Ivelina Mladenova

Hi you! I’m Ivelina, but most people call me Eve.

Interested in

1. PhD Related

• Probability & Stochastic Processes
  I’m generally more interested in the analysis of stochastic systems than purely geometric constructions.

• Stochastic Volatility & High-Dimensional Models
  A central theme in my work is modelling correlated stochastic systems, particularly in finance. I’m interested in volatility models such as Heston and Wishart processes, where the covariance structure itself evolves dynamically. More broadly, I like working with models that capture high-dimensional dependence, for example through evolving covariance matrices or integrated covariance processes across multiple assets.

• Numerical Methods for Stochastic PDEs
  Many of these models lead naturally to partial differential equations under some conditions. And for my PhD work I use computational approaches for solving high-dimensional PDEs, including Monte Carlo methods, Fourier pricing techniques, and numerical PDE solvers.

• Neural PDE Solvers & Operator Learning
  Since I need to solve high-dimensional problems, I have spent time learning and trying some modern machine-learning approaches to PDEs and operators, including Physics-Informed Neural Networks (PINNs), Deep Galerkin Methods (DGM), and operator-learning architectures such as DeepONets and Fourier-DeepONets. These approaches combine ideas from functional analysis, numerical analysis, and machine learning to approximate solutions of complex dynamical systems.

• Mathematical Foundations
  But theoretically seaking, many of these topics ultimately connect back to tools from functional analysis, which provides the framework for studying operators, PDEs, and function spaces that arise in stochastic modelling.

2. Personal interests

• Fractal & Fractional Analysis
  I’m also interested in fractal behaviour that appears in stochastic systems and time series. This includes topics such as fractional calculus, fractal derivatives, and processes with long-memory such as fractional Brownian motion. Since I like applied maths, these can be used for modelling rough signals, persistent correlations, and multi-scale phenomena.

• State-Space Models, Kalman Filtering & Particle Filtering
  Since my undergrad I have been interested in filtering and inference in state-space models, including methods such as the Kalman filter and particle filters.

  A particularly challenge is the curse of dimensionality in particle filtering: as the dimension of the state space increases, particle weights tend to collapse (a phenomenon often called particle degeneracy), effectively leaving only one particle with significant weight. I’m curious about current research directions that combine probabilistic modelling with machine learning to address these issues.

• Optimisation & Parameter Inference
  During my undergraduate studies I worked on optimisation-based parameter inference: simulating a simple Hawkes process and then estimating its parameters using the Expectation–Maximisation (EM) algorithm.

• Macroeconomic Time-Series Modelling
  For my MSc project I tested the Generalised Network Autoregressive (GNAR) time series model on a network of interacting macroeconomic variables. The goal was to model relationships between different nodes in the network and use these dynamics to forecast inflation rates.

Leadership:

• Part of Piscopia’s Local Committee.
• QMUL PhD Rep since Nov 2022.
• Lead the Laws, Limits, and Randomness contribution to the History of Maths QMUL.
• Various miscellaneous activities: organise Christmas dinners, social sec of rowing, helping organise the QMUL Undergraduate Research Seminars.