Forthcoming Seminars

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series
20 April 2021
10:00
to
11:30
Dr. Avi Mayorcas

Further Information: 

Structure: 4 x 1.5hr Lectures 

Lecture 1:  Introduction and Preliminaries

  • Introduction to randomness in PDE
  • Stochastic analysis in infinite dimensions
Abstract

The course will aim to provide an introduction to stochastic PDEs from the classical perspective, that being a mixture of stochastic analysis and PDE analysis. We will focus in particular on the variational approach to semi-linear parabolic problems, `a  la  Lions. There will also be comments on  other models and approaches.

  Suggested Pre-requisites: The course is broadly aimed at graduate students with some knowledge of PDE theory and/or stochastic  analysis. Familiarity with measure theory and functional analysis will be useful.

Lecture 1:  Introduction and Preliminaries

  • Introduction to randomness in PDE
  • Stochastic analysis in infinite dimensions

Literature: [DKM+09, Hai09, Par07, PR07, DPZ14]

Lecture 2: Variational Approach to Deterministic PDE

  • Variational approach to linear parabolic equations
  • Variational approaches to non-linear parabolic equations

Literature: [Par07, Eva10]

Lecture 3: Variational Approach to Parabolic SPDE

  • Itˆo’s formula in Hilbert spaces
  • Variational approach to monotone, coercive SPDE
  • Concrete examples

Literature: [PR07, Par07]

Lecture 4: Further Topics and Directions (time permitting)

  • Regularity of solutions
  • Ergodicity
  • Pathwise approach to SPDE

Literature: [Hai09, DKM+09, DPZ96, Hai14, GIP15]

References

[DKM+09] Robert Dalang, Davar Khoshnevisan, Carl Mueller, David Nualart, and Yimin Xiao. A minicourse on stochastic partial differential equations, vol- ume 1962 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 2009.

[DPZ96] G. Da Prato and J. Zabczyk. Ergodicity for Infinite Dimensional Systems. London Mathematical Society Lecture Note Series. Cambridge University Press, 1996.

[DPZ14] Giuseppe Da Prato and Jerzy Zabczyk. Stochastic Equations in Infinite Dimensions. Encyclopedia of Mathematics and its Applications. Cambridge University Press, 2 edition, 2014.

[Eva10] Lawrence Craig Evans. Partial Differential Equations. American Mathe- matical Society, 2010.

[GIP15] Massimiliano Gubinelli, Peter Imkeller, and Nicolas Perkowski. Paracon- trolled distributions and singular PDEs. Forum Math. Pi, 3:75, 2015.

[Hai09]  Martin Hairer.  An Introduction to Stochastic PDEs.  Technical  report, The University of Warwick / Courant Institute, 2009. Available at: http://hairer.org/notes/SPDEs.pdf

[Hai14] M. Hairer. A theory of regularity structures. Inventiones mathematicae, 198(2):269–504, 2014.

[Par07] Etienne  Pardoux. Stochastic  partial  differential  equations.  https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.405.4805&rep=rep1&type=pdf  2007.

[PR07] Claudia Pr´evˆot and Michael R¨ockner. A concise course on stochastic partial differential equations. Springer, 2007.

The join button will be published on the right (Above the view all button) 30 minutes before the seminar starts (login required).

21 April 2021
09:00
Abstract

Path signature has unique advantages on extracting high-order differential features of sequential data. Our team has been studying the path signature theory and actively applied it to various applications, including infant cognitive score prediction, human motion recognition, hand-written character recognition, hand-written text line recognition and writer identification etc. In this talk, I will share our most recent works on infant cognitive score prediction using deep path signature. The cognitive score can reveal individual’s abilities on intelligence, motion, language abilities. Recent research discovered that the cognitive ability is closely related with individual’s cortical structure and its development. We have proposed two frameworks to predict the cognitive score with different path signature features. For the first framework, we construct the temporal path signature along the age growth and extract signature features of developmental infant cortical features. By incorporating the cortical path signature into the multi-stream deep learning model, the individual cognitive score can be predicted with missing data issues. For the second framework, we propose deep path signature algorithm to compute the developmental feature and obtain the developmental connectivity matrix. Then we have designed the graph convolutional network for the score prediction. These two frameworks have been tested on two in-house cognitive data sets and reached the state-of-the-art results.

The join button will be published on the right (Above the view all button) 30 minutes before the seminar starts (login required).

21 April 2021
10:00
to
11:30
Dr. Avi Mayorcas

Further Information: 

Structure: 4 x 1.5hr Lectures 

Lecture 2: Variational Approach to Deterministic PDE

  • Variational approach to linear parabolic equations
  • Variational approaches to non-linear parabolic equations
Abstract

The course will aim to provide an introduction to stochastic PDEs from the classical perspective, that being a mixture of stochastic analysis and PDE analysis. We will focus in particular on the variational approach to semi-linear parabolic problems, `a  la  Lions. There will also be comments on  other models and approaches.

  Suggested Pre-requisites: The course is broadly aimed at graduate students with some knowledge of PDE theory and/or stochastic  analysis. Familiarity with measure theory and functional analysis will be useful.

The join button will be published on the right (Above the view all button) 30 minutes before the seminar starts (login required).

26 April 2021
16:00
THALEIA ZARIPHOPOULOU
Abstract

 

In my talk, I will introduce a family of human-machine interaction (HMI) models in optimal portfolio construction (robo-advising). Modeling difficulties stem from the limited ability to quantify the human’s risk preferences and describe their evolution, but also from the fact that the stochastic environment, in which the machine optimizes, adapts to real-time incoming information that is exogenous to the human. Furthermore, the human’s risk preferences and the machine’s states may evolve at different scales. This interaction creates an adaptive cooperative game with both asymmetric and incomplete information exchange between the two parties.

As a result, challenging questions arise on, among others, how frequently the two parties should communicate, what information can the machine accurately detect, infer and predict, how the human reacts to exogenous events, how to improve the inter-linked reliability between the human and the machine, and others. Such HMI models give rise to new, non-standard optimization problems that combine adaptive stochastic control, stochastic differential games, optimal stopping, multi-scales and learning.

 

 

  • Stochastic Analysis & Mathematical Finance Seminars
27 April 2021
10:00
to
11:30
Dr. Avi Mayorcas

Further Information: 

Structure: 4 x 1.5hr Lectures 

Lecture 3: Variational Approach to Parabolic SPDE

  • Itˆo’s formula in Hilbert spaces
  • Variational approach to monotone, coercive SPDE
  • Concrete examples
Abstract

The course will aim to provide an introduction to stochastic PDEs from the classical perspective, that being a mixture of stochastic analysis and PDE analysis. We will focus in particular on the variational approach to semi-linear parabolic problems, `a  la  Lions. There will also be comments on  other models and approaches.

  Suggested Pre-requisites: The course is broadly aimed at graduate students with some knowledge of PDE theory and/or stochastic  analysis. Familiarity with measure theory and functional analysis will be useful.

The join button will be published on the right (Above the view all button) 30 minutes before the seminar starts (login required).

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