensoring the off-shell Yang-Mills multiplets (4+4,NL =1)and(3+0,NR =0).
Across much of the ablation region of the western Greenland Ice Sheet, hydro-fracture events related to supraglacial lake drainages rapidly deliver large volumes of meltwater to the bed of the ice sheet. We investigate what triggers the rapid drainage of a large supraglacial lake using a Network Inversion Filter (NIF) to invert a dense local network of GPS observations over three summers (2011-2013). The NIF is used to determine the spatiotemporal variability in ice sheet behavior (1) prior to lake drainage, and in response to (2) vertical hydro-fracture crack propagation and closure, (3) the opening of a horizontal cavity at the ice-sheet bed that accommodates the rapid injection of melt-water, and (4) extra basal slip due to enhanced lubrication. We find that the opening and propagation of each summer’s lake-draining hydro-fracture is preceded by a local stress perturbation associated with ice sheet uplift and enhanced slip above pre-drainage background velocities. We hypothesize that these precursors are associated with the introduction of meltwater to the bed through neighboring moulin systems.
The first half of the lecture will begin by reviewing what is known about the
neural representation of faces in the primate visual system. How does the
visual system represent the spatial structure of faces, facial identity and
expression? We then discuss how depression is associated with negative
cognitive biases in the recognition of facial expression, whereby depressed
people interpret facial expressions more negatively. The second half of the
lecture presents computer simulations aimed at understanding how these facial
representations may develop through visual experience. We show how neural
representations of expression are linked to particular spatial relationships
between facial features. Building on this, we show how the synaptic connections
in the model may be rewired by visual training to eliminate the negative
cognitive biases seen in depression.
Pengyu Wei's title: Ranking ForexMaster Players
Abstract:
In this talk I will introduce ForexMaster, a simulated foreign exchange trading platform, and how I rank players on this platform. Different methods are compared. In particular, I use random forest and a carefully chosen feature set, which includes not only traditional performance measures like Sharp ratio, but also estimates from the Plackett-Luce ranking model, which has not been used in the financial modelling yet. I show players selected by this method have satisfactory out-of-sample performance, and the Plackett-Luce model plays an important role.
Alissa Kleinnijenhuis title: Stress Testing the European Banking System: Exposure Risk & Overlapping Portfolio Risk
Abstract:
Current regulatory stress testing, as for example done by the EBA, BoE and the FED, is microprudential, non-systemic. These stress tests do not take into account systemic risk, even though the official aim of the stress test is the "test the resilience of the financial system as a whole, and the individual banks therein, to another crisis".
Two papers are being developed that look at the interconnections between banks. One paper investigates the systemic risk in the European banking system due to interbank exposures, using EBA data. The other paper, looks at the trade-off between individual and systemic risk with overlapping portfolios. The above two "channels of contagion" for systemic risk can be incorporated in stress tests to include systemic components to the traditional non-systemic stress tests.
Blenders and food processors have been around for years. However, detailed understanding of the fluid and particle dynamics going on with in the multi-phase flow of the processing chamber as well as the influence of variables such as the vessel geometry, blade geometry, speeds, surface properties etc., are not well understood. SharkNinja would like Oxford Universities help in developing a model that can be used to gain insight into fluid dynamics within the food processing chamber with the goal being to develop a system that will produce better food processing performance as well as predict loading on food processing elements to enable data driven product design.
Many vacuum cleaners sold claim “no loss of suction” which is defined as having only a very small reduction in peak air power output over the life of the unit under normal operating conditions. This is commonly achieved by having a high efficiency cyclonic separator combined with a filter which the user washes at regular intervals (typically every 3 months). It has been observed that some vacuum cleaners show an increase in peak air watts output after a small amount of dust is deposited on the filter. This effect is beneficial since it prolongs the time between filter washing. SharkNinja are currently working on validating their theory as to why this occurs. SharkNinja would like Oxford University’s help in developing a model that can be used to better understand this effect and provide insight towards optimizing future designs.
Although a very simple system from a construction standpoint, creating a drip coffee maker that can be produce a range of coffee sizes from a single cup to a multi-cup carafe presents unique problems. Challenges within this system result from varying pressure heads on the inlet side, accurate measurement of relatively low flow rates, fluid motive force generated by boilers, and head above the boiler on the outlet side. Getting all of these parameters right to deliver the proper strength, proper temp, and proper volume of coffee requires in depth understanding of the fluid dynamics involved in the system. An ideal outcome from this work would be an adaptive model that enables a fluid system model to be created from building blocks. This system model would include component models for tubing, boilers, flow meters, filters, pumps, check valves, and the like.
We consider the decision problem of determining whether an exponential
polynomial has a real zero. This is motivated by reachability questions
for continuous-time linear dynamical systems, where exponential
polynomials naturally arise as solutions of linear differential equations.
The decidability of the Zero Problem is open in general and our results
concern restricted versions. We show decidability of a bounded
variant---asking for a zero in a given bounded interval---subject to
Schanuel's conjecture. In the unbounded case, we obtain partial
decidability results, using Baker's Theorem on linear forms in logarithms
as a key tool. We show also that decidability of the Zero Problem in full
generality would entail powerful new effectiveness results concerning
Diophantine approximation of algebraic numbers.
This is joint work with Ventsislav Chonev and Joel Ouaknine.
Deformation K-theory was introduced by G. Carlsson and gives an interesting invariant of a group G encoding higher homotopy information about its representation spaces. Lawson proved a relation between this object and a homotopy theoretic analogue of the representation ring. This talk will not contain many details, instead I will outline some basic constructions and hopefully communicate the main ideas.
A well-known result of Landsberger and Meilijson says that efficient risk-sharing rules for univariate risks are characterized by a so-called comonotonicity condition. In this talk, I'll first discuss a multivariate extension of this result (joint work with R.-A. Dana and A. Galichon). Then I will discuss the restrictions (in the form of systems of nonlinear PDEs) efficient risk sharing imposes on individual consumption as a function of aggregate consumption. I'll finally give an identification result on how to recover preferences from the knowledge of the risk sharing (joint work with M. Aloqeili and I. Ekeland).
The Möbius function plays a central role in number theory; both the prime number theorem and the Riemann Hypothesis are naturally formulated in terms of the amount of cancellations one gets when summing the Möbius function. In a recent joint work with Maksym Radziwill we have shown that the sum of the Möbius function exhibits cancellation in "almost all intervals" of arbitrarily slowly increasing length. This goes beyond what was previously known conditionally on the Riemann Hypothesis. Our result holds in fact in much greater generality, and has several further applications, some of which I will discuss in the talk. For instance the general result implies that between a fixed number of consecutive squares there is always an integer composed of only "small" prime factors. This settles a conjecture on "smooth" or "friable" numbers and is related to the running time of Lenstra's factoring algorithm.