Dmytro Karabash RESUME

**** ****** **** ****: 718-***-****

Information

New York, NY, 10027 E-mail: abo8fo@r.postjobfree.com, abo8fo@r.postjobfree.com

WWW: http://www.columbia.edu/ dk2204/

Probability: stochastic processes on manifolds, stochastic PDEs on manifolds, optimization, game

Research

theory, decision theory, control theory.

Interests

Topology: di erential and algebraic topology, singularity theory; want to establish probabilistic

topology.

Axiomatic set theory, non-ZFC systems of axioms.

Combinatorial Geometry.

Education

B.A. Mathematics, Columbia University, May 2008 (expected)

Cumulative GPA:3.845 Major GPA:3.975

Most Advanced Courses: Graduate Topics in Stochastic Calculus, Graduate Complex Analysis,

Graduate Analysis II, Graduate Probability II, Graduate Algebraic Topology II, Graduate Commu-

tative Algebra, Graduate Modern Geometry, Computational Learning Theory.

Undergraduate Research Program supervised by Robert Lipshitz

Research

Columbia University, Summer 2007 sponsored by I.I. Rabi Grant

Experience

Modi cation of the Sarkar-Wang algorithm and an analysis of its computational complexity; analysis

of the computational complexity of calculating H F K from a Heegaard diagram by means of the

modi ed Sarkar-Wang algorithm; comparison of the computational complexities of the Sarkar-Wang

algorithm and the Manolescu-Ozsv th-Sarkar algorithm.

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Supervised Research supervised by Ciprian Manolescu

Columbia University, Summer 2006 sponsored by I.I. Rabi Grant

A study of the Conley index of homogeneous singularities. Example of a singularity for which Conley

index is not a wedge of spheres.

Supervised Research supervised by Alexander Soifer

UCCS, Summer 2005 sponsored by I.I. Rabi Grant

Exploration of various problems in combinatorial geometry including problems around the 1-chromatic

number of the plane under di erent systems of axioms.

(Resulted in 6 publications and further collaboration; see publications.)

Supervised Research supervised by Vladimir Limansky

Independent Research, 2002-2003

Study of the asymptotic behavior of solution graph of the generalization of the Markov Diophantine

Equation.

Dmytro Karabash RESUME

Teaching Assistant Positions:

Teaching

Experience

Topology, Columbia University, Fall 2007

Honors Math IV, Columbia University, Spring 2007

Computational Learning Theory, Columbia University, Fall 2006

Calculus IV, Columbia University, Fall 2006

Linear Algebra, Columbia University, Spring 2006

Topology, Columbia University, Fall 2005

Number Theory, Academy in Math and Science at CCNY, Summer 2004

Hales, J., Karabash, D., Lock, M. T., A modi cation of the Sarkar-Wang algorithm and an analysis

Publications

of its computational complexity, preprint: arXiv:0711.4405.

Karabash, D., Soifer, A., Distance Graphs Whose Chromatic Number is A ected by the Underlying

Set Theory, accepted by Congressus Numerantium.

Karabash, D., On Soifer Fifty Dollar Problem. Part II: Disprove of the Conjecture, accepted by

Geombinatorics.

Karabash, D., On Soifer Fifty Dollar Problem. Part I: Construction, Geombinatorics XVII (2),

2007, 68-77.

Karabash, D., On the Conley Index for Homogeneous Critical Points, 2006, unpublished.

Karabash, D. Small Extension to Geometric Etudes, Geombinatorics XVI (2), 2006, 262-265.

Karabash, D., Soifer, A., A Sharper Upper Bound for Cover-Up Squared, Geombinatorics XVI(1),

2006, 219-226.

Karabash, D., Soifer, A., On Covering of Trigons, Geombinatorics XV(1), 2005, 13-17.

My work will also also appear in the following Alexander Soifer s books: Mathematical Coloring Book,

How does one cut a triangle?, Geometric Etudes in Combinatorial Mathematics (all to appear in

Springer in 2008 or 2009).

2007 Summer Undergraduate Research Program: On Sarkar-Wang Algorithm

Talks

Second Annual Rabi Scholar Symposium, Nov 10, 2007: A Modi cation of the Sarkar-Wang Algo-

rithm and an Analysis of its Computational Complexity

Various talks in undergraduate seminars courses in the fall of 2005 and fall of 2006

Talks given at Columbia University for Undergraduate Mathematical Society:

Some Elementary Optimal Stopping Problems, October 24, 2007

Around Markov Diophantine Equation, September 26, 2007

On Packings and Coverings, July 16, 2007

On the Conley Index for Homogeneous Critical Points, October 17, 2006

Symmetric Inequalities and Included Ellipses, June 26, 2006

A Fifty Dollar Problem, September 25, 2005

On Covering Trigons or How I Met Hexagon, July 18, 2005

Dmytro Karabash RESUME

I. I. Rabi Fellow, Columbia College, 2004-2008

Fellowships,

Honors and

The Professor Van Amringe Mathematical Prize, Columbia College, 2007 and 2006

Awards

William Lowell Putnam Mathematical Competition:

Honorable Mention, 2005

MAA Award for Top Score in New York, 2005 and 2004

Mathematical Contest in Modeling, Honorable Mention, 2006

(in a team with Rajesh Ramakrishnan and Tanoy Sinha)

King s Crown Leadership Copper Crown Award, Columbia College, 2007

Dean s List, Columbia College,

(Fall 2007, Spring 2007, Spring 2006, Fall 2005, Spring 2005, Fall 2004)

Columbia Mathematical Club: Founder, Senior President in 2007-2008, President in 2006-2007 and

Service:

2005-2006

Ukrainian Students Society: Vice-President in 2007-2008, President in 2006-2007, RIA Liaison in

2005-2006

Russian International Association (RIA), Event Planer 2005-2006

Webmaster for:

Russian International Association 2007-2008

I. I. Rabi Scholars Website 2006-2008

Ukrainian Student Society Website 2006-2008

Undergraduate Mathematical Society Website 2006-2008

Columbia Mathematics Club Website 2006-2008

Topics in Stochastic Calculus Course, Fall 2007

Languages: English, Russian, Ukrainian

Other Skills

Computer Skills: Mathematica, L TEX, basics of C++, basics of html, basics of Dreamweaver.

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