# Oleg KARPENKOV

### Graduate student, from November 2002

## Education:

- 1994-1997
- Moscow Mathematical Highschool number 57
- 1997-2002
- Moscow State University, undergraduate student
- 1997--2002
- Independent University of Moscow undergraduate student
- 2002--now
- Moscow State University graduate student
- 2002--now
- Independent University of Moscow graduate student

## Advisors:

Vladimir I. Arnold, Alexei B. Sossinski,
Vladimir M. Zakalyukin

## Research interests:

Number Theory (multidimensional continued fractions, extensions
over the field of rational numbers)

Knot theory (functionals on the space of knots, rational knots)

Singularity theory (boundary singularities, cusp singularities)

## Seminaras, Conferences and Trips
Abroad

- S\'eminaire scientifique OTAN, 41-e session —
été 2002
"Normal Forms, Bifurcations and Finiteness Problems in
Differential Equations" Montréal, Canada, July 2002
- Conference "Knots in Poland", Warsaw and Bedlewo, Poland , July
2003.
- May 1-15, 2004, Uneversité Paris XI Dauphine (France)
- May 15 - June 29, 2004, Institut de Mathématiques de Luminy
(France) Program "Jumelage CNRS-UIM".

## Publications:

- Combinatorics of multiboundary $B_n^l$ singularities and
Bernoulli---Euler numbers, Funct. An. Appl. 36(2002), no 1,
78-81.
- Energy of a knot: variational principles, Russian Jour. of
Math. Phys. vol. 9(2002), no 3, pp. 275-287.
- Energy of a knot: some new aspects, Fundamental Mathematics
Today, IUM, MCCME 2003
- On tori triangulations associated with two-dimensional
continued fractions of cubic irrationalitie,
Func. An. and Appl.,
vol.38(2004) no 2, pp. 28-37.
- On two-dimensional continued fractions for integer hyperbolic
matrices with small norm, Uspehi Mat. Nauk, vol. 59(2004), no. 5,
pp. 149--150.
- Classification of three-dimensional multistory completely
empty convex marked pyramids, To appear in Uspehi Mat. Nauk
(2005).