In this talk, aimed at a general audience, we will describe recent results on the characterization of norm forms—a classical object in algebraic number theory—in terms of their values at integer points. These results answer natural questions and are related to still-open conjectures of Littlewood (from 1930) and of Cassels and Swinnerton-Dyer (from 1955). The proofs rely on studying the actions of maximal tori of algebraic groups on homogeneous spaces of arithmetic origin.
Aiming to understand the relation to other "refined invariants", and especially their possible interpretation in quantum theory, we explain how to obtain a quadratic, A1-version of Donaldson-Thomas invariants from the motivic refinements first introduced in Kontsevich-Soibelman. Following ideas from Behrend, Bryan and Szendroi, we provide predictions for these invariants in a few simple examples, mainly the computation of DT invariants of A3. Our main goal is to draw relationships with the literature, including works of Levine, Denef and Loser, Azouri, Pepin-Lehaulleur, Srinivas among others. We begin with a brief introduction to A1-enumerative geometry and in the end, we pose some further questions on possible extensions of our definitions. This is joint work with Johannes Walcher. We also comment on joint work in progress with Ran Azouri.
In this talk we will explain the role that the Lie algebras play in the construction of 6-dimensional compact quotient spaces M=G/Γ, where Γ is a lattice, endowed with an invariant complex structure with holomorphically trivial canonical bundle.
Affine geometry is sometimes described as "what remains of Euclidean geometry when distances are forgotten". In this talk, I will report on a very recent discovery of an affine-invariant notion, which may be viewed as a distance from a point inside a convex domain to its boundary. This new concept stems from a suggestion of Conan Leung, who proposed to average the canonical tropical series, a fundamental notion of tropical optics, over the manifold of all tropical structures of fixed covolume on the given affine space. Very little of what we (Nikita Kalinin, Ernesto Lupercio and me) currently know, as well as necessary preliminaries, some observations and precise conjectures, will be covered during the talk, which mainly serves as an invitation to participate in developing this exciting new topic.
Simons Foundation
Grant 2022-2025
The Simons Foundation International, Ltd., (SFI) is funding a project of the International Center for Mathematical Sciences for the period 2022 – 2025.
The grant is aimed at supporting displaced scientists from Ukraine and other countries, organizing international scientific events with the participation of world-renowned and established mathematicians, and opening new research positions for young scientists.
Upcoming Events
- 30 April 2025 @ 16:00 - 17:30 EEST
Lecture Outline 1. Introduction to Binary Quadratic Forms and Conway’s Topographs. We will begin with the basics of binary quadratic forms and their classification, followed by an introduction to Conway’s topographs—a visual and geometric framework for understanding them.
- 7 May 2025 @ 16:00 - 17:30 EEST
Lecture Outline 2. Class Number Formula and Summation over Topographs. Building on the first lecture, we will explore the class number formula and how summation identities arise naturally from the structure of topographs.
- 14 May 2025 @ 16:00 - 17:30 EEST
Lecture Outline 3. Evaluation of Lattice Sums via Telescoping over Topographs. The final lecture will focus on telescoping techniques, demonstrating how they can be used to evaluate intricate lattice sums—such as the one above—with geometric meaning.
Special Announcement:
The Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences (IMI-BAS) announces four temporary (5-year) positions for R4 Leading researchers (Chairs), who are at the career stage at which they are already established leaders with a recognized track record of research achievements. The approved researchers will be affiliated with the International Center for Mathematical Sciences – Sofia (ICMS-Sofia), which is part of the Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences. The positions are financially supported by Simons Foundation grant and funds from the Ministry of Education and Science of the Republic of Bulgaria.
The goal is:
- acceleration of progress in mathematics,
- acceleration of ICMS-Sofia reputation worldwide,
- establishing ICMS-Sofia as a leading regional scientific center producing a pipeline for Bulgarian and international talents,
- expanding ICMS-Sofia influence to society in Bulgaria at large in outreach activities and integration with industry.
The approved Chairs must establish their own research groups, consisting of an established researcher, a postdoc, and/or a PhD student. The Chairs need to ensure a high international visibility of the research groups obtaining major results in hot areas of mathematics in the first 5 years. The Chair’s contract can be extended for another 5 years or lead to a permanent position in IMI-BAS.
The selection process will be done by a Recruitment committee and the final selection will be approved by the ICMS Advisory Board.
An evaluation by the above committee will be made after third (Intermediate Report) and fifth year (Final Report). The contracts will be extended upon the committee decision.
Payment to the Leading Researcher/Chair: up to 4800 EUR (9388 BGN) per month. The corresponding social insurance contributions due by the employer are not included in the above amount. Competitive salaries will be provided to the team members (senior staff, postdocs and PhD students). IMI-BAS will appoint the Chair and the team members under an employment contract.
Additionally, each research group will be offered an attractive amount of money for visitors and conferences.
Starting date is planned to be September 1, 2024, the earliest, but it can be negotiated if needed. The working language is English or Bulgarian.
Additional information will be available upon request.
Applications can be made in any field of the contemporary fundamental and applied Mathematics. There are no restrictions on the applicant’s nationality and gender.
Interested candidates should provide a CV, list of publications, and a project description (up to 10 pages). Letters of recommendation are not required but will be considered if provided. Please, send your applications by E-mail to director@math.bas.bg.
Deadline: Applications completed by July 31, 2024 will be given full consideration, although applications will be accepted until all positions are filled.
Annual conferences
Annual conference
Women in Mathematics in South-Eastern Europe
The mission of the initiative Women in Mathematics in South-Eastern Europe is to promote the role of female mathematicians.
The mission will be achieved through series of annual conferences with the main goal to celebrate women in Mathematics, to disseminate new results and create new long-term collaborations among scientists in South-Eastern Europe. We hope Women in Mathematics of South-Eastern Europe will attract the attention of young researchers and researchers from less-favoured countries.
The inaugural conference of the initiative Women in Mathematics in South-Eastern Europe took place in Dec 2020. A special distinguished guest of the inaugural conference was prof. Mina Teicher from the Department of Mathematics and Gonda Brain Research Center, Bar-Ilan University, Israel. Prof Teicher is also Director of Emmy Noether Institute for Mathematics.
Annual conference
The Annual Meeting of Young Bulgarian Mathematicians
This meeting has as its main objective bringing together young Bulgarian mathematicians working all over the world.
We envision two main outcomes:
- enriching relations between young mathematicians working in Bulgaria and the Bulgarian mathematical diaspora;
- enhancing the professional development of young Bulgarian mathematicians by presenting new opportunities using the national and European scientific programmes.
The inaugural event of the series was held May 19-20 2021 and commemorated the brightest Bulgarian holiday the Day of Bulgarian Enlightenment and Culture and the Slavоnic Alphabet May 24.
