Summer School "Contemporary Mathematics", 2012

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Summer School "Contemporary Mathematics", 2012
(July 19–30, 2012, Dubna)

Since 2001, Russian Academy of Sciences (Department of mathematical sciences), Steklov Mathematical Institute of RAS, Moscow Depatment for Education and the Moscow Center for Continuous Mathematical Education organize a summer school, unique in its choice of professors and participants.

During two weeks around a hundred students of high-school or from the first two years of university take part in 70–80 lectures and seminars.

Website:

https://www.mccme.ru/dubna/2012/program.htm

Photogallery

Chair of the scientific committee
Sosinskii Aleksei Bronislavovich

Institutions
Branch of Mathematical Sciences, Russian Academy of Sciences
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Department of education, Moscow city
Moscow Center for Continuous Mathematical Education


*Summer School "Contemporary Mathematics", 2012, Dubna, July 19–30, 2012*

	*July 9, 2012 (Mon)*

1.	Геометрия расположения, или первые шаги топологии. Лекция для лингвистов V. A. Uspenskii July 9, 2012, Dubna


	*July 20, 2012 (Fri)*

2.	What can the languages of mathematical logic express V. A. Uspenskii July 20, 2012 09:30, Dubna


3.	Root systems and Dynkin diagrams. Lecture 1 A. G. Kuznetsov July 20, 2012 11:15, Dubna


	*July 20, 2012 (Fri)*

4.	The law of quadratic reciprocity. Lecture 1 S. M. L'vovskii July 20, 2012 11:15, Dubna


5.	Billiards: periodic trajectories and conservation laws. Lecture 1 A. A. Glutsyuk July 20, 2012 11:15, Dubna


	*July 20, 2012 (Fri)*

6.	Knots: invariants and normal forms. Introduction A. B. Sosinskii July 20, 2012 15:30, Dubna


	*July 20, 2012 (Fri)*

7.	The Euler characteristic. Lecture 1 Yu. M. Burman July 20, 2012 17:00, Dubna


8.	Congruent numbers and elliptic curves. Lecture 1 A. I. Zykin July 20, 2012 17:00, Dubna


9.	Geometry and combinatorics of generating relations. Lecture 1 A. Ya. Belov July 20, 2012 17:00, Dubna


	*July 21, 2012 (Sat)*

10.	Root systems and Dynkin diagrams. Lecture 2 A. G. Kuznetsov July 21, 2012 09:30, Dubna


	*July 21, 2012 (Sat)*

11.	The law of quadratic reciprocity. Lecture 2 S. M. L'vovskii July 21, 2012 09:30, Dubna


12.	Billiards: periodic trajectories and conservation laws. Lecture 2 A. A. Glutsyuk July 21, 2012 09:30, Dubna


13.	Fast-growing functions (“Faster, higher, stronger”). Introductory lecture L. D. Beklemishev July 21, 2012 11:15, Dubna


14.	Qualitative theory of algorithms A. L. Semenov July 21, 2012 12:45, Dubna


15.	The Euler characteristic. Lecture 2 Yu. M. Burman July 21, 2012 15:30, Dubna


16.	Congruent numbers and elliptic curves. Lecture 2 A. I. Zykin July 21, 2012 15:30, Dubna


17.	Geometry and combinatorics of generating relations. Lecture 2 A. Ya. Belov July 21, 2012 15:30, Dubna


18.	Curves: real, complex and over finite fields. Lecture 1 R. M. Fedorov July 21, 2012 17:00, Dubna


19.	Knots: invariants and normal forms. Lecture 1 A. B. Sosinskii July 21, 2012 17:00, Dubna


20.	Szemeredi's theorem and dynamical systems. Lecture 1 V. V. Uspenskii July 21, 2012 17:00, Dubna


	*July 22, 2012 (Sun)*

21.	Root systems and Dynkin diagrams. Lecture 3 A. G. Kuznetsov July 22, 2012 09:30, Dubna


	*July 22, 2012 (Sun)*

22.	The law of quadratic reciprocity. Lecture 3 S. M. L'vovskii July 22, 2012 09:30, Dubna


23.	Billiards: periodic trajectories and conservation laws. Lecture 3 A. A. Glutsyuk July 22, 2012 09:30, Dubna


24.	The Euler characteristic. Lecture 3 Yu. M. Burman July 22, 2012 11:15, Dubna


25.	Congruent numbers and elliptic curves. Lecture 3 A. I. Zykin July 22, 2012 11:15, Dubna


26.	Geometry and combinatorics of generating relations. Lecture 3 A. Ya. Belov July 22, 2012 11:15, Dubna


27.	Конструирование интеллектуальных систем K. V. Anisimovich July 22, 2012 12:45, Dubna


28.	Geometric quantization. Lecture 1 A. A. Kirillov July 22, 2012 15:30, Dubna


29.	Fast-growing functions (“Faster, higher, stronger”). Lecture 1 L. D. Beklemishev July 22, 2012 17:00, Dubna


30.	Determinantal processes. Lecture 1 A. I. Bufetov, A. V. Komlov July 22, 2012 17:00, Dubna


31.	Introduction to Adele democracy. Lecture 1 G. B. Shabat July 22, 2012 17:00, Dubna


	*July 23, 2012 (Mon)*

32.	Methods of contemporary statistics. Lecture 1 A. V. Gasnikov July 23, 2012 09:30, Dubna


33.	Renormalization and universality in dynamical systems and in lattice models. Lecture 1 V. A. Kleptsyn July 23, 2012 09:30, Dubna


34.	Information theory and encoding. Lecture 1 V. N. Potapov July 23, 2012 09:30, Dubna


35.	Квантовые группы, узлы и полином Джонса. Лекция 1 I. V. Losev July 23, 2012 09:30, Dubna


36.	The law of quadratic reciprocity. Lecture 4 S. M. L'vovskii July 23, 2012 11:15, Dubna


37.	Geometric quantization. Lecture 2 A. A. Kirillov July 23, 2012 11:15, Dubna


38.	The Euler characteristic. Lecture 4 Yu. M. Burman July 23, 2012 12:45, Dubna


39.	Geometry and combinatorics of generating relations. Lecture 4 A. Ya. Belov July 23, 2012 12:45, Dubna


40.	Combinatorics of polyhedra: from Steinitz theorem to universality. Lecture 1 G. Yu. Panina July 23, 2012 15:30, Dubna


41.	Algebraic cobordisms and their applications. Lecture 1 I. A. Panin July 23, 2012 15:30, Dubna


42.	When the fortune teller is of no use. Lecture 1 M. A. Raskin July 23, 2012 15:30, Dubna


43.	Searching for lost algebra: towards Galois. Introductory lecture A. B. Skopenkov July 23, 2012 17:00, Dubna


	*July 24, 2012 (Tue)*

44.	The analogy between integers and polynomials. Lecture 1 Keith Conrad July 24, 2012 09:30, Dubna


45.	Geometry of discriminants and the equation solving complexity. Lecture 1 V. A. Vassiliev July 24, 2012 09:30, Dubna


	*July 24, 2012 (Tue)*

46.	Searching for lost algebra: towards Galois. Lecture 1 A. B. Skopenkov July 24, 2012 09:30, Dubna


47.	Fast-growing functions (“Faster, higher, stronger”). Lecture 2 L. D. Beklemishev July 24, 2012 11:15, Dubna


48.	Determinantal processes. Lecture 2 A. I. Bufetov, A. V. Komlov July 24, 2012 11:15, Dubna


49.	Introduction to Adele democracy. Lecture 2 G. B. Shabat July 24, 2012 11:15, Dubna


50.	Methods of contemporary statistics. Lecture 2 A. V. Gasnikov July 24, 2012 12:45, Dubna


51.	Discussion with V. I. Arnold on what is the mathematics V. M. Tikhomirov July 24, 2012 12:45, Dubna


52.	Combinatorics of polyhedra: from Steinitz theorem to universality. Lecture 2 G. Yu. Panina July 24, 2012 15:30, Dubna


53.	Algebraic cobordisms and their applications. Lecture 2 I. A. Panin July 24, 2012 15:30, Dubna


54.	When the fortune teller is of no use. Lecture 2 M. A. Raskin July 24, 2012 15:30, Dubna


55.	Renormalization and universality in dynamical systems and in lattice models. Lecture 2 V. A. Kleptsyn July 24, 2012 17:00, Dubna


56.	Information theory and encoding. Lecture 2 V. N. Potapov July 24, 2012 17:00, Dubna


57.	Quantum groups, knots and the Jones polynomial. Lecture 1 I. V. Losev July 24, 2012 17:00, Dubna


	*July 25, 2012 (Wed)*

58.	Extremal combinatorics. Lecture 1 A. A. Razborov July 25, 2012 09:30, Dubna


	*July 25, 2012 (Wed)*

59.	The analogy between integers and polynomials. Lecture 2 Keith Conrad July 25, 2012 11:15, Dubna


60.	Geometry of discriminants and the equation solving complexity. Lecture 2 V. A. Vassiliev July 25, 2012 11:15, Dubna


	*July 25, 2012 (Wed)*

61.	Searching for lost algebra: towards Galois. Lecture 2 A. B. Skopenkov July 25, 2012 11:15, Dubna


62.	Fast-growing functions (“Faster, higher, stronger”). Lecture 3 L. D. Beklemishev July 25, 2012 15:30, Dubna


63.	Determinantal processes. Lecture 3 A. I. Bufetov, A. V. Komlov July 25, 2012 15:30, Dubna


64.	Introduction to Adele democracy. Lecture 3 G. B. Shabat July 25, 2012 15:30, Dubna


65.	Curves: real, complex and over finite fields. Lecture 2 R. M. Fedorov July 25, 2012 17:00, Dubna


66.	Knots: invariants and normal forms. Lecture 2 A. B. Sosinskii July 25, 2012 17:00, Dubna


67.	Szemeredi's theorem and dynamical systems. Lecture 2 V. V. Uspenskii July 25, 2012 17:00, Dubna


	*July 26, 2012 (Thu)*

68.	The analogy between integers and polynomials. Lecture 3 Keith Conrad July 26, 2012 09:30, Dubna


69.	Geometry of discriminants and the equation solving complexity. Lecture 3 V. A. Vassiliev July 26, 2012 09:30, Dubna


70.	Searching for lost algebra: towards Galois. Lecture 3 A. B. Skopenkov July 26, 2012 09:30, Dubna


71.	Extremal combinatorics. Lecture 2 A. A. Razborov July 26, 2012 11:15, Dubna


72.	Quantum groups, knots and the Jones polynomial. Lecture 2 I. V. Losev July 26, 2012 12:45, Dubna


73.	Fast-growing functions (“Faster, higher, stronger”). Lecture 4 L. D. Beklemishev July 26, 2012 15:30, Dubna


74.	Determinantal processes. Lecture 4 A. I. Bufetov, A. V. Komlov July 26, 2012 15:30, Dubna


75.	Introduction to Adele democracy. Lecture 4 G. B. Shabat July 26, 2012 15:30, Dubna


76.	Variational problems. Lecture 1 V. Yu. Protasov July 26, 2012 17:00, Dubna


77.	Finite fields and sandpile groups. Lecture 1 S. V. Duzhin July 26, 2012 17:00, Dubna


78.	Проблема домино, апериодические плитки и квазикристаллы. Что такое проблема домино, что такое апериодические плитки, и почему они нам мешают T. Fernique July 26, 2012 17:00, Dubna


79.	Knot theory. Vassiliev invariants. Lecture 1 D. V. Mironov July 26, 2012 17:00, Dubna


	*July 27, 2012 (Fri)*

80.	Examples and applications of metric spaces I. V. Yaschenko July 27, 2012 09:30, Dubna


81.	Combinatorics of polyhedra: from Steinitz theorem to universality. Lecture 3 G. Yu. Panina July 27, 2012 11:15, Dubna


82.	Algebraic cobordisms and their applications. Lecture 3 I. A. Panin July 27, 2012 11:15, Dubna


83.	When the fortune teller is of no use. Lecture 3 M. A. Raskin July 27, 2012 11:15, Dubna


84.	Квантовые компьютеры L. E. Fedichkin July 27, 2012 12:45, Dubna


85.	Curves: real, complex and over finite fields. Lecture 3 R. M. Fedorov July 27, 2012 15:30, Dubna


86.	Knots: invariants and normal forms. Lecture 3 A. B. Sosinskii July 27, 2012 15:30, Dubna


87.	Szemeredi's theorem and dynamical systems. Lecture 3 V. V. Uspenskii July 27, 2012 15:30, Dubna


88.	Variational problems. Lecture 2 V. Yu. Protasov July 27, 2012 17:00, Dubna


89.	Finite fields and sandpile groups. Lecture 2 S. V. Duzhin July 27, 2012 17:00, Dubna


90.	Проблема домино, апериодические плитки и квазикристаллы. Как замостить плоскость плитками Робинсона? T. Fernique July 27, 2012 17:00, Dubna


91.	Knot theory. Vassiliev invariants. Lecture 2 D. V. Mironov July 27, 2012 17:00, Dubna


	*July 28, 2012 (Sat)*

92.	Methods of contemporary statistics. Lecture 3 A. V. Gasnikov July 28, 2012 11:15, Dubna


93.	Renormalization and universality in dynamical systems and in lattice models. Lecture 3 V. A. Kleptsyn July 28, 2012 11:15, Dubna


94.	Information theory and encoding. Lecture 3 V. N. Potapov July 28, 2012 11:15, Dubna


95.	Quantum groups, knots and the Jones polynomial. Lecture 3 I. V. Losev July 28, 2012 11:15, Dubna


96.	Variational problems. Lecture 3 V. Yu. Protasov July 28, 2012 15:30, Dubna


97.	Finite fields and sandpile groups. Lecture 3 S. V. Duzhin July 28, 2012 15:30, Dubna


98.	Проблема домино, апериодические плитки и квазикристаллы. Что такое проблема остановки, и почему разрешить её всё равно, что разрешить проблему домино T. Fernique July 28, 2012 15:30, Dubna


99.	Knot theory. Vassiliev invariants. Lecture 3 D. V. Mironov July 28, 2012 15:30, Dubna


	*July 28, 2012 (Sat)*

100.	The analogy between integers and polynomials. Lecture 4 Keith Conrad July 28, 2012 17:00, Dubna


	*July 28, 2012 (Sat)*

101.	Geometry of discriminants and the equation solving complexity. Lecture 4 V. A. Vassiliev July 28, 2012 17:00, Dubna


102.	Searching for lost algebra: towards Galois. Lecture 4 A. B. Skopenkov July 28, 2012 17:00, Dubna


	*July 29, 2012 (Sun)*

103.	Curves: real, complex and over finite fields. Lecture 4 R. M. Fedorov July 29, 2012 09:30, Dubna


104.	Knots: invariants and normal forms. Lecture 4 A. B. Sosinskii July 29, 2012 09:30, Dubna


105.	Szemeredi's theorem and dynamical systems. Lecture 4 V. V. Uspenskii July 29, 2012 09:30, Dubna


106.	Variational problems. Lecture 4 V. Yu. Protasov July 29, 2012 11:15, Dubna


107.	Finite fields and sandpile groups. Lecture 4 S. V. Duzhin July 29, 2012 11:15, Dubna


108.	Проблема домино, апериодические плитки и квазикристаллы. Почему апериодические плитки не только нам мешают, но и нас интересуют, и как их найти? T. Fernique July 29, 2012 11:15, Dubna


109.	Knot theory. Vassiliev invariants. Lecture 4 D. V. Mironov July 29, 2012 11:15, Dubna


110.	Systems of representatives and Vapnik–Chervonekis dimension. Lecture 2 A. M. Raigorodskii July 29, 2012 12:45, Dubna


111.	Methods of contemporary statistics. Lecture 4 A. V. Gasnikov July 29, 2012 15:30, Dubna


112.	Renormalization and universality in dynamical systems and in lattice models. Lecture 4 V. A. Kleptsyn July 29, 2012 15:30, Dubna


113.	Information theory and encoding. Lecture 4 V. N. Potapov July 29, 2012 15:30, Dubna


114.	Quantum groups, knots and the Jones polynomial. Lecture 4 I. V. Losev July 29, 2012 15:30, Dubna


115.	Combinatorics of polyhedra: from Steinitz theorem to universality. Lecture 4 G. Yu. Panina July 29, 2012 17:00, Dubna


116.	Algebraic cobordisms and their applications. Lecture 4 I. A. Panin July 29, 2012 17:00, Dubna


117.	When the fortune teller is of no use. Lecture 4 M. A. Raskin July 29, 2012 17:00, Dubna

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