Past Forthcoming Seminars

7 November 2017
14:30
Yuji Nakatsukasa
Abstract

Classical algorithms for numerical integration (quadrature/cubature) proceed by approximating the integrand with a simple function (e.g. a polynomial), and integrate the approximant exactly. In high-dimensional integration, such methods quickly become infeasible due to the curse of dimensionality.


A common alternative is the Monte Carlo method (MC), which simply takes the average of random samples, improving the estimate as more and more samples are taken. The main issue with MC is its slow "sqrt(variance/#samples)" convergence, and various techniques have been proposed to reduce the variance.


In this work we reveal a numerical analyst's interpretation of MC: it approximates the integrand with a simple(st) function, and integrates that function exactly. This observation leads naturally to MC-like methods that combines MC with function approximation theory, including polynomial approximation and sparse grids. The resulting method can be regarded as another variance reduction technique for Monte Carlo.

  • Numerical Analysis Group Internal Seminar
7 November 2017
14:00
Bartolomeo Stellato
Abstract

We develop a general purpose solver for quadratic programs based on operator splitting. We introduce a novel splitting that requires the solution of a quasi-definite linear system with the same coefficient matrix in each iteration. The resulting algorithm is very robust, and once the initial factorization is carried out, division free; it also eliminates requirements on the problem data such as positive definiteness of the objective function or linear independence of the constraint functions. Moreover, it is able to detect primal or dual infeasible problems providing infeasibility certificates. The method supports caching the factorization of the quasi-definite system and warm starting, making it efficient for solving parametrized problems arising in finance, control, and machine learning. Our open-source C implementation OSQP has a small footprint and is library-free. Numerical benchmarks on problems arising from several application domains show that OSQP is typically 10x faster than interior-point methods, especially when factorization caching or warm start is used.


This is joint work with Goran Banjac, Paul Goulart, Alberto Bemporad and Stephen Boyd
 

  • Numerical Analysis Group Internal Seminar
7 November 2017
12:00
Roxana Pamfil
Abstract

Identifying clusters or "communities" of densely connected nodes in networks is an active area of research, with relevance to many applications. Recent advances in the field have focused especially on temporal, multiplex, and other kinds of multilayer networks.

One method for detecting communities in multilayer networks is to maximise a generalised version of an objective function known as modularity. Writing down multilayer modularity requires the specification of two types of resolution parameters, and choosing appropriate values is crucial for uncovering meaningful community structure. In the simplest case, there are just two parameters, one controlling the sizes of detected communities, and the other influencing how much communities change from layer to layer. By establishing an equivalence between modularity optimisation and a multilayer maximum-likelihood approach to community detection, we are able to determine statistically optimal values for these two parameters. 

When applied to existing multilayer benchmarks, our optimized approach performs significantly better than using parameter choices guided by heuristics. We also apply the method to supermarket data, revealing changes in consumer behaviour over time.

7 November 2017
12:00
Gabriele Veneziano
Abstract

I will start with a quick reminder of what we have learned so far about
transplanckian-energy collisions of particles, strings and branes.
I will then address the (so-far unsolved) problem of gravitational
bremsstrahlung from massless particle collisions at leading order in the
gravitational deflection angle.
Two completely different calculations, one classical and one quantum, lead
to the same final, though somewhat puzzling, result.

 

  • Quantum Field Theory Seminar
6 November 2017
16:00
Abstract

For liquid films with a thickness in the order of 10¹−10³ molecule layers, classical models of continuum mechanics do not always give a precise description of thin-film evolution: While morphologies of film dewetting are captured by thin-film models, discrepancies arise with respect to time-scales of dewetting.

In this talk, we study stochastic thin-film equations. By multiplicative noise inside an additional convective term, these stochastic partial differential equations differ from their deterministic counterparts, which are fourth-order degenerate parabolic. First, we present some numerical simulations which indicate that the aforementioned discrepancies may be overcome under the influence of noise.

In the main part of the talk, we prove existence of almost surely nonnegative martingale solutions. Combining spatial semi-discretization with appropriate stopping time arguments, arbitrary moments of coupled energy/entropy functionals can be controlled.

Having established Hölder regularity of approximate solutions, the convergence proof is then based on compactness arguments - in particular on Jakubowski’s generalization of Skorokhod’s theorem - weak convergence methods, and recent tools for martingale convergence.

The results have been obtained in collaboration with K. Mecke and M. Rauscher and with J. Fischer, respectively

  • Partial Differential Equations Seminar
6 November 2017
15:45
Abstract

This talk concerns a twenty-thousand-year old mistake: The natural numbers record only the result of counting and not the process of counting. As algebra is rooted in the natural numbers, the higher algebra of Joyal and Lurie is rooted in a more basic notion of number which also records the process of counting. Long advocated by Waldhausen, the arithmetic of these more basic numbers should eliminate denominators. Notable manifestations of this vision include the Bökstedt-Hsiang-Madsen topological cyclic homology, which receives a denominator-free Chern character, and the related Bhatt-Morrow-Scholze integral p-adic Hodge theory, which makes it possible to exploit torsion cohomology classes in arithmetic geometry. Moreover, for schemes smooth and proper over a finite field, the analogue of de Rham cohomology in this setting naturally gives rise to a cohomological interpretation of the Hasse-Weil zeta function by regularized determinants as envisioned by Deninger.

6 November 2017
14:15
Marco Golla
Abstract


We give new obstructions to the existence of planar open books on contact structures, in terms of the homology of their fillings. I will talk about applications to links of surface singularities, Seifert fibred spaces, and integer homology spheres. No prior knowledge of contact or symplectic topology will be assumed. This is joint work with Paolo Ghiggini and Olga Plamenevskaya.
 

  • Geometry and Analysis Seminar
6 November 2017
14:15
IGOR WIGMAN
Abstract

This talk is based on a joint work with Dmitry Beliaev.

We study the volume distribution of nodal domains of families of naturally arising Gaussian random field on generic manifolds, namely random band-limited functions. It is found that in the high energy limit a typical instance obeys a deterministic universal law, independent of the manifold. Some of the basic qualitative properties of this law, such as its support, monotonicity and continuity of the cumulative probability function, are established.

  • Stochastic Analysis Seminar

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