The Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences (IMI-BAS) announces a temporary postdoctoral position, funded by the Bulgarian Scientific Programme “Enhancing the Research Capacity in Mathematical Sciences” (PIKOM). The duration of the position is 12 months under the programme. The starting date is October 1, 2024, but it is flexible. Working language is English or Bulgarian.

The following research topics are available, although excellent candidates with strong track record are also invited to suggest a topic of their own.

Topic 1: Stochastic processes, special functions, exponential functionals

Annotation: Successful candidates will work in the research group of Prof. Mladen Savov, which has expertise in Lévy processes, semi-Markov processes, random measures, reinforced processes, exchangeable sequences, etc. Depending on the preferences and/or background of the candidates, the work may be theoretical, relying on heavy analytical apparatus, or applied, being related to financial mathematics, Bayesian statistics, etc.

Advisor: Prof. Mladen Savov

Topic 2: Computational topology of solitons

Annotation: The well-established research area of algebraic topology currently goes interdisciplinary with computer science in many directions. The Topological Data Analysis gives new opportunities in visualization for modeling and special mapping. A study on metrics used or simplicial complexes are reliable for future results in the area of mathematics.

Today, the machine learning from one side is a tool for the analysis in topology optimization, topological persistence and optimal homology problems, from other side the topological features in machine learning are new area of research, topological layers in neural networks, topological autoencoders, and topological analysis for the evaluation of generative adversarial networks are in general aspects of topology machine learning.

On practical point of view, the results in this area are important for solitary-like waves research, biomedical Image analysis, neuroscience, physics and many others.

That gives us opportunity to establish and scale up an interdisciplinary team of researchers to apply for funding for fundamental science research in interdisciplinary field.

Advisors: Prof. D.Sc. Sevdzhan Hakkaev (Mathematics), PhD; Assoc. Prof. Galina Momcheva, PhD (Computer Science)

Topic 3: Codes and designs in polynomials metric spaces

Annotation: Derivation and investigation of universal bounds for parameters of codes and designs in polynomial metric spaces with the Euclidean spheres, projective spaces, the Hamming and Johnson spaces as major examples.

Advisor: Prof. Peter Boyvalenkov

Topic 4: Optimal management of constrained distributed systems

Annotation: For the last two decades we are seeing a massive adoption of many, heterogeneous (complex and constraint), stationary and mobile hardware devices across the globe, which are connected between each other with different types of networks, forming the nowadays distributed systems such as Cloud/Edge/Fog/Swarm platforms. The optimal management of the computational (CPU, GPU, memory) and network (latency, bandwidth) resources in them is complex task (NP-hard), which is tackled by different approaches such as math optimization (Integer-Linear Programming), artificial intelligence (Reinforcement Learning, deep neural networks) and heuristics-based algorithms. My aim is to analyze and solve the above problem not only on a theoretical and simulation level, but in practice - on a real-world hardware clusters, using the latest technology stack. Additional aim is to harness the potential of the distributed resources for execution of novel high-demand applications, like deep neural networks and Large Language Models (LLM) on top of constrained devices, which problem is tackled by quantization and parallelization.

Advisor: Assoc. Prof. Hristo Kostadinov

Topic 5: Birational geometry

Annotation: This is a joint position with the Institute of the Mathematical Sciences of the Americas at the University of Miami (IMSA). The candidate will spend 2 semesters in the International Center for Mathematical Sciences – Sofia (ICMS-Sofia), https://icms.bg/, which is affiliated with the Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences, and 2 semesters in the Institute of the Mathematical Sciences of the Americas at the University of Miami (IMSA), https://www.imsa.miami.edu/.

The project includes further developments of the recently introduced new birational invariants by L. Katzarkov and M. Kontsevich - atoms. The connection between these invariants and the topological modular forms will be studied.

The candidate should have a good knowledge of birational geometry (over different fields).

Advisor: Prof. Ludmil Katzarkov

Topic 6: Modeling of quality in service systems

Annotation: Quality of Service (QoS) prediction in next-generation smart informational service networks: overall human-machine interaction (including users, service providers and technical means), computing, telecommunications, cloud, with smart informational services, with the studies of the connections between QoS and QoE (Quality of Experience) which are necessary for the prediction of the users’ behavior and overall system performance management.

The main goal is the development of theory, models and tools for quality prediction in overall systems (holistic systems) for informational services, which allow fast, convenient and most accurate quality determination for the purposes of design, re-dimensioning and operational management of next generation smart networks.

Advisor: Assoc. Prof. Velin Andonov, PhD.

How to apply: The interested candidates should provide a CV, list of publications, and a research statement sent to pdj@math.bas.bg with a copy to director@math.bas.bg   by July 26, 2024. They should also arrange for two letters of recommendation to be sent by the referees to the same addresses. The application must point out on which of the topics above you'd like to work, or state explicitly that you suggest another topic.