# Alexander M. Budylin

Associate professor, PhD

Students’ pages are here and here

### Directions of research

• Semiclassical asymptotics
• Pseudodifferential equations
• Spectral theory

### Basic research papers

1. On the asymptotic behavior of spectral characteristics of an integral operator with difference kernel on expanding regions (with Buslaev V.S.)
1986, Soviet Math.Dokl., vol.33, \No 2, p.400-403 .
2. Reflection operators and their applications to asymptotic investigations of semiclassical integral equations. (With Buslaev V.S.)
1991, Advances in Soviet Math., AMS, Providence, vol. 7, p.107-157 .
3. Semiclassical asymptotics of the resolvent of the integral convolution operator with the sine-kernel on a finite interval. (With Buslaev V.S.)
1996, St.Petersburg Math.J., vol.7, \No 6, p.925-942 .
4. Semiclassical pseudodifferential operators with double discontinuous symbols and their application to the problems of quantum statistical physics. (With Buslaev V.S.)
2001, Operator Theory: Advances and Aplications, v.126.
5. Quasiclassical asymptotics for solutions of the matrix conjugation problem with rapid oscillation of off-diagonal entries. 2014, St. Petersburg mathematical journal, vol. 25, n.2, pp. 205-222.

### Teaching

• Lectures «Higher mathematics» for 2nd year students, General stream
• Seminars «Higher mathematics» for 2nd year students
• Seminars «Group theory» for 4th year students (Department of higher mathematics and mathematical physics)
• Lectures «Theory of Lie groups and Lie algebras» for 4th year students (Department of higher mathematics and mathematical physics)
• Seminars «Theory of Lie groups and Lie algebras» for 4th year students (Department of higher mathematics and mathematical physics)
• Seminars «History and methodology of mathematical physics» for 5th year students (Department of higher mathematics and mathematical physics)