# Nathan S. Feldman

Curriculum Vitae

Radford Professor of Mathematics

Department of Mathematics

Washington and Lee University

Lexington, VA 24450

Phone: 540-458-8033

Fax: 540-458-8479

e-mail: feldmanN at wlu dot edu

WWW: https://feldman.academic.wlu.edu

## EDUCATION:

**Ph.D. in Math** University of Tennessee 1997

Thesis: The Self-Commutator of a Subnormal Operator

**
M.S. in Math **University of Tennessee 1993

**Thesis: Rigidity of Complete Hyperbolic Manifolds and Riemann Surfaces**

**Utah State University 1990**

B.S. in Math

B.S. in Math

## PROFESSIONAL EXPERIENCE:

2015 - 2018 Mathematics Department Chair

2012 - Present Radford Professor of Mathematics at Washington & Lee University

2010 - 2012 Professor at Washington & Lee University

2004 - 2010 Associate Professor at Washington & Lee University

1999 - 2004 Assistant Professor at Washington & Lee University

1997 - 1999 Visiting Research Instructor (Postdoc) at Michigan State University

1990 - 1997 Graduate Teaching Assistant at University of Tennessee, Knoxville

Fall 1989 Instructor at Utah State University

## PROFESSIONAL MEMBERSHIPS & GRANTS:

Member of American Mathematical Society, Mathematical Association of America, and Pi Mu Epsilon

1999 - 2002 NSF Research Grant - Operator Theory and Complex Analysis

My Ph.D. advisor was John B. Conway, his advisor was Herron Collins,... see my Mathematical Lineage

## RESEARCH:

My research area is analysis. I specialize in operator theory and complex analysis. More precisely, I study linear operators on Hilbert space that are "close to normal operators", such as subnormal and hyponormal operators. One topic of interest involves the study of the cyclic behavior of adjoints of subnormal and hyponormal operators. Recent work involves invariant convex sets for linear operators, convex-cyclic operators and convex-polynomial approximation.

## INVITED & CONTRIBUTED TALKS

**2017**

SEAM 33 at SEAM (the South Eastern Analysis Meeting) at the University of Tennessee, Knoxville, March 17-19, 2017.

**Title:** *Convex-Cyclicity & Convex-Polynomial Approximation*

**2016**

NEAM 1 at SUNY-Brockport, Brockport, NY, October 14-16, 2016

**Title: ***Convex-Polynomial Interpolation, Approximation & Invariant Convex Sets
*

**2015**

SEAM 31 at University of Georgia, Athens, GA, March 9th, 2015

**Title: ***A Convex-Stone Weierstrass Theorem & Convex Dynamics
*

Distinguished Visiting Professor at Bucknell University, Lewisburg, PA,

October 26 - 30, 2015

**Colloquium Talk: ***Invariant Convex Sets for Linear Operators*

**Seminar Talk:** *Dynamics & Chaos
*

**2014**

Distinguished Visiting Professor at Bucknell University, Lewisburg, PA,

April 28 - May 2, 2014

**Colloquium Talk:** *Mathematics, Magic, and Mystery*

**Seminar Talk:** *The Dynamics of Linear Operators*

Analysis Seminar at Bucknell University, Lewisburg, PA, Oct. 7, 2014

Title: *Convex-Cyclic Matrices & Operators*

Analysis Seminar at Bucknell University, Lewisburg, PA, Oct. 28, 2014

**Title: ***A Convex Stone-Weierstrass Theorem*

Analysis Seminar at Bucknell University, Lewisburg, PA, Nov. 11, 2014

Title: *Convex-Polynomial Approximation
*

**2013**

SEAM 29 at Virginia Tech, March 15th, 2013

**Title: ***n-**Weakly Dense Orbits of Linear Operators*

**
**Colloquium at Brigham Young University, April 9, 2013

**The Dynamics of Linear Operators**

Title:

Title:

Invited Speaker:

Invited Speaker:

*The Dynamics of Linear Operators*

**2012**

VOTCAM at Virginia Commonwealth University, Richmond, VA**
**November 3, 2012

Title:

Title:

*Dynamics of Linear Operators*

*and Matrices*

**2011**

John Conway Day & SEAM XXVII at Univeristy of Florida, Gainsville

March 17-19, 2011

**Invited Speaker:** *The Cyclic Behavior of Cosubnormal Operators*

Analysis Seminar at Univ. of Virginia, November 15, 2011

**Title: ***Dynamics of Linear Operators*

**2010**

Distinguished Visiting Professor at Bucknell University, Lewisburg, PA,

April 19 - 23, 2010

**Colloquium Talk:** *The Dynamics of Linear Operators*

**Seminar Talk:** *The Dynamics of Linear Operators II*

Functional Analysis Valencia 2010 at University of Valencia, Spain, June 7 - 11, 2010

On the Occasion of the 80th Birthday of Professor Manuel Valdivia

**Invited Speaker** at the Special Session on Linear Dynamics

**Title: ***n-Weakly Hypercyclic and n-Weakly Supercyclic Operators*

AMS Sectional Meeting at University of Richmond, November 6-7, 2010

**Invited Speaker - Title: ***n-Weakly Hypercyclic Operators*

**2009**

Joint AMS-MAA Meeting at Washington DC, January 8, 2009

**Title: ***Hypercyclic** Operators with a Prescribed Spectrum*

Distinguished Visiting Professor at Bucknell University, Lewisburg, PA

April 6 - 10, 2009

**Colloquium Talk:** *A unified approach to some major theorems in topology.*

**Student Talk:** *Which line best approximates a function?*

**2008**

SEAM XXIV at Vanderbilt University, March 5-8, 2008

**Title:** *Somewhere Dense Orbits of Tuples of Operators*

Invited Speaker at the 5th Advanced Course in Operator Theory and Complex Analysis in Sevilla, Spain, June 24-26, 2008

**Title:** *Hypercyclic** Operators with Prescribed Spectrum*

**Colloquium Talk** at Universitat Politecnica de Valencia, Valencia Spain, June 26-27, 2008

**Title:*** Inverse Limits of Hypercyclic Operators*

Analysis Seminar, George Washington University, Sept. 29, 2008

**Title: ***Invariant Subspaces in the Hardy Space of the Slit Disk*

**2007**

**Colloquium Talk** at University of Richmond, February 19, 2007

**Title:** *How far from normal are you?*

SEAM XXIII at University of Richmond, March 9-11, 2007

Title:*Invariant Subspaces on the Slit Disk*

AMS Sectional Meeting at Tucson, Arizona, April 21-22, 2007

Title:*Invariant Subspaces on the Slit Disk*

**2006**

Distinguished Visiting Professor at Bucknell University, Lewisburg, PA, Feb. 12 - 18, 2006

**Colloquium Talk:** *How far from normal are you?*

**Seminar Talk:** *The distance to the normal matrices: Part II*

SEAM XXII at University of Florida, Gainesville, March 1-5, 2006

Title:*Hypercyclic** Pairs of Operators*

GPOTS - Great Plains Operator Theory Symposium at University of Iowa, May 24-28, 2006

**Featured Speaker, Title: ***Subnormality** & C*-algebras*

Oberwolfach, Germany, Mini-Conference on* "Hypercyclicity and Linear Chaos", *August 13-19, 2006

**Title: ***Hypercyclic** Tuples of Operators*

**2005**

**VOTCAM at University of Richmond, Richmond, VA February 5, 2005
Title: Subnormal Generators of C*-algebras and Spectral Pictures of Toeplitz Operators**

Organizer of SEAM XXI held at Washington & Lee University, Lexington, VA, April 8-9, 2005

Distinguished Visiting Professor at Bucknell University, Lewisburg, PA, May 1 - 7, 2005

Colloquium Talk: *Special Generators of C*-algebras I*

Seminar Talk: *Special Generators of C*-algebras II*

Oberwolfach, Germany, Mini-Conference on* "Operators on Spaces of Analytic Functions", *August 14-20, 2005

Title:* Interpolating Measures for Subnormal Operators*

Colloquium at Washington & Lee University, September 22, 2005

Title:* ** Oberwolfach & Generalized Eigenvectors*

**2004**

**SEAM XX at University of Alabama, Tuscaloosa, March 26-27, 2004**

**Title: Subnormal generators of C*-algebras**

Distinguished Visiting Professor at Bucknell University, Lewisburg, PA, May 10 - 14, 2004

**Colloquium Talk: Linear Operators and Generalized Eigenvectors**

**2003**

SEAM XIX at University of Tennessee, Knoxville, March 21 - 23, 2003

**Title: ** *Exotic Orbits for Linear Operators*

__Distinguished Visiting Professor__ at Bucknell University, Lewisburg, PA

April 14 - 18, 2003

**Colloquium Talk:** *Understanding the real parts of Calculus through the imaginary parts*

**Seminar Talk:** *The C*-algebra generated by a subnormal operator*

Colloquium at Washington & Lee University, April 24, 2003

**Title: **

*Dynamics of Linear Operators*

YAMS at Furman University, Greenville, SC July 8 - 12, 2003, Invited Speaker

**Title:** *The Fredholm Index of Toeplitz Operators with Continuous Symbols*

**2002**

SEAM XVIII at University of North Carolina, Chapel Hill, March 15 - 17, 2002

**Title:** *Spectral Picture's of Irreducible Subnormal Operators*

Analysis Seminar at Washington & Lee University, May 21, 2002

**Title:** *Orbits of Linear Operators*

VOTCAM at University of Richmond, Richmond, VA September 12, 2002

**Title: ** *Generalized Eigenvectors and Interpolating Measures for Subnormal Operators*

**2001**

** **SEAM XVII at University of Georgia, Athens, GA, March 2-3, 2001

**Title: ** *Somewhere Dense Orbits are Everywhere Dense*

YAMS at Furman University, Greenville, SC, July 10-14, 2001, 30 min., Invited Speaker

**Title:** *The Dynamics of Cosubnormal Operators*

__Distinguished Visiting Professor__ at Bucknell University, Lewisburg, PA

Sept. 3-7, 2001

**Colloquium Talk:** *Dynamics and Chaos*

**Seminar Talk:** *The Dynamics of Linear Operators*

Wabash Modern Analysis Miniconference at Indiana Univ., Sept. 8-9, 2001

**Title:** *Countably** Hypercyclic Operators*

Analysis Seminar, University of Tennessee, Knoxville, Oct. 1, 2001

**Title:** *The Dynamics of Linear Operators*

Trends in Banach Spaces and Operator Theory at Univ. of Memphis, Oct. 5-9, 2001

**Title: ***Orbits of Linear Operators*

**2000**

SEAM XVI at University of Virginia, March 17-18, 2000

**Title: ***Hypercyclic** and Supercyclic Cohyponormal Operators*

Analysis Seminar at Univ. of Virginia, April 11, 2000

**Title: ***The Cyclic behavior of Cosubnormal Operators*

Wabash Modern Analysis Miniconference at Indianapolis, October 14-15, 2000

**Title: ***Hyponormal** Operators with Hypercyclic or Supercyclic Adjoints*

Colloquium at Brigham Young University, November 20, 2000

**Title:** *The Dynamics of Linear Operators*

**1999**

Joint AMS-MAA Meeting at San Antonio, TX January 13-16, 1999

**Title: ***Pure Subnormal Operators have Cyclic Adjoints*

Colloquium at University of Pittsburgh, January 22, 1999

**Title: ***Cyclic Subnormal Operators and Trace Estimates*

Colloquium at Washington & Lee University, February 8, 1999

**Title: ***The Most Important Matrix*

Colloquium at University of California, Riverside, February 12, 1999

**Title: ***Pure Subnormal Operators have Cyclic Adjoints*

Analysis Seminar at Wayne State University, March 30, 1999

**Title: ***Pure Subnormal Operators have Cyclic Adjoints*

Colloquium at Bowling Green State University, April 12, 1999

**Title: ***Pure Subnormal Operators have Cyclic Adjoints*

SEAM XV at Vanderbilt University, May 20--23, 1999

**Title: ***Subnormal Operators with Hypercyclic Adjoints*

Colloquium at Mississippi State University, November 5, 1999

**Title:** Hypercyclic and Supercyclic Cosubnormal Operators

**1998**

AMS Sectional Meeting at Kansas State Univ., March 27-28, 1998

**Title: When**

*is zero an eigenvalue for the self-commutator of a subnormal operator?*

Colloquium at Michigan State University, April 16, 1998

**Title: ***Subnormal Operators and C* algebras*

GPOTS - Great Plains Operator Theory Symposium at Kansas State, May 27-31, 1998

**Title: ***Pure Subnormal Operators have Cyclic Adjoints*

Canadian Math. Soc. Summer Meeting at Univ. of New Brunswick, St. Johns

June 13-15, 1998, 25 min. Invited Speaker

**Title: ***Pure Subnormal Operators have Cyclic Adjoints*

Wabash Modern Analysis Miniconference at Indianapolis, October 10-11, 1998

**Title: ***Pure Subnormal Operators have Cyclic Adjoints*

**1997**

Analysis Seminar at Virginia Tech, Blacksburg Va., Jan. 20, 1997, Invited Speaker

**Title: ***The Self-Commutator of a Subnormal Operator*

SEAM XIII at Gainesville, Florida, March 14-16, 1997, 20 min.

**Title: ***The Berger-Shaw Theorem for Cyclic Subnormal Operators*

Wabash Modern Analysis Miniconference at Indianapolis, Sept. 20-21 1997, 20 min.

**Title:*** Essentially Subnormal Operators*

Analysis Seminar at Univ. of Michigan, Ann Arbor, Nov. 11, 1997, Invited Speaker

**Title: ***Subnormal Operators and Pseudocontinuations*

**1996**

Young Analysts Meeting of the Southeast (YAMS 2) at Maggie Valley, NC, November 9-10, 1996, 50 min. Invited Speaker

**Title: ***The Self-Commutator of a Subnormal Operator*

**1995**

South Eastern Analysis Meeting (SEAM XI) at Georgia Tech., March 3-5, 1995, 20 min.

**Title: ***On the failure of spectral mapping theorems for subnormal operators*

Workshop on Holomorphic Spaces at MSRI, October 16-20, 1995, 25 min.

**Title: ***Integrability** of Hardy space functions and pointwise multipliers of the Hardy space into the Bergman space*