Mark Tomforde

POSITIONS HELD

Visiting Assistant Professor, College of William & Mary, 2005-2006

NSF Postdoctoral Fellow, University of Iowa, 2002-2005

Instructor of Mathematics, Dartmouth College, 1999-2002

EDUCATION

Advisor: Dana P. Williams
Thesis: Extensions of graph C*-algebras

graduated Summa Cum Laude and with departmental honors in mathematics

RESEARCH

Interests

Publications

• Graph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence (with Takeshi Katsura, Paul S. Muhly, and Aidan Sims), submitted.

• Equiangular tight frames from complex Seidel matrices containing cube roots of unity (with Bernhard Bodmann and Vern I. Paulsen), Linear Algebra Appl., to appear.

• Vector spaces with an order unit (with Vern I. Paulsen), Indiana Univ. Math. J., to appear.

• Ultragraph C*-algebras via topological quivers (with Takeshi Katsura, Paul S. Muhly, and Aidan Sims), Studia Math. 187 (2008), 137--155.

• Uniqueness theorems and ideal structure for Leavitt path algebras , J. Algebra 318 (2007), 270--299.

• The structure of graph C*-algebras and generalizations, Chapter in the book "Graph Algebras: Bridging the gap between analysis and algebra", Eds. Gonzalo Aranda Pino, Francesc Perera Domenech, and Mercedes Siles Molina, Servicio de Publicaciones de la Universidad de Malaga, Malaga, Spain, 2006.

• Strong Shift Equivalence of C*-correspondences (with Paul S. Muhly and David Pask), Israel J. Math. 167 (2008), 315--346.

• Strong Shift Equivalence in the C*-algebraic setting: Graphs and C*-correspondences , Contemporary Mathematics, Proceedings of the 25th Meeting of the Great Plains Operator Theory Symposium, American Mathematical Society, Providence, RI, 221-230.

• Topological quivers (with Paul S. Muhly), Internat. J. Math. 16 (2005), 693--756.

• The C*-algebras of arbitrary graphs (with Doug Drinen), Rocky Mountain J. Math. 35 (2005), 105--135.

• Classification theorems for the C*-algebras of graphs with sinks (with Iain Raeburn and Dana P. Williams), Bull. Austral. Math. Soc. 70 (2004), 143-161.

• Adding tails to C*-correspondences (with Paul S. Muhly), Documenta Math. 9 (2004), 79-106.

• Stability of C*-algebras associated to graphs, Proc. Amer. Math. Soc. 132 (2004), 1787-1795.

• A unified approach to Exel-Laca algebras and C*-algebras associated to graphs, J. Operator Theory 50 (2003), 345-368.

• Simplicity of ultragraph algebras, Indiana Univ. Math. J. 52 (2003), 901-926.

• Computing Ext for graph algebras, J. Operator Theory 49 (2003), 363-387.

• The ordered K₀-group of a graph C*-algebra, C. R. Math. Acad. Sci. Soc. R. Can. 25 (2003), 19-25.

• Computing K-theory and Ext for graph C*-algebras (with Doug Drinen), Illinois J. Math. 46 (2002), 81-91.

• Ext classes and embeddings for C*-algebras of graphs with sinks, New York J. Math. 7 (2001), 233-256.

Invited Addresses and Workshops

• Operator Algebras, Dynamics, and Classification workshop at Texas A&M University.
  • Graph algebras and the Classification Program

• Visiting Honorary Fellow at the University of Wollongong, Australia, May 2008 -- June 2008
  • "Ordered vector spaces with an order unit"

• C*-algebras Associated to Discrete and Dynamical Systems workshop held at the Banff International Research Station (BIRS) in Banff, Canada, January 2008

• Japan-US Operator Algebra Seminar and West Coast Operator Algebra Seminar, University of Hawai'i at Manoa, January 2007
  • "Leavitt path algebras: At the crossroads of Algebra and Functional Analysis"

• Graph Algebra Workshop at the University of Málaga (Spain), July 2006
  • "Ideal structure of graph C*-algebras"
  • "Arbitrary graph algebras and desingularization"
  • "K-theory and the classification of simple graph C*-algebras"
  • "Generalizations of graph C*-algebras"

• Distinguished Visitor at the University of Nebraska, Lincoln, March 2006
  • "Adding tails to C*-correspondences"
  • "C*-algebras of directed graphs"

Presentations

• "Equiangular tight frames from complex Seidel matrices", Great Plains Operator Theory Symposium, University of Cincinnati, June 2008
• "Graded Uniqueness for Leavitt path algebras", Great Plains Operator Theory Symposium, University of Nebraska, Lincoln, May 2007
• "Leavitt path algebras: At the crossroads of Algebra and Functional Analysis", Colloquium, University of Houston, January 2007
• "An introduction to graph C*-algebras", Texas A&M University, October 2006
• "Graphs, Tracial States, and C*-algebras", University of Mississippi, April 2006
• "C*-algebras of directed graphs", University of Mississippi, April 2006
• "C*-algebras of directed graphs", University of Houston, April 2006
• "Graphs, Tracial States, and C*-algebras", Fairfield University, March 2006
• "C*-algebras and their presentations", Fairfield University, March 2006
• "C*-algebras of directed graphs", University of Hawai'i, Manoa, February 2006
• "C*-algebras, Graphs, and Topological Quivers", University of Denver, February 2006
• "C*-algebras of directed graphs", Washington and Lee University, January 2006
• "C*-algebras of directed graphs", Susquehanna University, October 2005
• "Using directed graphs to describe C*-algebras", College of William & Mary, October 2005
• "Strong Shift Equivalence for C*-correspondences", Great Plains Operator Theory Symposium, University of Central Florida, June 2005
• "Strong Shift Equivalence in the C*-algebra setting" (Colloquium), University of Iowa, April 2005
• "C*-algebras, Graphs, and Topological Quivers", The College of William & Mary, January 2005
• "Topological Quivers", University of Newcastle, Australia, August 2004
• "An introduction to Ultragraph C*-algebras", NSF-CBMS Conference on Graph Algebras, University of Iowa, June 2004
• "C*-algebras associated to Topological Quivers", Great Plains Operator Theory Symposium, University of Illinois, Urbana-Champaign, June 2003
• "Gauge-Invariant Uniqueness for Relative Cuntz-Pimsner algebras", Iowa-Nebraska Functional Analysis Seminar, Drake University, October 2002
• "Tracial states of graph algebras", Great Plains Operator Theory Symposium, University of North Carolina at Charlotte, February 2002
• "Simplicity of C*-algebras associated to graphs", University of Oregon, February 2002
• "C*-algebras of infinite graphs", University of Western Michigan, February 2002
• "Functional Analysis, C*-algebras, and directed graphs", Davidson College, January 2002
• "C*-algebras of labeled graphs", University of Newcastle, Australia, September 2001
• "Computing Ext for graph C*-algebras", Great Plains Operator Theory Symposium, University of New Hampshire, June 2001
• "Creating C*-algebras from directed graphs", Allegheny College, March 2001
• "C*-algebras generated by partial isometries and projections", College of the Holy Cross, February 2001
• "Simplicity for C*-algebras of graphs", University of Denver, February 2001
• "An overview of K-theory", Graduate Student Seminar, Dartmouth College, Fall 2000
• "Extensions of graph algebras", Great Plains Operator Theory Symposium, Puerto Rico, May 2000
• "C*-algebras of graphs", Graduate Student Seminar, Dartmouth College, Spring 2000

Grants and External Funding

• NSA Grant in Algebra, PI: Mark Tomforde, "Leavitt path algebras and their generalizations", $30,000, January, 2009 -- January, 2011.
• University of Houston Departmental Mini-Grant for research on the topic of Leavitt path algebras in Functional Analysis and Algebra, $10,000, Summer 2008.
• University of Houston Departmental Mini-Grant to develop the course ``Honors Linear Algebra", to be added to the sequence of Honors Calculus and Honors ODE's for freshmen and sophomores, $10,000, Summer 2008.
• REU Supplement to NSF grant DMS-0604429 (held by Martin Golubitsky and Kresimir Josic), $44,000, September 2007 -- August 2009.
• University of Houston Departmental Mini-Grant to develop the course Math 3397 ``Transitions to Mathematics", a first proofs course for undergraduates, $10,000, Summer 2007.
• NSF Mathematical Sciences Postdoctoral Research Fellowship (PI), $108,000, September 2002 -- July 2005.
• NSF-CBMS Regional Conference in the Mathematical Sciences "Graph Algebras: Operator Algebras We Can See" (Co-PI), with Paul Muhly and Iain Raeburn, $31,000, June 2004.

TEACHING EXPERIENCE

Math 6342: Topology (Graduate Course), Fall 2008
Math 6395: Topics in C*-algebras (Graduate Course), Spring 2008
Math 3397: Transitions to Advanced Mathematics, Fall 2007
Math 3333: Intermediate Real Analysis, Spring 2007
Math 4377: Advanced Linear Algebra, Fall 2006

Math 214 (Section 2): Foundations of Mathematics, Spring 2006
Math 112 (Section 01/02): Calculus II, Spring 2006
Math 211 (Section 01): Linear Algebra, Fall 2005
Math 112 (Section 01/02): Calculus II, Fall 2005
Math 112 (Section 05/06): Calculus II, Fall 2005

Math 118: Complex Analysis (Graduate Course), Fall 2004
Math 50: Abstract Algebra I, Spring 2004
Math 25: Calculus I, Fall 2003

Math 1: Calculus, Fall 2001
Math 24: Honors Linear Algebra, Fall 2000
Math 2: Calculus, Winter 2000

• Math 6395, "Topics in C*-algebras", Spring 2008.
  
  This is a graduate course I developed to introduce students in Functional Analysis to a wide variety of topics related to C*-algebras and Operator Algebras.
  
  
• Math 3397, "Transitions to Advanced Mathematics", Fall 2007.
  
  I developed this course to help our undergraduate math majors make the transition to upper-level proof-based courses in our department. It is intended for students to take prior to proof-writing courses (e.g., Math 3333) or for junior and senior math majors who are having difficulty in proof-based courses. The course focused on teaching the students how to communicate mathematically, and develop skills in writing proofs and speaking about mathematics.
  

• Michael Kroh, Topic: Lattices of saturated hereditary subsets in directed graphs, University of Houston, Spring 2008 -- Present.
• Rachel Hodos, Topic: Frames in finite-dimensional spaces, Spring 2007.

• Abraham Isgur, Topic: Graph traces on directed graphs, Fall 2005 -- Summer 2006.
• Joe Dorfler, Topic: Graph traces on directed graphs, Fall 2005 -- Spring 2006.
• Erin Catlett, Topic: Lattices of ideals in graph C*-algebras, Fall 2005 -- Spring 2006.
• Meg Poston, Topic: Lattices of ideals in graph C*-algebras, Fall 2005 -- Spring 2006.

• Matt Johnson, Topic: Graph traces on directed graphs, Fall 2003 -- Spring 2005.
• Jon Chaika, (supervised jointly with Paul Muhly), Topic: Quantum computation and completely positive maps, Fall 2002 -- Spring 2003.

Matt Johnson, The graph traces of finite graphs and applications to tracial states of C*-algebras, New York J. Math. 11 (2005), 649--658.

Math 15: IMPS (Multivariable Calculus), Winter 1999
Math 15: IMPS (Differential Equations and Calculus), Fall 1998
Math 15: IMPS (Multivariable Calculus), Winter 1998
Math 17: Multivariable Calculus, Fall 1997

SERVICE

• Colloquium Committee, member, Fall 2008 -- present
  
  
• Colloquium Committee, Co-chair, Fall 2007 -- Spring 2008
  
  
• Undergraduate Curriculum Committee, member, Fall 2007 -- present
  
  
• Analysis Seminar Organizer, Fall 2006 -- present
  
  

• Reviewer for NSA grant proposal, February 2007

• Acta Mathematica Sinica
  
  
• Algebras and Representation Theory
  
  
• Cubo Mathematics Journal
  
  
• Ergodic Theory and Dynamical Systems (x2)
  
  
• Houston Journal of Mathematics (x2)
  
  
• Indiana University Mathematics Journal (x2)
  
  
• Journal für die Reine und Angewandte Mathematik (Crelle's Journal) (x2)
  
  
• Journal of Algebra
  
  
• Journal of Operator Theory (x3)
  
  
• Journal of Mathematical Analysis and Applications (x3)
  
  
• Journal of Pure and Applied Algebra
  
  
• Mathematische Zeitschrift
  
  
• Monatshefte für Mathematik (x2)
  
  
• New York Journal of Mathematics (x2)
  
  
• Proceedings of the American Mathematical Society
  
  
• Rocky Mountain Journal of Mathematics
  
  
• Transactions of the American Mathematical Society (x3)

• Mathematical Reviews and MathSciNet (Mathematical Reviews on the Web), 2003 -- present

• Examiner, Ph.D. Thesis committee for Mrinal Raghupathi in Mathematics (Chair: Vern I. Paulsen), University of Houston, April 2008.
  
  
• Outside Examiner, Ph.D. Thesis committee for Lisa Orloff Clark in Mathematics (Chair: Dana P. Williams), Dartmouth College, May 2004.
  
  
• Outside Examiner, Ph.D. Thesis committee for Aidan Sims in Mathematics (Chair: Iain Raeburn), University of Newcastle, Australia, December 2003.
  
  
• Outside Examiner, Ph.D. Thesis committee for Menassie Ephrem in Mathematics (Chair: Jack Spielberg), Arizona State University, August 2003.

• NSF-CBMS Regional Conference in the Mathematical Sciences, "Graph Algebras: Operator Algebras We Can See", Principal Lecturer: Iain Raeburn, hosted by Paul Muhly and myself at the University of Iowa, June 2004.

HONORS, AWARDS, AND ACTIVITIES

• AMS Project NExT Fellow, 2003-2004
• NSF Postdoctoral Fellowship, 2002-2005
• Graduate Fellowship, Dartmouth College, 1997-2002
• Graduate Student Seminar Coordinator, Dartmouth College, 2000-2002
• Institute for Advanced Study/Park City Math Institute, participant, Summer 1997
• Barry M. Goldwater Scholarship for Excellence in Mathematics and Science, 1996
• NSF Research Experience for Undergraduates, University of Oklahoma, participant, Summer 1996
• Institute for Advanced Study/Park City Math Institute, participant, Summer 1995
• National Merit Scholar, 1993
• Member of AMS and MAA, 1993-present

REFERENCES

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