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

Useful 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

Google Maps location of the Institute:
https://goo.gl/maps/X7BoSAstaWPxd2zr8

We recommend the following route from hotel Rai to the Institute:
https://goo.gl/maps/VLZYuw2Hv3LRJeYq8

We recommend the following route from hotel Europa to the Institute:
https://goo.gl/maps/dRazoPrpZWVvCo326

Wi-Fi SSID:
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

  1. Tamas Agoston, Alfréd Renyi Institute of Mathematics, Budapest, Hungary
  2. Bogdan Alexandrov, Sofia University, Bulgaria
  3. Lyubomir Andreev, Sofia University, Bulgaria
  4. Anxhela Beluli, American University in Bulgaria, Blagoevgrad, Bulgaria
  5. Iavor Boradjiev, Institute of Solid State Physics, Bulgarian Academy of Sciences, Sofia, Bulgaria
  6. Vilislav Boutchaktchiev, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
  7. Marina Chomakova, Sofia University, Bulgaria
  8. Peter Dalakov, American University in Bulgaria, Blagoevgrad and Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
  9. George Dimitrov, University of Vienna
  10. Vladimir Dobrev, Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria
  11. Deyan Dzhundrekov, Sofia University, Bulgaria
  12. Veselin Filev, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
  13. Ilia Gaiur, School of Mathematics at University of Birmingham, UK
  14. Alexander Ganchev, American University in Bulgaria, Blagoevgrad and Institute for Nuclear Research and Nuclear Energy, Sofia
  15. Tatiana Gateva-Ivanova, American University in Bulgaria, Blagoevgrad, Bulgaria
  16. Igor Gutorov, American University in Bulgaria, Blagoevgrad, Bulgaria
  17. Kiril Hristov, Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria
  18. Milen Hristov, University of Veliko Turnovo, Bulgaria
  19. Elitza Hristova, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
  20. Nikolay Ikonomov, Institute of Mathematics and Informatics, Sofia, Bulgaria
  21. Hristo Iliev, American University in Bulgaria, Blagoevgrad and Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
  22. Antonia Kaisheva, American University in Bulgaria, Blagoevgrad, Bulgaria
  23. Azniv Kasparian, Sofia University, Bulgaria
  24. Boyan Kugiyski, Sofia University, Bulgaria
  25. Sergey Litvinenko, American University in Bulgaria, Blagoevgrad, Bulgaria
  26. Mario Maican, Institute of Mathematics of the Romanian Academy, Bucharest, Romania
  27. Vladislava Milenković (Stanković), University of Niš, Serbia
  28.  Dimitar Mladenov, Sofia University, Bulgaria
  29. Janos Nagy, Alfréd Renyi Institute of Mathematics, Budapest, Hungary
  30. Nikolay Nikolov, Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria
  31. Vitantonio Peragine, Geometry and Mathematical Physics, SISSA, Trieste, Italy
  32. Peter Petrov, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences and University of Transport, Sofia, Bulgaria
  33.  Nikola Stanchev, Sofia University, Bulgaria
  34. Mića Stanković, University of Niš, Serbia
  35. Veronika Starodub, American University in Bulgaria, Blagoevgrad, Bulgaria
  36. Miroslav Stoenchev, Sofia University, Bulgaria
  37. Veselina Tavkova, Plovdiv University, Bulgaria
  38. Berkan Uze, Bogazici University, Istanbul, Turkey
  39. Yulian Tsankov, Sofia University, Bulgaria
  40. Stanislav Varbev, Institute of Solid State Physics, Bulgarian Academy of Sciences, Sofia, Bulgaria
  41. Stanislav Velkov, Sofia University, Bulgaria
  42. Nenad Vesić, University of Niš, Serbia
  43. Tsvetan Vetsov,  Sofia University, Bulgaria
  44. Milos Vukadinovic, American University in Bulgaria, Blagoevgrad, Bulgaria
  45. Ivan Yakovlev, Higher School of Economics  and Skolkovo Institute of Science and Technology, Moscow, Russia
  46. Milan Zlatanovic, University of Niš, Serbia
  47. Pál Zsámboki, Alfréd Rényi Institute of Mathematics, Budapest, Hungary

Selected moments