Department of Moscow Institute of Physics and Technology based at Steklov Mathematical Institute
“Methods of Modern Mathematics”

About the Department

The department “Methods of Modern Mathematics” of Moscow Institute of Physics and Technology, Phystech School of Applied Mathematics and Informatics, was established in 2020 within Steklov Mathematical Institute. The head of the department is Dmitrii Valer’evich Treschev, academician of RAS, who is also the director of Steklov Mathematical Institute. The deputy head of the department is Alexander Nikolaevich Pechen, Professor of RAS, Doctor of Sciences in Physical and Mathematical Sciences. The department offers a Master's Program in contemporary mathematics. Enrolled students have an opportunity to do research under the supervision of leading researchers from Steklov Mathematical Institute. The program allows students to follow one of the following two tracks: “Algorithmic Problems in Logic, Algebra, and Number Theory” and “Methods of Quantum Technologies and Mathematical Physics,” which correspond to two degree majors.

Algorithmic Problems in Logic, Algebra, and Number Theory

The “algorithmic” track yields a master’s degree in the major “Informatics and Computing Technique” and offers courses in mathematical logic, including non-classical logics and applications of logic in computer science, discrete random processes, additive combinatorics, group theory and combinatorics of words etc. The diversity of the courses of this track is designed to reflect diverse interests of its students, which range from “pure” to applied mathematics.

The contact person for the algorithmic track is Stepan Lvovich Kuznetsov, sk@mi-ras.ru.

Curriculum:

• 1^st term
  • Provability and Formal Arithmetic (L. D. Beklemishev, T. L. Yavorskaya)
  • Geometric Group Theory, Part I (I. G. Lysenok)
  • Introduction to Computational Complexity Theory (V. V. Podolskii)
  • Number Theory, Part I (M. R. Gabdullin)
  • Convergence of Random Processes (V. I. Afanasyev)
• 2^d term
  • Non-classical Logics (L. D. Beklemishev)
  • Structural Proof Theory and Algebraic Logic (S. L. Kuznetsov)
  • Set Theory, Part I (D. I. Saveliev)
  • Geometric Group Theory, Part II (I. G. Lysenok)
  • Number Theory, Part II (M. R. Gabdullin)
• 3^d term
  • Lambda Calculus (S. L. Kuznetsov)
  • Algorithmic Problems in Algebra (A. L. Talambutsa)
  • Set Theory, Part II (D. I. Saveliev)
  • Provability and Formal Arithmetic, additional topics (L. D. Beklemishev, T. L. Yavorskaya)
  • Number Theory, Part III (I. S. Rezvyakova)

Mathematical Methods of Quantum Technologies

The “quantum” track yields a master’s degree in the major “Applied Mathematics and Physics” and offers courses in quantum information theory, control of quantum systems, quantum cryptography and quantum communications, quantum computation and algorithms, theory of open quantum systems. These courses discuss both basic fundamental results and various applied methods closely connected with modern practical problems in the rapidly developing field of quantum technologies.

The contact person for the quantum track is Alexander Nikolaevich Pechen, apechen@gmail.com

Curriculum:

• 1^st term
  • Mathematical Foundations of Quantum Information Theory. Part I (A. S. Holevo)
  • Control of Quantum Sys-tems (A. N. Pechen, O. V. Morzhin)
  • Classical and Quantum Stochastic Processes. Part I (G. G. Amosov)
  • Foundations of the Theory of Open Quantum Systems. Part I (A. E. Teretenkov)
  • Introduction to Computational Complexity Theory (V. V. Podolskii)
• 2^d term
  • Mathematical Foundations of Quantum Information Theory. Part II (A. S. Holevo)
  • Classical and Quantum Stochastic Processes. Part II (G. G. Amosov)
  • Foundations of the Theory of Open Quantum Systems. Part II (A. E. Teretenkov)
  • Introduction to Integrable Systems. Part I (A. V. Zotov)
  • Functional integrals and applications in quantum theory and statistical mechanics (O. G. Smolyanov, V. Zh. Sakbaev)
  • Quantum Computation (A. S. Trushechkin)
• 3^d term
  • Quantum Tensor Networks (S. N. Filippov)
  • Functional integrals and applications in quantum theory and statistical mechanics. Part II (O. G. Smolyanov, V. Zh. Sakbaev)
  • Introduction to Integrable Systems. Part II (A. V. Zotov)
  • Geometric Methods in Quantum Information (D. S. Ageev)
  • Quantum Cryptography (D. A. Kronberg)

Faculty

• D. V. Treschev, Dr. Phys.-Math. Sci., Professor, Acad. of RAS, Director of Steklov Math. Inst.

• A. N. Pechen, Dr. Phys.-Math. Sci., Professor of RAS, Leading Scientific Researcher, Head of the Dept. of Mathematical Methods for Quantum Technologies at Steklov Math. Inst.

• Natalia Vladimirovna Dorofeeva (e-mail: dorofeeva.nv@mipt.ru )

• V. I. Afanasyev, Dr. Phys.-Math. Sci., Leading Scientific Researcher, Steklov Math. Inst. (Dept. of Discrete Mathematics)
• L. D. Beklemishev, Dr. Phys.-Math. Sci., Acad. of RAS, Chief Scientific Researcher, Head of Dept., Steklov Math. Inst. (Dept. of Mathematical Logic)
• M. R. Gabdullin, Cand. Phys.-Math. Sci., Scientific Researcher, Steklov Math. Inst. (Dept. of Number Theory)
• S. L. Kuznetsov, Cand. Phys.-Math. Sci., Senior Scientific Researcher, Steklov Math. Inst. (Dept. of Mathematical Logic)
• I. G. Lysenok, Dr. Phys.-Math. Sci., Leading Scientific Researcher, Steklov Math. Inst. (Dept. of Mathematical Logic)
• V. V. Podolskii, Cand. Phys.-Math. Sci., Senior Scientific Researcher, Steklov Math. Inst. (Dept. of Mathematical Logic)
• I. S. Rezvyakova, Cand. Phys.-Math. Sci., Senior Scientific Researcher, Steklov Math. Inst. (Dept. of Number Theory)
• D. I. Saveliev, Acting Senior Scientific Researcher, Inst. for Information Transmission Problems of RAS (Lab # 13 “Algebra and Number Theory”)
• A. L. Talambutsa, Cand. Phys.-Math. Sci., Scientific Researcher, Steklov Math. Inst. (Dept. of Mathematical Logic)
• T. L. Yavorskaya, Cand. Phys.-Math. Sci., Associate Professor, Lomonosov Moscow State University (Dept. of Mathematical Logic and Theory of Algorithms)

• G. G. Amosov, Dr. Phys.-Math. Sci., Leading Scientific Researcher, Steklov Math. Inst. (Dept. of Probability Theory and Mathemat-ical Statistics)
• S. N. Filippov, Cand. Phys.-Math. Sci., Head of Lab., MIPT (Lab. of Quantum Information Theory)
• A. S. Holevo, Dr. Phys.-Math. Sci., Acad. of RAS, Chief Scientific Researcher, Head of Dept., Steklov Math. Inst. (Dept. of Probability Theory and Mathematical Statistics)
• D. A. Kronberg, Cand. Phys.-Math. Sci., Senior Scientific Researcher, Steklov Math. Inst. (Dept. of Mathematical Methods for Quantum Technologies)
• O. V. Morzhin, Cand. Phys.-Math. Sci., Senior Scientific Researcher, Steklov Math. Inst. (Dept. of Mathematical Methods for Quantum Technologies)
• A. N. Pechen, Dr. Phys.-Math. Sci., Professor of RAS, Leading Scientific Researcher, Head of Dept., Steklov Math. Inst. (Dept. of Mathematical Methods for Quantum Technologies)
• V. Zh. Sakbaev, Dr. Phys.-Math. Sci., Professor, MIPT (Higher Mathematics Dept.)
• O. G. Smolyanov, Dr. Phys.-Math. Sci., Professor, Lomonosov Moscow State University (Dept. of Theory of Functions and Functional Analysis)
• A. E. Teretenkov, Cand. Phys.-Math. Sci., Scientific Researcher, Steklov Math. Inst. (Dept. of Mathematical Methods for Quantum Technologies)
• A. S. Trushechkin, Dr. Phys.-Math. Sci., Senior Scientific Researcher, Steklov Math. Inst. (Dept. of Mathematical Physics)
• A. V. Zotov, Dr. Phys.-Math. Sci., Leading Scientific Researcher, Steklov Math. Inst. (Dept. of Theoretical Physics)

Timetable

Spring 2020/2021

• Monday
  • 10:00–11:25 A. S. Trushechkin (Q) “Quantum computation”
  • 11:30–12:55 T. L. Yavorskaya (A) “Nonclassical Logics”
  • 13:00–14:25 I. S. Rezvyakova (A) “Number Theory II”
  • 13:35–15:00 A. S. Holevo (Q) “Mathematical foundations of quantum information science II”
  • 15:05–16:30 D. I. Saveliev (A) “Set Theory I”
  • 16:45–18:10 S. L. Kuznetsov (A) “Structural Proof Theory and Algebraic Logic”
• Tuesday
  • 10:00–11:25 A. E. Teretenkov (Q) “Foundations of the theory of open quantum systems II”
  • 11:30–12:55 G. G. Amosov (Q) “Classical and Quantum Stochastic Processes II”
  • 13:35–15:00 A. V. Zotov (Q) “Introduction to Integrable Systems I”
  • 16:35–18:00 O. G. Smolyanov, V. Zh. Sakbaev (Q) “Functional integrals and applications in quantum theory and statistical mechanics I”

Autumn 2020/2021

• Monday
  • 10:00–11:25 M. R. Gabdullin (A) “Number Theory”
  • 13:35–15:00 A. S. Holevo (Q) “Mathematical Foundations of Quantum Information Science. Part I”
  • 15:05–16:30 A. N. Pechen, O. V. Morzhin (Q) “Control of Quantum Systems”
• Tuesday
  • 10:00–11:25 A. E. Teretenkov (Q) “Foundations of the Theory of Open Quantum Systems. Part I”
  • 11:30–12:55 G. G. Amosov (Q) “Classical and Quantum Stochastic Processes. Part I”
  • 13:00–14:20 V. I. Afanasyev (A) “Convergence of Random Processes”
  • 14:30–16:00 L. D. Beklemishev, T. L. Yavorskaya (A) “Provability and Formal Arithmetic”
  • 16:15–17:45 V. V. Podolskii (A/Q) “Introduction to Computational Complexity Theory”