76 University Drive
Hazleton, PA 18202-8025
Biography
I have two Ph.D. degrees in mathematics: one from Tashkent State University, Uzbekistan, 1987, and one from North Dakota State University, 1999.
My family moved to the USA in 1994, shortly after the breakup of the Soviet Union.
Research Interests
Functional Analysis Operator Algebras Non-commutative Integration Ergodic Theory
Publications
A geometric proof of the binomial identity, The Mathematical Gazette - November, 2024
Collaborator: Frantisek Marko, Co-Author
Notes on noncommutative ergodic theorems, Proceedings of the American Mathematical Society - June, 2024
Essential Precalculus: An Integrated Approach, Fifth Edition - May, 2024
Collaborator: Jose Jimenez, Co-Author
Trigonometry in 30 Brief Lessons: An Integrated Approach, First Edition - May, 2024
Collaborator: Jose Jimenez, Co-Author
Two comments on the binomial theorem, The College Mathematics Journal - 2023
Collaborator: Frantisek Marko, Co-Author
Essential Precalculus: An Integrated Approach, Fourth Edition - August, 2023
Collaborator: Jose Jimenez, Co-Author
Individual ergodic theorems with infinite measure, Colloquium Mathematicum - 2022
Collaborators: Vladimir Chilin, Co-Author; Dogan Comez, Secondary Author
Essential Precalculus: An Integrated Approach, Third Edition - August, 2022
Collaborator: Jose Jimenez, Co-Author
On individual ergodic theorems for semifinite von Neumann algebras, Journal of Mathematical Analysis and Applications - 2021
Collaborator: Vladimir Chilin, Co-Author
Almost uniform convergence in Wiener-Wintner ergodic theorem, Studia Mathematica - 2021
Collaborator: Vladimir Chilin, Co-Author
Essential Precalculus: An Integrated Rigorous Approach, Second Edition - August, 2021
Collaborator: Jose Jimenez, Co-Author
Geometry of figurate numbers and sums of powers of consecutive natural numbers, The American Mathematical Monthly - 2020
Collaborator: Frantisek Marko, Co-Author
Noncommutative weighted individual ergodic theorems with continuous time, Infinite Dimensional Analysis, Quantum Probability and Related Topics - 2020
Collaborator: Vladimir Chilin, Co-Author
Sums of powers of consecutive integers and Pascal's triangle, The College Mathematical Journal - 2020
Collaborator: Frantisek Marko, Co-Author
Non-commutative Wiener-Wintner ergodic theorem - September, 2020
Collaborator: Vladimir Chilin, Primary Author
Almost uniform and strong convergences in ergodic theorems for symmetric spaces, Acta Mathematica Hungarica - 2019
Collaborator: Vladimir Chilin, Co-Author
Local ergodic theorems in symmetric spaces of measurable operators, Integral Equations and Operator Theory - 2019
Collaborator: Vladimir Chilin, Co-Author
Individual ergodic theorems for sigma-finite measure spaces - September, 2019
Collaborator: Vladimir Chilin, Co-Author
Individual and mean ergodic theorems for symmetric function spaces - September, 2018
Collaborator: Vladimir Chilin, Author
Functions and logic in solving equations and inequalities - March, 2018
Collaborator: Elena Litvinova, Co-Author
The validity space of Dunford-Schwartz pointwise ergodic theorem, Journal of Mathematical Analysis and Applications - March, 2018
Collaborator: Vladimir Chilin, Co-Author
Almost uniform convergence in noncommutative Dunford-Schwartz ergodic theorem, Comptes Rendus Mathematique - 2017
On Steiner-Routh's theorem for simplices, American Mathematical Monthly - 2017
Collaborator: Frantisek Marko, Co-Author
Individual ergodic theorems in noncommutative Orlicz spaces, Positivity - February, 2017
Collaborator: Vladimir Chilin, Co-Author
Ergodic theorems in fully symmetric spaces of measurable operators, Studia Mathematica - October, 2015
Collaborator: Vladimir Chilin, Co-Author
A non-commutative Wiener-Wintner theorem, Illinois Journal of Mathematics - September, 2015
Functions and their inverses - July, 2015
Collaborator: Elena Litvinova, Co-Author
Routh's theorem for tetrahedra, Geometriae Dedicata - January, 2015
Collaborator: Frantisek Marko, Co-Author
On continuity at zero of the maximal operator for a semifinite measure, Colloquium Mathematicum - June, 2014
Interval method of solving inequalities - March, 2014
Collaborator: Elena Litvinova, Co-Author
Ergodic averages with vector-valued Besicovitch weights, Positivity - 2013
Collaborator: Dogan Comez, Secondary Author
Uniform equicontinuity of sequences of measurable operators and non-commutative ergodic theorems, Proceedings of the American Mathematical Society - July, 2012
On the Banach-Steinhaus theorem for topological groups, American Mathematical Monthly - November, 2011
A Banach Principle for L^{\infinity} with semifinite measure, Journal of Mathematical Analysis and Applications - July 1, 2011
Collaborator: Vladimir Chilin, Secondary Author
A Banach Principle for semifinite von Neumann algebras, SIGMA - 2006
Collaborator: Vladimir Chilin, Co-Author
Ergodic averages with generalized weights, Studia Mathematica - 2006
Collaborator: Dogan Comez, Co-Author
Uniform equicontinuity for sequences of homomorphisms into the ring of measurable operators, Methods of Functional Analysis and Topology - 2006
Collaborator: Vladimir Chilin, Co-Author
The Banach Principle for topological groups, Atti Sem. Mat. Fis. Univ. Modena e Reggio Emilia - December, 2005
A few remarks in non-commutative ergodic theory, Journal of Operator Theory - March, 2005
Collaborators: Vladimir Chilin, Co-Author; Adam Skalski, Co-Author
Data collection based approach to teaching problem solving for education majors - September, 2004
Collaborator: Jane Foderaro, Co-Author
On individual subsequential ergodic theorem in von Neumann algebras, Studia Mathematica - 2001
Collaborator: Farrukh Mukhamedov
On Besicovitch weighted ergodic theorem in von Neumann algebras - 2000
Banach principle in the space of tau-measurable operators, Studia Mathematica - 2000
Collaborator: Michael Goldstein, Co-Author
Norm convergence of moving averages for tau-integrable operators, Rocky Mountain Journal of Mathematics - 2000
Collaborator: Dogan Comez, Co-Author
A description of commutative symmetric operator algebras in the Pontryagin space P1, Journal of Operator Theory - 1997
Collaborators: Oleg Bendersky; Vladimir Chilin
Non-degenerate bicyclic WJ*-algebras in Pontryagin space, Dokl. Akad. Nauk Rep. Uzbekistan - 1993
Bicyclic WJ*-algebras in the Pontryagin space of type P1, Functional Analysis and Applications - 1992
Separating and cyclic vectors of commutative WJ*-algebras in the Pontryagin space, Analysis Algebra Probability Theory, Tashkent Gos. Univ. - 1988
Description of commutative symmetric algebras in the Pontryagin space P1 , Dokl. Akad. Nauk UzSSR - 1987
Weakly closed symmetric commutative algebras of operators in the space P1 , Math. Analysis Probability Theory, Tashkent Gos. Univ. - 1985
Education
Ph D, Functional Analysis, North Dakota State University
Ph D, Functional Analysis, Romanovsky Mathematical Institute
MS, Functional Analysis, Tashkent State University
BS, Functional Analysis, Tashkent State University
Papers and Presentations
September 14, 2024
Oral Presentations
Almost Uniform Convergence in the Wiener-Wintner Ergodic Theorem
1198th AMS Meeting
University of Texas in San Antonio, San Antonio, TX
We extend almost everywhere convergence in the Wiener-Wintner ergodic theorem to a generally stronger almost uniform convergence and, in the case of infinite measure, present a universal space for which this convergence holds. We then extend this result to the case with Besicovitch weights.
June 13, 2024
Seminars
Noncommutative Ergodic Theorems for Nets
Functional Analysis and Applications Seminar
The National University of Uzbekistan, Tashkent, Uzbekistan
June 8, 2023
Seminars
On individual convergence in the space of tau-measurable operators
Functional Analysis and Applications Seminar
The Institute of Mathematics of the National Academy of Sciences, Tashkent, Uzbekistan
April 22, 2023
Oral Presentations
Inequalities in Algebra and Analysis: The Method of Intervals
University College Mathematics Division Meeting
University College, PA
June 11, 2020
Seminars
Almost Uniform Convergence in Wiener-Wintner Ergodic Theorem
Functional Analysis and Applications Seminar
The National University of Uzbekistan, Tashkent, Uzbekistan
April 25, 2020
Oral Presentations
Teaching pre-calculus at Hazleton
University College Mathematics Division Meeting
University College, PA
May 30, 2019
Seminars
Individual Ergodic Theorems for Infinite Measure
Functional Analysis and Applications Seminar
The National University of Uzbekistan
February 14, 2019
Seminars
Ergodic theorems in Banach ideals of compact operators
Functional Analysis and Applications Seminar
National University of Uzbekistan
October 23, 2018
Seminars
On convergence of ergodic averages for Dunford-Schwartz operators in fully symmetric spaces
Mathematics Department Colloquium
North Dakota State University, Fargo, ND
October 23, 2018
Seminars
Some recent advances in noncommutative ergodic theory
Analysis Seminar
North Dakota State University, Fargo, ND
September 6, 2018
Seminars
Noncommutative weighted individual ergodic theorems with continuous time
Functional Analysis and Applications Seminar
Tashkent, Uzbekistan
October 6, 2017
Oral Presentations
Local ergodic theorems in symmetric spaces of measurable operators
Uzbekistan-Israel International Conference Contemporary Problems in Mathematics and Physics, October 6-10, 2017
Tashkent, Uzbekistan
August 8, 2017 - August 12, 2017
Papers
Validity space of noncommutative ergodic theorem
2nd USA-Uzbekistan Conference on Analysis and Mathematical Physics, August 8-12, 2017
Urgench, Uzbekistan
June 5, 2017
Oral Presentations
Individual ergodic theorems in semifinite von Neumann algebras
XIX International Conference Geometry, Integrability and Quantization, June 2-7, 2017
Varna, Bulgaria
May 2, 2017
Oral Presentations
Almost uniform convergence in noncommutative individual ergodic theorem
Modern Problems of the Dynamical Systems and Their Applications, May 1-3, 2017
Tashkent, Uzbekistan
April 1, 2017
Oral Presentations
An integrated approach to teaching pre-calculus
University College Mathematics Division Meeting
University College, PA
A new pre-calculus text-book written jointy with Dr. Jimenez presented.
March 23, 2017
Oral Presentations
One-sided convergence in noncommutative individual ergodic theorems
Functional Analysis and Applications Seminar
Tashkent, Uzbekistan
December 15, 2016
Oral Presentations
Pointwise ergodic theorems in function symmetric spaces
Weekly Tashkent City Seminar on Functional Analysis and its Application
Tashkent, Uzbekistan
June 27, 2016
Oral Presentations
Individual ergodic theorems in noncommutative symmetric spaces
26th International Conference on Operator Theory, June 27-July 2, 2016
West University, Timisoara, Romania
Let M be a semifinite von Neumann algebra equipped with a faithful normal semifinite trace tau. Let L^0 be the algebra of tau-measurable operators affiliated with M , L^p the corresponding noncommutative Lp-space, 1<= p
April 16, 2016
Oral Presentations
Individual ergodic theorem in noncommutative Orlicz spaces
1120th AMS Meeting, April 16-17, 2016
North Dakota State University, Fargo, ND
For a non-commutative Orlicz space associated with a semifinite von Neumann algebra and an Orlicz function satisfying (delta_2,Delta_2)-condition, we establish a non-commutative version of Dunford-Schwartz individual ergodic theorem.
October 15, 2015
Oral Presentations
Ergodic theorems for absolute contractions in symmetric spaces
Functional Analysis and Applications Seminar
Tashkent, Uzbekistan
July 7, 2015
Virtual
Functions and their inverses
7th Conference on Education and New Learning Technologies
Barcelona, Spain
A review of elementary methods of solving inequalities is offered. It includes traditional Case-by-Case (which we call the Method of Equivalent Transformations) and Graphing methods and a non-traditional Interval Method. We compare the Interval Method with the other two methods of solving inequalities. It is shown that if one chooses to employ the Interval Method, then the principal difference between solving inequalities and the corresponding equations practically disappears. The Interval Method is based on a simple observation, and we believe that many instructors use it in one form or another. We aim to present this method clearly and systematically and provide a number of examples to outline its possible applications. This material may be of interest to college/high school instructors who teach pre-calculus or/and calculus courses.
April 25, 2015
Oral Presentations
Routh’s theorem for tetrahedra and simplices
University College Mathematics Division Meeting
University College, PA
March 28, 2015
Oral Presentations
On positive linear operators in Lp-spaces of a semifinite measure
1109th AMS Meeting, March 27-29, 2015
University of Alabama, Huntsville, AL
We show that, in the case of semifinite measure, Garsia’s class of the so-called positive contractions (see also Krengel’s book) coincides with the class of positive Dunford-Shcwartz operators.
September 18, 2014
Oral Presentations
Individual and statistic ergodic theorems in noncommutative symmetric spaces
Functional Analysis and Applications Seminar
Tashkent, Uzbekistan
May 21, 2014
Oral Presentations
A non-commutative Wiener-Wintner theorem
1st USA-Uzbekistan Conference on Analysis and Mathematical Physics, May 19-23, 2014
Fullerton, CA
For a von Neumann algebra M with a faithful normal tracial state and a positive ergodic trace-invariant homomorpsism in L1(M) such that it does not increase the norm in M, we establish a non-commutative counterpart of the classical Wiener-Wintner ergodic theorem.
March 22, 2014
Oral Presentations
On pointwise ergodic theorems for infinite measure
1097th AMS Meeting, March 21-23, 2014
University of Tennessee, Knoxville, TN
For an absolute contraction in L1-space of semi-finite measure, we establish the pointwise convergence of general and Besicovitch weighted ergodic averages of functions in Lp-spaces. These results are extended to not necessarily positive operators as well. Also, Wiener-Wintner ergodic theorem is proved for the case of sigma-finite measure.
March 11, 2014
Virtual
Methods of solving inequalities
INTED 2014 8th International Technology, Education and Development Conference
Valencia, Spain
A review of elementary methods of solving inequalities is offered. It includes traditional Case-by-Case (which we call the Method of Equivalent Transformations) and Graphing methods and a non-traditional Interval Method. We compare the Interval Method with the other two methods of solving inequalities. It is shown that if one chooses to employ the Interval Method, then the principal difference between solving inequalities and the corresponding equations practically disappears. The Interval Method is based on a simple observation, and we believe that many instructors use it in one form or another. We aim to present this method clearly and systematically and provide a number of examples to outline its possible applications. This material may be of interest to college/high school instructors who teach pre-calculus or/and calculus courses.
2013
Seminars
Topics in Pre-calculus
PSU Hazleton Math Department Seminar
Penn State Hazleton
May 14, 2013
Lectures
On the Banach Principle and individual ergodic theorems in semifinite measure spaces
Seminar presentations
North Dakota State University, Fargo, ND
April 27, 2013
Oral Presentations
On individual ergodic theorems in non-commutative Lp-spaces for p>1
1090th AMS Meeting, April 26-28, 2013
Iowa State University, Ames, IA
2012
Seminars
Topics in Pre-calculus
PSU Hazleton Math Department Seminar
Penn State Hazleton
2011
Seminars
Topics in Pre-calculus
PSU Hazleton Math Department Seminar
Penn State Hazleton
June, 2011
Lectures
Uniform equicontinuity of sequences of measurable operators and non-commutative ergodic theorems
Seminar presentation
Institute of Mathematics of the Ukrainian Academy of Sciences, Kiev, Ukraine
The notion of uniform equicontinuity in measure at zero for sequences of additive maps from a normed space into the space of measurable operators associated with a semifinite von Neumann algebra is discussed. It is shown that uniform equicontinuity in measure at zero on a dense subset implies the uniform equicontinuity in measure at zero on the entire space, which is then applied to derive some non-commutative ergodic theorems.
April 9, 2011
Oral Presentations
Word problems with “arithmetic” solutions
University College Mathematics Division Meeting
Pennsylvania State University, University Park, PA
March 12, 2011
Oral Presentations
Methods of solving inequalities
History and Pedagogy of Mathematics Americas Section Meeting
American University, Washington, DC
We offer a relatively comprehensive review of elementary methods of solving inequalities and show that the difference between solving equations and corresponding inequalities can be made practically negligible if one chooses to use the so called interval method.
September 08, 2005
Oral Presentations
Criteria of the almost uniform convergence for sequences of homomorphisms into the ring of measurable operators
Operator Algebras and Quantum Probability Conference
Tashkent, Uzbekistan
June 20, 2005
Oral Presentations
A Banach Principle for a von Neumann algebra
VI International Conference Symmetry in Nonlinear Mathematical Physics
Kiev, Ukraine
September 27, 2004
Oral Presentations
Data Collection Based Approach to Teaching Problem Solving for Education Majors
2004 International College Teaching Methods & Styles Conference
Reno, Nevada
July 15, 2004
Oral Presentations
The Banach Principle for Topological Groups
XI Meeting on Measure Theory and Real Analysis
Ischia, NA, Italy
We show that the classical Banach Principle can be extended to sequences of continuous homomorphisms on topological groups of the second Baire category.
April 12, 2003
Oral Presentations
Word Problem Solving and Math 200
CWC Mathematics Division Meeting
Pennsylvania State University, University Park, PA
April 5, 2003
Oral Presentations
Non-commutative individual ergodic theorem with generalized Besicovitch weights
985th AMS Meeting
Indiana University, Bloomington, IN
December, 2001
Seminars
Norm convergence of moving averages for intergable operators
Seminar presentation
North Dakota State University, Fargo, ND
November 10, 2001
Oral Presentations
Non-commutative Banach Principle and its applications
972nd AMS Meeting
University of California, Irvine, CA
November, 2000
Seminars
On non-commutative Banach Principle
Seminar presentation
Ben-Gurion University of the Negev, Beer-Sheva, Israel
June, 2000
Seminars
Individual ergodic theorem for operator-weighted averages
Seminar presentation
Tashkent State University, Tashkent, Uzbekistan
April 2, 2000
Oral Presentations
Convergence of operator-weighted ergodic averages
952nd AMS Meeting
University of Massachusetts, Lowell, MA
March 19, 1999
Oral Presentations
Banach Principle for integrable operators
941st AMS Meeting
University of Illinois, Urbana, IL