Third Annual Meeting of Young Bulgarian Mathematicians

Event dates:

July 13-14, 2023

Event type:

In person

The International Center for Mathematical Sciences – Sofia is organizing for a third consecutive year a meeting of young Bulgarian mathematicians from around the world.

The conference will take place at the Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences (IMI-BAS) on July 13 – 14, 2023. It is a satellite event of the conference Mathematics Days in Sofia.

Special guest of the event is Prof. Martin Vechev from ETH Zurich and INSAIT. Martin Vechev is a Full Professor at the Department of Computer Science at ETH Zurich where he leads the Secure, Reliable and Intelligent Systems Lab (https://www.sri.inf.ethz.ch/). His main research interests lie at the intersection of machine learning, probabilistic reasoning and programming languages. Prior to ETH, he was a Research Staff Member at the IBM T. J. Watson Research Center in New York, USA and he obtained his PhD from Cambridge University, England. He is the recipient of numerous scientific awards including the ACM SIGPLAN Robin Milner Award for outstanding contributions to programming languages and his research has been awarded with two ERC grants (Starting and Consolidator). He is a co-founder of 3 deep-tech companies and the architect and scientific director of INSAIT (https://insait.ai), a new computer science and AI institute in Sofia, Bulgaria founded in partnership with ETH Zurich and EPFL.

We envision two main outcomes of this meeting:

  • Enriching the relations between young mathematicians working in Bulgaria and the Bulgarian mathematical diaspora;
  • Enhancing the professional development of young Bulgarian mathematicians by presenting to them new career opportunities through national and European scientific programs.
Programme Committee
  • Prof. Oleg Mushkarov, IMI-BAS
  • Dr. Antoni Rangachev, IMI-BAS

Invited speakers

Martin Vechev

ETH Zurich and INSAIT

Borislav Mladenov

UC Berkeley, USA

Ina Petkova

Dartmouth College, USA

Nikola Konstantinov

INSAIT, Bulgaria

Stoyan Apostolov

Sofia University, Bulgaria

Stoyan Dimitrov

Rutgers University, USA

Programme

July 13, 2023

14:00 – 14:05 Opening Session

Deep Learning with Guarantees

Abstract: Creating deep learning models that are provably robust, fair and secure is a fundamental challenge of societal importance. In this lecture I will discuss some of the latest and most promising research results and future directions we are exploring towards addressing this challenge. These directions include both new verification techniques based on convex relaxations and branch-and-bound methods as well as new certified training methods and optimization problems which produce more verifiable machine learning models.

Knot Floer homology and contact knot theory

Abstract: A knot is a circle in 3-space. A main problem in knot theory is distinguishing knots (two knots are equivalent if we can continuously deform one into the other).  One way to approach this is by studying algebraic “knot invariants” — algebraic objects associated to knots, which do not change as the knot is deformed. In 1928, J. Alexander described a knot invariant, now called the Alexander polynomial. In the early 2000s, Ozsváth and Szabó constructed a refinement of the Alexander polynomial, called knot Floer homology. We will sketch definitions of both invariants, and mention some of their applications. We will finish by discussing a recent application to low-dimensional contact topology (joint with Jubeir, Schwartz, Winkeler, and Wong).

15:35 – 16:00   Coffee break

Seiberg-Witten duality for hyperkähler manifolds, deformation quantisation and formality of differential graded algebras associated to holomorphic Lagrangians

Abstract: I will start by explaining Kapustin’s Seiberg-Witten conjectural duality between A and B-branes on hyperkähler manifolds. I will use this conjectural framework and work of Ivan Smith and Solomon-Verbitsky on the A side to motivate results and explicit conjectures on the B side. In particular, I will calculate the space which counts massless open strings connecting a Lagrangian D-brane wrapped on a holomorphic Lagrangian L to itself with suitable gauge bundles. This space is the cohomology of a differential graded algebra. I will state a formality result for this dga and, time permitting, mention various generalisations to pairs of Lagrangians, DG categories and some open questions.

July 14, 2023

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Why would you want to count? Problems and results illustrating a set of reasons.

Abstract: While counting questions were among the first that people asked and pursued, the branch of enumerative combinatorics is relatively new. We will discuss some recent results on various enumerative questions, illustrating applications of different kinds in theoretical computer science and statistics. The talk will be for the general audience.

Statistical Aspects of Trustworthy Machine Learning

Abstract: Modern machine learning methods often require large amounts of labeled data for training. Therefore, it has become a standard practice to collect data from external sources, e.g. via crowdsourcing, by web crawling or through collaboration with other institutions. Unfortunately, the quality of these sources is not always guaranteed and this may results in noise, biases and even systematic manipulations entering the training data.

In this talk I will present some results on the statistical limits of learning in the presence of training data corruption. In particular, I will speak about the hardness of achieving algorithmic fairness when a subset of the data is prone to adversarial manipulations. I will also discuss several results on the sample complexity of learning from multiple unreliable data sources. Finally, I will present recent work that provides statistical and stochastic optimization guarantees for collaborative learning in the presence of conflicting participants’ incentives.

15:30 – 16:00   Coffee break

Transversality Concepts in Variational Analysis

Abstract: We investigate the most important transversality concepts in variational analysis. We talk about some of the motivation behind them and their applications. We derive new, metric style characterizations, in a unified manner, which also establishes previously unknown relations between them. This also shows that while some of them are originally defined relying on the dual structure of the space, they are essentially metric properties. We also use these characterizations to prove in a new way characterizations of the respective metric regularity counterparts. In this way, it is essentially seen, that one can build the theory starting from transversality, rather than regularity (as was originally done).

Supported by the Ministry of Education and Science of the Republic of Bulgaria through the Scientific Programme “Enhancing the Research Capacity in Mathematical Sciences (PIKOM)”, Agreement № DO1-67/05.05.2022