combinatorics,
singularity theory,
multiboundary singularities,
energies of knots,
variational principles of energies of knots,
many-dimensional continued fractions.
Subject:
1. Consider generalizations of the boundary singularities $B_n$ of the functions on the real line to the case where the boundary consists of a finite number of ($l$) points. These singularities $B_n^l$ could also arise in higher dimensional case, when the boundary is an immersed hypersurface. We obtain some recurrent equation on the numbers of connected components of very nice M-morsification spaces of the multiboundary singularities $B_n^l$. This helps us to express $K_n^l$ numbers (for $l=2, 3, 4, ...$) by Bernoulli–Euler numbers. We also find the corresponding generating functions.
Biography
1997 – now, student of Moscow State University; 1997 – now, student of Higher College of Math. of Independent University of Moscow.
Main publications:
Karpenkov O. N. Kombinatorika multikraevykh osobennostei serii $B_n^l$ i chisla Bernulli–Eilera // Funkts. analiz i ego pril. Prinyato k pechati v 2002.
T. Boiko, O. Karpenkov, “Martin Integral Representation for Nonharmonic Functions
and Discrete Co-Pizzetti Series”, Math. Notes, 106:5 (2019), 659–673
2018
2.
T. Boiko, O. Karpenkov, B. Rakhimberdiev, “On Periodic Asymmetric Extrapolation”, Math. Notes, 104:5 (2018), 642–654
2010
3.
O. N. Karpenkov, “Determination of Periods of Geometric Continued Fractions for Two-Dimensional Algebraic Hyperbolic Operators”, Mat. Zametki, 88:1 (2010), 30–42; Math. Notes, 88:1 (2010), 28–38
O. N. Karpenkov, “On an Invariant Möbius Measure and the Gauss–Kuzmin Face Distribution”, Trudy Mat. Inst. Steklova, 258 (2007), 79–92; Proc. Steklov Inst. Math., 258 (2007), 74–86
O. N. Karpenkov, “On existence and uniqueness conditions for an integer triangle with given angles”, Uspekhi Mat. Nauk, 61:6(372) (2006), 185–186; Russian Math. Surveys, 61:6 (2006), 1178–1179
O. N. Karpenkov, “On Tori Triangulations Associated with Two-Dimensional Continued Fractions of Cubic Irrationalities”, Funktsional. Anal. i Prilozhen., 38:2 (2004), 28–37; Funct. Anal. Appl., 38:2 (2004), 102–110
O. N. Karpenkov, “Two-dimensional continued fractions of hyperbolic integer matrices
with small norm”, Uspekhi Mat. Nauk, 59:5(359) (2004), 149–150; Russian Math. Surveys, 59:5 (2004), 959–960
O. N. Karpenkov, “Combinatorics of Multiboundary Singularities $B_n^l$ and the Bernoulli–Euler Numbers”, Funktsional. Anal. i Prilozhen., 36:1 (2002), 78–81; Funct. Anal. Appl., 36:1 (2002), 65–67
2017
11.
A. Chernavski, D. Fuchs, S. Gusein-Zade, Yu. Ilyashenko, O. Karpenkov, A. Kirillov, S. Lando, S. Matveev, M. Skopenkov, V. Tikhomirov, M. Tsfasman, V. Vassiliev, “Alexei Bronislavovich Sossinsky turns 80”, Mosc. Math. J., 17:3 (2017), 555–558
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