March 3-5, 2020
Place: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences
Type: Educational Workshop
Registration Deadline: February 25, 2020
Prof. Carlos Simpson, CNRS, Université Côte d’Azur, Nice, will give a series of lectures on Hodge theory and local systems in the period March 3-5, 2020. The goal of this educational workshop is to introduce a new cutting edge areas in modern Mathematics and to survey some of the directions of VICHREN GRANT CKGA.
The workshop is supported by the Simons Collaborative Grant – HMS, NRU HSE, RF government grant, ag. 14.641.31.000, Simons Principle Investigator Grant, Bulgarian National Scientific Program “VIHREN”, Project № KP-06-DV-7.
Prof. Carlos Simpson will cover the following topics:
- Kähler manifolds, Laplacians and the Kähler identities
- the Hodge decomposition on cohomology
- smooth morphisms or families of varieties
- monodromy, the Gauss-Manin connection, motivic local systems
- variation of Hodge structures
- Zucker’s theorem: cohomology with coefficients in a VHS
- Norm estimates, nilpotent and SL2-orbit theorems
- character varieties, harmonic bundles and Higgs bundles
- C*-action and deformation to a VHS, spectral curves and the Hitchin fibration
- Dolbeault cohomology with VHS coefficients, Higgs bundle coefficients
- rigid local systems and motivicity conjecture
Other lecturers will be Prof. Alexander Efimov (Steklov Mathematical Institute of the Russian Academy of Sciences, National Research University Higher School of Economics), Prof. Ludmil Katzarkov (University of Miami, USA; Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences; National Research University Higher School of Economics, Russian Federation), Prof. Viсtor Przyjalkowski (Steklov Mathematical Institute of the Russian Academy of Sciences, National Research University Higher School of Economics), Prof. Dmitry Kaledin (Steklov Mathematical Institute of the Russian Academy of Sciences and National Research University Higher School of Economics, Russian Federation).
They will give lectures on the following topics:
Prof. Viсtor Przyjalkowski: Geometry of Landau-Ginzburg Models
Abstract: We discuss geometric and numerical properties of Landau-Ginzburg models of Fano varieties that reflect geometric and numerical properties of the initial Fano varieties. The main example is the threefold case.
Prof. Alexander Efimov: Overview of Non-commutative Hodge to de Rham Degeneration and its Generalizations
Abstract: We will recall the statement of Hodge to de Rham degeneration conjecture (which is now Kaledin’s theorem) and our counterexamples to its generalized versions formulated by Kontsevich.
Prof. Ludmil Katzarkov: Some Applications of Non-commutative Hodge Structures
Abstract: We will consider some applications of non-commutative Hodge structures to birational geometry.
Prof. Dmitry Kaledin: Motivic Structures in Non-commutative Geometry
Abstract: I am going to give an overview of various motivic structures that appear in non-commutative geometry with an emphasys on recent results (especially in p-adic Hodge theory).
Programme
03.03.2020 | 04.03.2020 | 05.03.2020 |
---|---|---|
08:30 – 09:00 Registration
09:00 – 09:30 Opening ceremony 09:30 – 10:30 C. Simpson Coffee break 11:00 – 12:00 C. Simpson Lunch 14:30 – 15:30 V. Przyjalkowski 16:00 Office Hours 17:00 Welcome party |
09:00 – 10:00 C. Simpson
Coffee break 10:30 – 11:30 C. Simpson Lunch 14:30 – 15:30 D. Kaledin Coffee break 16:00 – 17:00 L. Katzarkov |
09:00 – 10:00 C. Simpson
Coffee break 10:30 – 11:30 C. Simpson Lunch 14:30 – 15:30 A. Efimov 16:00 Office Hours |
Recordings
Usefull Information
The opening ceremony of the workshop “Hodge Theory and Local Systems” will be in:
Hall 256, 2-nd floor
Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences
Sofia, Acad. G Bonchev str., bl 8
The workshop will be held in:
Hall 403, 4-th floor
Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences
Sofia, Acad. G Bonchev str., bl 8
https://goo.gl/maps/X7BoSAstaWPxd2zr8
https://goo.gl/maps/VLZYuw2Hv3LRJeYq8
https://goo.gl/maps/dRazoPrpZWVvCo326
When in hall 403, connect freely to icms.bg_Guest
Hotel Europa
“Geo Milev” district, 1 “Liditse” str.Google Maps: https://goo.gl/maps/4krzZGm2cuGKA2Pa8 Phone:
++359 2 970 1500 Website:
http://www.hotel-europe-bg.com/en/
Hotel Rai
“Geo Milev” district, 6 “acad. Nikola Obreshkov” str.Google Maps: https://goo.gl/maps/MgtEkAK4DyD5YCGJ6 Phone:
++359 2 971 1443 Website:
https://www.hotel-rai.com/indexen.html
Transportation
The most convenient way to get your hotel from the airport is by taxi. Once you leave the baggage claim hall, turn right. There is a taxi rank of the company OK Super Trans outside of the building (the desk of this company is just across the hall). The fare to your hotel is about 10-12 leva (5-6 euro). Do not use a taxi offered by individuals.
The public transportation is also convenient and is cheaper (ticket price per one trip is 1.60 leva). Ask the information desk for the details if you want to take a bus.
The Institute of Mathematics and Informatics is not far from your hotel:
https://goo.gl/maps/X7BoSAstaWPxd2zr8
- Tamas Agoston, Alfréd Renyi Institute of Mathematics, Budapest, Hungary
- Bogdan Alexandrov, Sofia University, Bulgaria
- Lyubomir Andreev, Sofia University, Bulgaria
- Anxhela Beluli, American University in Bulgaria, Blagoevgrad, Bulgaria
- Iavor Boradjiev, Institute of Solid State Physics, Bulgarian Academy of Sciences, Sofia, Bulgaria
- Vilislav Boutchaktchiev, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
- Marina Chomakova, Sofia University, Bulgaria
- Peter Dalakov, American University in Bulgaria, Blagoevgrad and Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
- George Dimitrov, University of Vienna
- Vladimir Dobrev, Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria
- Deyan Dzhundrekov, Sofia University, Bulgaria
- Veselin Filev, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
- Ilia Gaiur, School of Mathematics at University of Birmingham, UK
- Alexander Ganchev, American University in Bulgaria, Blagoevgrad and Institute for Nuclear Research and Nuclear Energy, Sofia
- Tatiana Gateva-Ivanova, American University in Bulgaria, Blagoevgrad, Bulgaria
- Igor Gutorov, American University in Bulgaria, Blagoevgrad, Bulgaria
- Kiril Hristov, Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria
- Milen Hristov, University of Veliko Turnovo, Bulgaria
- Elitza Hristova, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
- Nikolay Ikonomov, Institute of Mathematics and Informatics, Sofia, Bulgaria
- Hristo Iliev, American University in Bulgaria, Blagoevgrad and Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
- Antonia Kaisheva, American University in Bulgaria, Blagoevgrad, Bulgaria
- Azniv Kasparian, Sofia University, Bulgaria
- Boyan Kugiyski, Sofia University, Bulgaria
- Sergey Litvinenko, American University in Bulgaria, Blagoevgrad, Bulgaria
- Mario Maican, Institute of Mathematics of the Romanian Academy, Bucharest, Romania
- Vladislava Milenković (Stanković), University of Niš, Serbia
- Dimitar Mladenov, Sofia University, Bulgaria
- Janos Nagy, Alfréd Renyi Institute of Mathematics, Budapest, Hungary
- Nikolay Nikolov, Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria
- Vitantonio Peragine, Geometry and Mathematical Physics, SISSA, Trieste, Italy
- Peter Petrov, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences and University of Transport, Sofia, Bulgaria
- Nikola Stanchev, Sofia University, Bulgaria
- Mića Stanković, University of Niš, Serbia
- Veronika Starodub, American University in Bulgaria, Blagoevgrad, Bulgaria
- Miroslav Stoenchev, Sofia University, Bulgaria
- Veselina Tavkova, Plovdiv University, Bulgaria
- Berkan Uze, Bogazici University, Istanbul, Turkey
- Yulian Tsankov, Sofia University, Bulgaria
- Stanislav Varbev, Institute of Solid State Physics, Bulgarian Academy of Sciences, Sofia, Bulgaria
- Stanislav Velkov, Sofia University, Bulgaria
- Nenad Vesić, University of Niš, Serbia
- Tsvetan Vetsov, Sofia University, Bulgaria
- Milos Vukadinovic, American University in Bulgaria, Blagoevgrad, Bulgaria
- Ivan Yakovlev, Higher School of Economics and Skolkovo Institute of Science and Technology, Moscow, Russia
- Milan Zlatanovic, University of Niš, Serbia
- Pál Zsámboki, Alfréd Rényi Institute of Mathematics, Budapest, Hungary