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These lectures will present a board survey of recent work on new q-series invariants of 3-manifolds labeled by Spin-C structures. While the original motivation for studying these invariants is rooted in topology, they exhibit a number of unexpected properties and connections to other areas of mathematics, e.g. turn out to be characters of logarithmic vertex algebras. The integer coefficients of these q-series invariants can be understood as the answer to a certain enumerative problem, and when q tends to special values these invariants relate to other invariants of 3-manifolds labeled by Spin and Spin-C structures.
From Turaev to Rokhlin via VOA Characters and Curve Counting, by Sergey Gukov
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We will start these series by reviewing the general framework of geometric Langlands correspondence, and state the main conjectures in the de Rham and Betti settings. We will also recall V. Lafforgue's theorem about the spectral decomposition in the classical Langlands over function fields. We will then proceed to the formulation of "restricted" Langlands correspondence, which unifies the different contexts. We will state the restricted version of the geometric Langlands conjecture, and explain its relation with the classical Langlands conjecture via the operation of categorical trace.
Geometric Langlands, by Dennis Gaitsgory
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One of the key developments in combinatorics and algebra of recent years has been the discovery of Lefschetz principles beyond Hodge structures, resolving several long-standing conjectures. I will provide an overview of recent developments, and discuss joint work with Johanna Steinmeyer, Stavros Papadakis and Vasiliki Petrotou.
Lefschetz theorems beyond Hodge structures, by Karim Adiprasito

About us

The newly established International Center for Mathematical Sciences – Sofia is a dynamic research unit  for developing and dissemination of cutting edge new directions in Mathematics. It is affiliated with the Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences which is providing the infrastructure for the activities of the Center. The Center is supported by the Ministry of Education and Science of the Republic of Bulgaria. The Activities of the ICMS – Sofia are carried out in collaboration with the Institute of the Mathematical Sciences of the Americas at the University of Miami (IMSA) and Higher School of Economics, National Research University, Moscow (HSE University). The ICMS-Sofia is also working in collaboration with Bulgarian universities and institutes of the Bulgarian Academy of Sciences.

The Center was created following inspirational discussions with many members of the mathematical community in Bulgaria and the Bulgarian mathematical diaspora. In July 2019,  ICMS-Sofia initiated its full-scale presence on the European mathematical scene with the full support of Acad. Julian Revalski, President of the Bulgarian Academy of Sciences.

The first director of ICMS-Sofia was Acad. Blagovest Sendov.

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Events and activities

Annual conference

Women in Mathematics in South-Eastern Europe

2020
2021
2022

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.

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Annual conference

The Annual Meeting of Young Bulgarian Mathematicians

2021

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.

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Selected Activities 2020-2021

Sendov’s conjecture for sufficiently high degree polynomials

by Terrence Tao, University of California, Los Angeles (UCLA) |
January 26, 2021

Colloquium talk in memory of Acad. Blagovest Sendov by Terence Tao, University of California, Los Angeles (UCLA.) Winner of the Fields Medal 2006, the Breakthrough Prize in Mathematics 2014, the Crafoord Prize 2012.

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Hodge Theory and Local Systems

by Carlos Simpson, CNRS, Université Côte d’Azur, Nice |
March 3-5, 2020

Prof. Carlos Simpson, Alexander Efimov, Ludmil Katzarkov, Viсtor Przyjalkowski and Dmitry Kaledin gave series of lectures on Hodge theory and local systems in the period March 3-5, 2020

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ICMS-IMSA Working Seminar

by Rene Mboro, Rodolfo Aguilar, ICMS-Sofia and IMSA |
August 20, 2021

Prof Rene Mboro gave a talk On determinantal cubic hypersurfaces (after Iliev-Manivel, Beauville,…) Prof Rodolfo Aguilar gave a talk on Quantum representations of fundamental groups of curves with infinite image. 

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Lectures of Steven Cantrel and Mina Teicher

by Robert Steven Cantrel, IMSA and Mina Teicher, |
June 30, 2021

Prof Robert Steven Cantrel gave a talk A Journey from Math to Biology and Back Again … and Again and prof. Mina Teicher gave a talk The Mathematics of Beauty

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News

Homological Mirror Symmetry and Applications

January 21st, 2021|

ICMS invites you to attend the virtual conference Homological Mirror Symmetry and Applications, January 19 – 22, 2021. Jointly organized with the Institute of the Mathematical Sciences of the Americas at the University of Miami (IMSA)

Noncommutative Geometry Conference

December 15th, 2020|

In 2020 Alexander Efimov, a Research Fellow at the International Laboratory for Mirror Symmetry and Automorphic Forms (HSE University) and a Senior Researcher at the Algebraic Geometry Section of Steklov Mathematical Institute of RAS, has been awarded by the European Mathematical Society’s Prize.

Our esteemed collaborators

Carlos Simpson
Alexander Efimov
Victor Przyjalkowski
,
Yu-We Fan
Ivan Cheltsov
Maxim Kontsevich
Artan Sheshmani
Ernesto Lupercio
Tony Yue YU