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

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

Publications:

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