Tue, 06 Jun 2017
17:00
C1

### Discrete Fourier Analysis and spectral properties

(Imperial College London)
Abstract

We present some recent results on the study of Schatten-von Neumann properties for
operators on compact manifolds. We will explain the  point of view of kernels and full symbols. In both cases

one relies on a suitable Discrete Fourier analysis depending on the domain.

We will also discuss about operators on $L^p$ spaces by using the notion of nuclear operator in the sense of

Grothendieck and deduce Grothendieck-Lidskii trace formulas in terms of the matrix-symbol. We present examples

for fractional powers of differential operators.  (Joint work with Michael Ruzhansky)

Mon, 12 Jun 2017

14:15 - 15:15
L3

### Boguslaw Zegarlinski - title tbc

BOGUSLAW ZEGARLINSKI
(Imperial College London)
Abstract

TBC

Mon, 22 May 2017

15:45 - 16:45
L3

### A Stratonovich-to-Skorohod conversion formula for integrals with respect to Gaussian rough paths

THOMAS CASS
(Imperial College London)
Abstract

Lyons’ theory of rough paths allows us to solve stochastic differential equations driven by a Gaussian processes X of finite p-variation. The rough integral of the solutions against X again exists. We show that the solution also belong to the domain of the divergence operator of the Malliavin derivative, so that the 'Skorohod integral' of the solution with respect to X can also be defined. The latter operation has some properties in common with the Ito integral, and a natural question is to find a closed-form conversion formula between this rough integral and its Malliavin divergence. This is particularly useful in applications, where often one wants to compute the (conditional) expectation of the rough integral. In the case of Brownian motion our formula reduces to the classical Stratonovich-to-Ito conversion formula. There is an interesting difference between the formulae obtained in the cases 2<=p<3 and 3<=p<4, and we consider the reasons for this difference. We elaborate on the connection with previous work in which the integrand is generally assumed to be the gradient of a smooth function of X_{t}; we show that our formula can recover these results as special cases. This is joint work with Nengli Lim.

Thu, 19 Jan 2017

16:00 - 17:00
L3

### Networks and Function

Mike Field
(Imperial College London)
Abstract

Averaging, either spatial or temporal, is a powerful technique in complex multi-scale systems.

However, in some situations it can be difficult to justify.

For example, many real-world networks in technology, engineering and biology have a function and exhibit dynamics that cannot always be adequately reproduced using network models given by the smooth dynamical systems and fixed network topology that typically result from averaging. Motivated by examples from neuroscience and engineering, we describe a model for what we call a "functional asynchronous network". The model allows for changes in network topology through decoupling of nodes and stopping and restarting of nodes, local times, adaptivity and control. Our long-term goal is to obtain an understanding of structure (why the network works) and how function is optimized (through bifurcation).

We describe a prototypical theorem that yields a functional decomposition for a large class of functional asynchronous networks. The result allows us to express the function of a dynamical network in terms of individual nodes and constituent subnetworks.

Thu, 09 Feb 2017

16:00 - 17:00
L6

### A logarithmic interpretation of Edixhoven's jumps for Jacobians

Johannes Nicaise
(Imperial College London)
Abstract

Let A be an abelian variety over a strictly henselian discretely valued field K. In his 1992 paper "Néron models and tame ramification", Edixhoven has constructed a filtration on the special fiber of the Néron model of A that measures the behaviour of the Néron model with respect to tamely ramified extensions of K. The filtration is indexed by rational numbers in [0,1], and if A is wildly ramified, it is an open problem whether the places where it jumps are always rational. I will explain how an interpretation of the filtration in terms of logarithmic geometry leads to explicit formulas for the jumps in the case where A is a Jacobian, which confirms in particular that they are rational. This is joint work with Dennis Eriksson and Lars Halvard Halle.

Sat, 10 Dec 2016

10:00 - 10:30
L5

### Some results on the Signature and Cubature for the fractional Brownian motions for H>1/2

RICCARDO PASSEGGERI
(Imperial College London)
Thu, 24 Nov 2016

16:00 - 17:30
L4

### The Randomised Heston model

Jack Jacquier
(Imperial College London)
Abstract

We propose a randomised version of the Heston model--a widely used stochastic volatility model in mathematical finance--assuming that the starting point of the variance process is a random variable. In such a system, we study the small- and large-time behaviours of the implied volatility, and show that the proposed randomisation generates a short-maturity smile much steeper (`with explosion') than in the standard Heston model, thereby palliating the deficiency of classical stochastic volatility models in short time. We precisely quantify the speed of explosion of the smile for short maturities in terms of the right tail of the initial distribution, and in particular show that an explosion rate of $t^\gamma$ (gamma in [0,1/2]) for the squared implied volatility--as observed on market data--can be obtained by a suitable choice of randomisation. The proofs are based on large deviations techniques and the theory of regular variations. Joint work with Fangwei Shi (Imperial College London)

Mon, 09 May 2016

15:45 - 16:45
C6

### Global quantizations with and without symmetries

MICHAEL RUZHANSKY
(Imperial College London)
Abstract

In this talk we will give an overview of the recent research on global quantizations on spaces of different types: compact and nilpotent Lie groups, general locally compact groups, compact manifolds with boundary.

Fri, 27 May 2016

13:00 - 14:30
L6

### Deep Learning for Modeling Financial Data

Justin Sirignano, postdoc at Imperial College.
(Imperial College London)
Abstract
Deep learning has emerged as one of the forefront areas in machine learning, achieving major success in imaging, speech recognition, and natural language processing. We apply deep learning to two areas in finance: (1) mortgage delinquency and prepayment and (2) limit order books. Using datasets unprecedented in size, we show that deep neural networks outperform several status quo approaches. Due to the heavy computational cost from both the size of the models and the data, we use GPU clusters to train the models.
Tue, 09 Feb 2016

14:00 - 15:00
L4

### Virtual signed Euler characteristics and the Vafa-Witten equations

Richard Thomas
(Imperial College London)
Abstract

I will describe 5 definitions of Euler characteristic for a space with perfect obstruction theory (i.e. a well-behaved moduli space), and their inter-relations. This is joint work with Yunfeng Jiang. Then I will describe work of Yuuji Tanaka on how to this can be used to give two possible definitions of Vafa-Witten invariants of projective surfaces in the stable=semistable case.

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