il woo

Il Woo Cho


Dr. Cho's research interests include free probability, operator algebra and theory, combinatorics, and groupoid dynamical systems.

See Courses Taught

Education and Training

  • PhD, MA, University of Iowa
  • BA, Sungkyunkwan University, Korea


Semicircular-Like Laws and The Semicircular Law Induced by Orthogonal Projections (2018). Complex Analysis and Operator Theory. pp 1-38.

Semicircular-Like and Semicircular Laws on Banach *-Probability Spaces Induced by Dynamical Systems of the Finite Adele Ring (2018). Advances in Operator Theory (AOT). Dedicated to Stefan Banach for 125-th Birthday. Special Issue: Trends in Operators on Banach Spaces.

Acting Semicircular Elements Induced by Orthogonal Projections on von Neumann Algebras (2017). Mathematics. 5(4), 74.

Matrices Induced by Arithmetic Functions Acting on Certain Krein Spaces (2017). Special Matrices. Vol. 5, Issue 1. pp 258-289.

Free Stochastic Integrals for Weighted-Semicircular Motion Induced by Orthogonal Projections (2017). Monograph Chapter for Appl. Math. Anal: Theo., Methods & Appl. Published by Taylor & Francis

Banach *-Algebras Generated by Elements Induced by Certain Orthogonal Projections (2018). (With Prof. Palle Jorgensen). Opuscula Mathematica, 38, no. 4. pp. 501-535.

Adelic Analysis and Functional Analysis on the Finite Adele Ring. Opuscula Mathematica, 38, no. 2, (2018) 139 - 185.

Analysis of Free Products of General Linear Groups and Hecke Algebras Over Primes. Contemp. Math. Proceedings Volume for the Special Session on Harmonic Analysis at Joint Math. Meeting 2017 (With Prof. Palle Jorgensen)

Circular and Circular-Like Elements Induced by Orthogonal Projections (2017). Applied Math. Sci.

Free Probability on C*-Algebras Induced by Hecke Algebras over Primes, Jul., 2017. (With Prof. Palle Jorgensen) Discrete & Continous Dynam. Syst. Ser-S.

Semicircular-Like and Semicircular Laws Induced by Certain C*-Probability Spaces over the Finite Adele Ring. Operator Theory: Advances & Applications. Vol. 263, (2018). pp 237 - 280. Published by Springer International Publishing. With Prof. Palle Jorgensen. 

Difference Between Semicircular-Like Laws Induced by p-Adic Number Fields and the Semicircular Law. 2017, 5(5) pp 165-190. Turkish Journal of Analysis and Number Theory. DOI: 10.12691/tjant-5-5-4

p-Adic Free Stochastic Integrals for p-Adic Weighted-Semicircular Motions Determined by Primes p. Libertas Mathematica (New Series). vol 36, no. 2, (2016). pp 65 - 110. (Communicated with Prof. Florin Radulescu).

Cho, I. W., & Jorgensen, P. E. (2017). Free Products of C*-Probability Spaces from p-Adic Hecke Algebras. In Advances in Complex Analysis and Operator Theory (pp. 55-99). Birkhäuser, Cham. Special Issues Dedicated to Prof. Daniel Alpay for his 60th Birthday.

p-Adic Number Fields Acting on W*-Probability Spaces. Turkish Journal of Analysis and Number Theory, 2017, Vol. 5, No. 2, 31-56.

Free Semicircular Families in Free Product Banach *-Algebras Induced by p-Adic Number Fields Over Primes p. DOI: 10.1007/s11785-016-0625-5. Complex Analysis and Operator Theory (2017). vol. 11, no. 3. pp 507 - 565.

Semicircular Elements Induced by p-Adic Number Fields. Opuscula Mathematica, vol 35. no. 5, (2017). pp 665 - 703. (With Prof. Palle Jorgensen).

Correction: An Application of Free Probability to Arithmetic Functions, Oct. 2016. CAOT (With Prof. Palle Jorgensen) DOI: 10.1007/s11785-016-0604-x

Free Probability on W*-Dynamical Systems Determined by the Generalized Linear (2-by-2) Groups over p-Adic Number Fields: Generalized Hecke Algebras. DOI: 10.1007/s40574-016-0111-z. Bollettino dell'Unione Math. Italiana, vol 10, no. 4, (2017). pp725 - 764.

Free Probability on Hecke Algebras and the Euler Totient Function. Aug., 2016. J. Alg. & Numb. Theo. Acad

Non-factorizable C-valued functions induced by finite connected graphs (2017). Opuscula Mathematica. Vol 37,2. Pp 225-263.

Matricial Representations of Certain Finitely Presented Groups Generated by Order-2 Generators and Their Applications. Jul., 2016 Rose-Hulman Undergraduate Mathematics Journal

Undergraduate Research with Mr. Ryan Golden. American Journal of Undergraduate Research, vol. 14, issue 3, (2017). pp 45 - 68.

Certain Semigroup C*-Algebras Induced by Free-Probabilistic Representations of Hecke Algebras. Jul., 2016. Applied Math. & Comput. Sci

Structure Theorems of Von Neumann Algebras Induced by Bijective Monads. Jun., 2016. International J. Research & Reviews in Applied Science

Free Products on Hecke Algebras. Jun., 2016. Mathematika

Ilwoo Cho and Palle E. T. Jorgensen (2017). Krein-space operators determined by free product algebras induced by primes and graphs. Spec. Matrices. 5:1-35.

A Harmonic Analysis of Directed Graphs from Arithmetic Functions and Primes, Apr. 2016. Birkhauser / Springer Book Project: Lecture Note Series with a title: Novel Methods in Harmonic Analysis with Applications to Numerical Analysis and Data Processing, Volume 2. (Applied and Numerical Harmonic Analysis)

Certain Group Dynamical Systems Induced by Hecke Algebras. Opuscula Mathematica. vol 36, no. 3, (2016). pp 337 - 373.

Free Probability on Hecke Algebras Induced by The Finite Adele Ring. Sep., 2015. J. Alg. Numb. Theo. Academia

Free W*-Dynamical Systems From p-Adic Number Fields and the Euler Totient Function. Mathematics. (With Prof. Palle Jorgensen) DOI: 10.3390/math3041095. vol  3 (2015). pp 1095 - 1138.

Asymptotic Free Probability for Arithmetic Functions and Factorization of Dirichlet Series. Analysis and Mathematical Physics 6.3 (2016): 255-295. (With Prof. Palle Jorgensen & Prof. Tim Gillespie).

Matrices Induced by Arithmetic Functions, Primes, and Groupoid Actions of Directed Graphs. Special Matrices, 3(1), 123-154. (With Prof. Palle Jorgensen). DOI: 10.1515/spma-2015-0012.

Free Probability on Hecke Algebras and Certain Group C*-Algebras Induced by Hecke Algebras. Opuscula Mathematica. vol 36, no.2, (2016). pp 153 - 187.

Dynamical systems on arithmetic functions determined by primes. Banach Journal of Mathematical Analysis. Vol 9,1. (2015). Pp 173--215. doi:10.15352/bjma/09-1-15.

Complex-Valued Functions Induced by Graphs and Their Factorizations. DOI: 10.1007/s11785-015-0470-y . CAOT, 10, no. 7, (2016). pp 1453 - 1499.

On Dynamical Systems Induced by the Adele Ring (2015). GJSFR: Math

On Dynamical Systems Induced by p-Adic Number Fields. Opuscula Mathematica. vol 35, no. 4, (2015). pp 445 - 484.

Free Probability on Hecke Algebras. With Dr. Tim Gillespie. DOI: 10.1007/s11785-014-0403-1. Compl. Anal. Oper. Theo., vol 9, issue 7, (2015). pp 1491 - 1531.

A Von Neumann Algebra Over the Adele Ring and the Euler Totient Function. Operator Theory. November 2014. Pp. 1-47.

Representations and Corresponding Operators Induced by Hecke Algebras. Complex Analysis and Operator Theory, 10(3), 437-477. Doi: 10.1007/s11785-014-0418-7.

An Application of Free Probability to Arithmetic Functions (2015). Complex Analysis and Operator Theory, 9(7), 1457-1489.(With Prof. Palle Jorgensen). DOI: 10.1007/s 11785-014-0378-y

Krein-Space Representations of Arithmetic Functions Determined by Primes. Algebras and Representation Theory, 17(6), 1809-1841. (With Prof. Palle Jorgensen) DOI: 10.1007/s 10468-014-9473-z

Complex-Valued Functions Induced by Graphs. Feb., 2014 CAOT. DOI: 10.1007/s11785-014-0368-0

Actions of Arithmetic Functions on Matrices and Corresponding Representations. Annals of Functional Analysis, 5(2), 90-117. (With Prof. Palle Jorgensen)

Arithmetic Functions in Harmonic Analysis and Operator Theory (2014). Operator Theory, 1-36. (With Prof. Palle Jorgensen)

p-Adic Banach-Space Operators and Adelic Banach-Space Operators (2014). Opuscula Mathematica, 34.

Classification on Arithmetic Functions and Corresponding Free-Moment L-Functions (2013). Bulletin of Korean Math. Soc.

Krein-Space Operators Induced by Dirichlet Characters. Contemporary Mathematics: Commutative and Noncommutative Harmonic Analysis and Applications,pp  3-33. (With Prof. Palle Jorgensen) Special Issue of Contemporary Mathematics, American Mathematical Society.

Free Distributional Data of Arithmetic Functions and Corresponding Generating Functions Determined by Gaps of Primes (2014). Complex Analysis and Operator Theory, 8(2), 537-570.DOI: 10.1007/s11785-013-0311-9

Operators Induced by Prime Numbers (2012). Methods and Applications of Analysis, 19(4), 313-340.

K-Groups of a C*-Algebra Generated by a Single Operator. Complex Analysis and Operator Theory, 8(7), 1405-1434. DOI: 10.1007/s11785-013-0285-7

The Index Semigroup and K-Groups of Graph-Groupoid C*-Algebras (2014). Complex Analysis and Operator Theory, 8(1), 57-109. DOI: 10.1007/s11785-012-0271-5

Operator Algebras Induced by Monads. (With Prof. Palle Jorgensen) July 2012, JAMC.

K-Theory Induced by a Single Partial Isometry. June 2012, Opuscula Math.

C*-Algebraic K-Theory Induced by Graphs. Mar. 2012, American J. Math. Math. Sci.

Operators Induced by Graphs (2012). Letters in Mathematical Physics. 102(3), 323-369.DOI: 10.1007/s11005-012-0575-4  (With Prof. Palle Jorgensen)

Index Semigroup and Indexing on von Neumann Algebras. Nov. 2011, CAOT, DOI: 10.1007/s11785-011-0208-4

Operator-Algebraic Quotient Structures Induced by Graphs II (2013). Complex Analysis and Operator Theory, 7(4), 695-738. DOI: 10.1007/s11785-011-0204-8

Algebras in Resistance Networks and Their Representations. (With Prof. Palle Jorgensen) Jul., 2011, Funct. Anal. & Other Math.

Symmetry in Tensor Algebras Over Hilbert Space. (With Prof. Palle Jorgensen) Jun., 2011, Illinois Journal of Math.

Free Probability on Operator Algebras Induced by Currents in Electric Resistance Networks (2012). Int. J. Funct. Anal. Oper. Theory Appl, 4(1), 1-50., (With Prof. Palle Jorgensen).

Histories Distorted by Partial Isometries. DOI:10.4303/jpm/P110301. J. Phy. Math., vol 3, (2011).

Entropy of Graphs and Information-Theoretical Characterization of Graphs with Fractal Property. May, 2011. Adv. Appl. Math. Sci.

Index-Morphism on Finite Trees and Classification of von Neumann Algebras Induced by Finite Trees. Apr. 2011 Invited Paper (Chapter) in a Book: "Quantum Mechanics," InTech Open Access Publisher

Free Probability Induced by Electric Resistance Networks on Energy Hilbert Spaces. (With Prof. Palle Jorgensen). Opuscula Math, 31, no. 4, (2011) 549 - 598.

Index on von Neumann Algebras Induced by Graphs. Jan. 2011 Appl. Math. Sci.

Graph-Matrices and Matricial Graph C*-Algebras. Dec., 2010 B. of KMS

Measure-Framing on Graphs, and Corresponding von Neumann Algebras. Nov., 2010 AM

Fractals in Von Neumann Algebras. Aug., 2010 AM

Moment Computations of Graphs with Fractal Property. (With Prof. Palle Jorgensen). DOI: 10.1007/s12190-010-0440-5. J. Appl. Math. Comput., 37, (2011) 377 - 406)

Frames, Fractals and Radial Operators in Hilbert Space. J. Math. Sci.: Adv. Appl., vol. 5, no. 2, (2010) 333 - 393)

Graph Fractaloids: Classification and Application of Graph Groupoids with Fractal Property. Jul., 2010, Book: Classification and Application of Fractals NOVA Publisher

Towers of von Neumann Algebras Induced by Graphs. Jul., 2010, Oriental J. Math.

Directed Graphs, von Neumann Algebras, and Index, (With Prof. Palle Jorgensen). ART DOI: 10.1007/s10468-010-9233-7. Alg. Rep. Theo, Vol 15, issue 1, (2012) 53 - 108.

Diagram Groupoids and von Neumann Algebras. DOI: 10.1007/s11785-010-0103-4. Compl. Anal. Oper. Theo, 6, (2012) 843 - 895.

Group-Framing and Corresponding von Neumann Algebras. Adv. Appl. Math Sci., 2, vol. 5, (2010) 111 - 164.

Free Graph Stochastic Processes, Sep., 2009, JAMI

C*-Dynamical Systems Induced by Partial Isometries, (With Prof. Palle Jorgensen) June, 2009, AAMS (Adv. & Appl. Math Sci., 1 vol. 2, (2010) 21 - 59)

Fractal Property in B(H) Induced by Partial Isometries, Apr., 2009, CAOT, DOI:10.1007/s11785-009-0035-z (Compl. Anal. Oper. Theo. 5, no. 1, (2011) 1 - 40)

Application of Automata and Graphs: Labeling Operators in Hilbert Space II, (With Prof. Palle Jorgensen) Mar., 2009, JMP DOI:10.1063/1.3141524

Graph-Matrices over Additive Graph Groupoids, Jan., 2009, JAMC

C*-Subalgebras Generated by a Single Operatort in B(H), (With Prof. Palle Jorgensen) Dec., 2008, ACTA. Appl. Math: Special Issues DOI:10.1007/s10440-009-9478-5 (ACTA Appl. Math, 108, (2009) 625 - 664)

Graph Groupoids and Corresponding Representations, Dec., 2008, NOVA Publisher (Invited Paper) Group Theory: Classes, Representations and Connections, and Applications, ISBN: 978-1-60876-175-3

Von Neumann Algebras Generated by Automata, Dec. 2008, NOVA Publisher (Invited Paper) Graphene: Research, Technology and Applications ISBN: 978-1-60692-666-6

Application of Automata and Graphs: Labeling Operators in Hilbert Space I, (With Prof. Palle Jorgensen) Oct., 2008, ACTA Appl. Math: Special Issues DOI: 10.1063/1.3141524

Scalar-Valued Free Probability on a Graph von Neumann Algebra, Oct., 2008, J. of KMS. DOI: 10.4134/JKMS.2010.47.3.601, (J. Korean Math. Soc., 47, no 3, (2010) 601 - 631)

Vertex-Compressed Algebras in a Graph von Neumann Algebra, Aug., 2008, ACTA Appl. Math, DOI: 10.1007/s10440-008-9314-3 (ACTA Appl. Math., 108, no. 2, 315 - 351)

C*-Subalgebras Generated by Partial Isometries, (With Prof. Palle Jorgensen) Aug., 2008, JMP, DOI: 10.1063/1.3056588

Operator Algebraic Quotient Structures Induced by Directed Graphs, Mar., 2008, CAOT, DOI: 10.1007/s11785-008-0065-y

Group Freeness and Certain Amalgamated Freeness, Nov., 2007, JKMS (J. of KMS, 45, no. 3, (2008) 597 - 609)

C*-Algebras Generated by Partial Isometries, (With Prof. Palle Jorgensen) Sep., 2007, JAMC, (JAMC, 26, (2008) 1 - 48)

Measures on Graphs and Certain Groupoid Measures, Aug., 2007, CAOT (Compl. Anal. Oper. Theory, 2, (2008) 1 - 28)

Characterization of the Amalgamated Free Blocks of a Graph von Neumann Algebra, Mar., 2007, CAOT (Compl. Anal. Oper. Theory, 1, (2007) 367-398)

The Moments of Certain Perturbed Operators of the Radial Operator in the Free Group Factor L(F_N), Feb. 2007, JAA (J. of analysis & Applications, vol. 5, no. 3, (2007) 137 - 165)

Direct Producted W*-Probability Spaces and Corresponding Amalgamated Free Stochastic Integration, Feb. 2007, Bulletin of Korean Math. Soc. (Bull. Korean Math. Soc. 44 (2007), No. 1, 131 - 150)

Strictly Free Additively Stable Random Variables, Nov., 2006, FEJMS.

Graph Von Neumann Algebras, Nov., 2006, ACTA Applied Math. (ACTA Appl Math, (2007) 95 95 - 134)

See Monographs and Books

More About Dr. Cho

Courses Taught
  • College Algebra
  • Calculus: pre, I, II, and III
  • Elementary Functions
  • Business Math
  • Trigonometry
Conferences and Seminars

Chapman Univ. Conference, 2017 Signal Processing & Linear Systems, Nov. 2017
Title : Semicircular Elements Induced by Orthogonal Projections on Separable Hilbert Space: Signal Processes with Stochastic Data?

Seoul National University, Korean Operator Theory Annual Conference (KOTAK), July 2016
Title : Semicircular Elements Induced by p-Adic Number Fields

Univ. of Iowa, Prof. Yangbo Ye's Number Theory Seminar, Oct. 2014
Title : Graph-Zeta Functions and Applications

PARC Workshop 2013: Operator Theory and Its Application @ Seoul Nt. Univ., June 2013
Title : Non-Archimedean Banach-Space Operators over Adelic Structures

Seoul National University, PARC Seminar, June 2013
Title: Free Probabilistic Models and Representations on Arithmetic Functions

FIC, CASA with Chief Inspector) June & July, 2011

Seoul National University, PARC Operator Theory Seminar, June, 2011
Title : Distortion on Histories

Seoul National University, Operator Theory Mini Seminar, June 2011
Title : Index Semigroup and their Actions

Univ. of South Dakota, Dep. of Math.) Mar., 2010 : 1-hour talk
Title : Distorted Histories

Research and Development Team of Korean Airport Corporation), July 2009 : 4-hour lecture
Title : Space Modulation Factors and Wave Patterns

Seoul National Univ., June 2009 : 2-hour talk
Title : C*-Subalgebras Generated by a Single Operator in B(H)

Assumption High School, Davenport, Iowa, Mar. 2009
Title: Math? Why? How? What?

Fractal Measure Workshop, Univ. of Iowa, Hosted by Prof. P. Jorgensen), Feb. 2009

Seoul National Univ.) Jul., 2008 : 2-hour talk
Title : Directed Graphs and Hilbert Space Operators

Groupoid Fest, University of Iowa) Nov 2007 : talk
Title : Graph Groupoids and Corresponding Operator Algebras.

GPOTS 2007 May, 2007 : Small-Talk
Title : Graph Groupoids and Corresponding Von Neumann Algebras

Seoul Nt. Univ., Prof. W. Y. Lee's Operator Theory Seminar, July 2006
Title : Von Neumann Algebras Induced by Finite Directed Graphs

SIDIM, Univ. of Turabo, Puerto Rico, Feb 2006 : Small-Talk
Title : Graph Measures and the Corresponding Measure Theory

St. Ambrose University, Feb 2005 : Small-Talk
Title : Free Semigroupoids and Graph Groupoids of the Given Countable directed Graphs

MAA and AMS Annual Joint Meeting, Jan 2005

East Coast Operator Algebra Symposium, Oct 2004

Seoul National University, July 2004 : 1-hr talk
Title : Amalgamated Free Distributional Data and Some Good Examples

KOTAC (Korea Operator Theory and its Application Conference), June 2004

GPOTS 2004 (Great Plain Operator Theory Seminar), May, 2004 : Small-Talk
Title : Graph W*-Probability Theory

COSy (Canada Symposium of Operator Theory) May, 2004 : Small-Talk
Title : Moments of the Generating Operator of (L(F_2)) *_L(F_1) (L(F_2))

INFAS (Iowa-Nebraska Functional Analysis Seminar) 2002 (Spring)

INFAS (Iowa-Nebraska Functional Analysis Seminar), Fall 2001

KOTAC (Korea Operator Theory and its Application Conference), 1998

Monographs and Books

Representation of Arithmetic Functions and Free Probability (2015). Lambert Academic Publishing. ISBN-10: 3659385697

Monograph : The Index Semigroup Induced by Finite Trees, (2011) LAPublisher. ISBN: 978-3-8465-9015-7.

Book : Algebra on Graph Groupoids and Application, (2011). Science Publisher, and CRC Press / Taylor & Fransis Group

Monograph : Index Theory on Graphs, (2011) ISNB: 978-3-639-33271-1. VDM Publisher

Book (Multi-authors) : Graph Fractaloids: Classification & Application of Graph Groupoids with Fractal Property, (2010). Chapter: HandBook on Classification and Application of Fractals NOVA Publisher. Invited Article (a Chapter) of the above Book ISBN: 978-1-61324-198-1.

Monograph : Operations on Graphs, Groupoids, and Operator Algebras, (2010). ISBN: 978-8383-5271-8 LAPublisher

Monograph : Frames on Graphs and Corresponding von Neumann Algebras, (2010). ISBN: 978-3-639-24020-7 VDM Publisher.

Monograph : Free Calculus on Operator Algebras, (2009) ISBN : 978-3-8383-2519-4 LAPublisher.

Monograph : Distorted Histories, (2009). ISBN : 978-3-639-21083-5 VDM Publisher.

Monograph : Graph Groupoids and Partial Isometries, (2009). ISBN: 978-3-8383-1397-9 LAPublisher

Monograph : Fractals on Graphs, (2009) ISBN: 978-3-639-19447-0 VDM Publisher.


Il Woo Cho

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