Torsten Ehrhardt Associate Professor Department of Mathematics University of California, Santa Cruz

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1 Torsten Ehrhardt Associate Professor Department of Mathematics University of California, Santa Cruz Education 2004 Habilitation degree, Technische Universität Chemnitz, Germany 1997 Ph.D. in Mathematics, Technische Universität Chemnitz, Germany Theses advisor: Bernd Silbermann 1994 Diploma in Mathematics, Technische Universität Chemnitz, Germany Theses advisor: Bernd Silbermann Academic career 7/08 present Associate Professor University of California at Santa Cruz 3/08 6/09 Assistant and Associate Professor POSTECH, South Korea (on leave from UCSC) 7/04 6/08 Assistant Professor University of California at Santa Cruz 11/98 9/04 Assistant Professor ( Wissenschaftlicher Assistent ) Technische Universität Chemnitz, Germany 1/03 3/03 Visiting Researcher ( Wetenschappelijk onderzoeker ) Erasmus Universiteit Rotterdam, The Netherlands 2/99 7/99 Postdoctoral Fellow Mathematical Sciences Research Institute, Berkeley 10/97 11/98 Postdoctoral Fellow Technische Universität Chemnitz, Germany 5/97 9/97 Scientific Assistant ( Wissenschaftlicher Mitarbeiter ) Technische Universität Chemnitz, Germany

2 Honors and Awards 1998 University prize of the Technische Universität Chemnitz (The prize honors outstanding scientific achievements.) 1990 Second prize at the 31st International Mathematical Olympiad in Beijing Fellowships 2004 approval of 1-year Research Fellowship from DFG (German Science Foundation) for a research visit in the U.S. (offer declined) month Postdoctoral Fellowship from MSRI for the participation in the program on Random Matrices month Fellowship from DAAD (German Academic Exchange Service) for a research visit in U.S. Grants 2009 NSF grant DMS , 2 years, $167,394 Topics in Operator Theory with Applications to Random Matrices, awarded June 15, 2009 Professional Service Editor for the Bulletin of the Korean Mathematical Society (since 03/2009) Referee for various journals, in particular, in the area of Operator Theory

3 Publications 42. T. Ehrhardt, The asymptotics of a Bessel-kernel determinant which arises in Random Matrix Theory, submitted. 41. T. Ehrhardt, A.P. Nolasco, F.-O. Speck, Boundary integral methods for wedge diffraction problems: the angle 2π/n, Dirichlet and Neumann conditions, submitted. 40. T. Ehrhardt, S. Roch, B. Silbermann, The Szegö-Widom Limit theorem for operators with almost periodic diagonal, submitted. 39. E.L. Basor, Y. Chen, T. Ehrhardt, Painlevé V and time-dependent Jacobi polynomials, J. Phys. A: Math. Theor. 43 (2010), E.L. Basor, T.Ehrhardt, Determinant computations for some classes of Toeplitz- Hankel matrices, Oper. Matrices 3, no. 2 (2009), H. Bart, T. Ehrhardt, B. Silbermann, Trace conditions for regular spectral behavior of vector-valued analytic functions, Linear Alg. Appl. 430, no. 8-9 (2009), E.L. Basor, T.Ehrhardt, Asymptotics of block Toeplitz determinants and the classical dimer model, Comm. Math. Phys. 274 (2007), T.Ehrhardt, Determinant calculations for the block Szegö-Widom Limit Theorem, Math. Nachr. 280 (2007), T.Ehrhardt, Dyson s constants in the asymptotics of the determinants of Wiener-Hopf- Hankel operators with the sine kernel, Comm. Math. Phys. 272 (2007), T. Ehrhardt, C. van der Mee, L. Rodman, I.M. Spitkovsky, Factorization in weighted Wiener matrix algebras on linearly ordered Abelian groups, Integral Equations and Operator Theory 58 (2007), E.L. Basor, T. Ehrhardt, Factorization theory for a class of Toeplitz + Hankel operators and the A p -condition, J. Operator Theory 55 (2006), T. Ehrhardt, Dyson s constant in the asymptotics of the Fredholm determinant of the sine kernel, Comm. Math. Phys. 262 (2006), E.L. Basor, T. Ehrhardt, On the asymptotics of certain Wiener-Hopf-plus-Hankel determinants, New York J. Math. 11 (2005), , H. Bart, T. Ehrhardt, B. Silbermann, Logarithmic Residues in the Banach algebra generated by the compact operators and the identity, Math. Nachr. 268 (2004), E.L. Basor, T. Ehrhardt, Factorization theory for a class of Toeplitz + Hankel operators, J. Operator Theory 51 (2004),

4 27. T. Ehrhardt, Invertibility theory for Toeplitz plus Hankel operators and singular integral operators with flip, J. Funct. Analysis 208 (2004), E.L. Basor, T. Ehrhardt, H. Widom, On the determinant of certain Wiener-Hopf plus Hankel operators, Integral Equations Operator Theory 47 (2003), T. Ehrhardt, A generalization of Pincus formula and Toeplitz operator determinants, Arch. Math. (Basel) 80 (2003), E.L. Basor, T. Ehrhardt, Asymptotics of determinants of Bessel operators, Comm. Math. Physics 234 (2003), T. Ehrhardt, C.V.M. van der Mee, Canonical factorization of continuous functions on the d-torus, Proc. Amer. Math. Soc. 131, no. 3 (2003), T. Ehrhardt, A new algebraic approach to the Szegő-Widom Limit Theorem, Acta Math. Hungar. 99, no. 3 (2003), T. Ehrhardt, F.-O. Speck, Transformation techniques towards the factorization of non-rational 2 2 matrix functions, Linear Algebra Appl. 353 (2002), E.L. Basor, T. Ehrhardt, Asymptotic formulas for the determinants of symmetric Toeplitz plus Hankel matrices, in: Oper. Theory Adv. Appl., Vol. 135, Birkhäuser, Basel 2002, H. Bart, T. Ehrhardt, B. Silbermann, Sums of idempotents in the Banach algebra generated by the compact operators and the identity, in: Oper. Theory Adv. Appl., Vol. 135, Birkhäuser, Basel 2002, E.L. Basor, T. Ehrhardt, Some identities for determinants of structured matrices, Linear Algebra Appl (2002), H. Bart, T. Ehrhardt, B. Silbermann, Logarithmic residues of analytic Banach algebra valued functions possessing simply meromorphic inverses, Linear Algebra Appl. 341 (2002), H. Bart, T. Ehrhardt, B. Silbermann, Logarithmic residues of Fredholm operator valued functions and sums of finite rank projections, in: Oper. Theory Adv. Appl., Vol. 130, Birkhäuser, Basel, 2002, T. Ehrhardt, I. M. Spitkovsky, Factorization of piecewise constant matrix functions and systems of linear differential equations, Algebra i Analiz 13, no. 6 (2001), (in Russian), English version in: St. Petersburg Math. J. 13, no. 6 (2002), T. Ehrhardt, S. Rabanovich, Yu. Samoĭlenko, B. Silbermann, On the decomposition of the identity into a sum of idempotents, Methods Funct. Anal. Topology 7, no. 2 (2001), E.L. Basor, T. Ehrhardt, Asymptotic formulas for determinants of a sum of finite Toeplitz and Hankel matrices, Math. Nachr. 228 (2001), 5 45.

5 12. T. Ehrhardt, A status report on the asymptotic behavior of Toeplitz determinants with Fisher Hartwig singularities, in: Oper. Theory Adv. Appl., Vol. 124, Birkhäuser, Basel, 2001, H. Bart, T. Ehrhardt, B. Silbermann, Logarithmic residues and sums of idempotents in matrix algebras, in: Oper. Theory Adv. Appl., Vol. 122, Birkhäuser, Basel, 2001, T. Ehrhardt, B. Shao, Asymptotic behavior of variable coefficient Toeplitz determinants, J. Fourier Anal. Appl. 7, no. 1 (2001), T. Ehrhardt, B. Silbermann, Approximate identities and stability of discrete convolution operators with flip, in: Oper. Theory Adv. Appl., Vol. 110, Birkhäuser, Basel, 1999, E.L. Basor, T. Ehrhardt, On a class of Toeplitz + Hankel operators, New York J. Math. 5 (1999), 1 16, 7. H. Bart, T. Ehrhardt, B. Silbermann, Logarithmic residues, generalized idempotents, and sums of idempotents in Banach algebras, Integral Equations Operator Theory 29, no. 2 (1997), T. Ehrhardt, B. Silbermann, Toeplitz determinants with one Fisher-Hartwig singularity, J. Funct. Anal. 148, no. 1 (1997), T. Ehrhardt, S. Roch, B. Silbermann, Finite section method for singular integrals with operator-valued PQC-coefficients, in: Oper. Theory Adv. Appl., Vol. 90, Birkhäuser, Basel, 1996, T. Ehrhardt, S. Roch, B. Silbermann, Symbol calculus for singular integrals with operator-valued PQC-coefficients, in: Oper. Theory Adv. Appl., Vol. 90, Birkhäuser, Basel, 1996, T. Ehrhardt, Finite sums of idempotents and logarithmic residues on connected domains, Integral Equations Operator Theory 21, no. 2 (1995), H. Bart, T. Ehrhardt, B. Silbermann, Logarithmic residues in Banach algebras, Integral Equations Operator Theory 19, no. 2 (1994), H. Bart, T. Ehrhardt, B. Silbermann, Zero sums of idempotents in Banach algebras, Integral Equations Operator Theory 19, no. 2 (1994), Other writings 1. T. Ehrhardt, B. Silbermann, Szegö limit theorems, in: Supplement III, Encyclopaedia of Mathematics, Managing Editor: M. Hazewinkel, Kluwer Academic Publishers, 2002,

6 Theses 2. T. Ehrhardt, Factorization theory for Toeplitz + Hankel operators and singular integral operator with flip, Habilitation theses, Technische Universität Chemnitz, 2004, ii+253 pages, 1. T. Ehrhardt, Toeplitz determinants with several Fisher-Hartwig singularities, Ph.D. theses, Technische Universität Chemnitz, 1997, 111 pages. Participation at professional meetings th KOTAC International Conference 2009 Operator Theory and its Applications, June 18-20, 2009, Kyungbuk National University, Daegu, Korea, invited speaker On logarithmic residues of vector-valued functions. 24. Global KMS 2008 Fall Conference, Oct , 2008, Jeju, Korea, talk: Determinant computations for some Toeplitz-Hankel matrices. 23. CRM Workshop on Random Matrices, related topics, and applications, Aug , 2008, Montreal, Canada, invited talk: Linear statistics of the Ginibre ensemble and determinants of modified Toeplitz matrices. 22. International Workshop on Operator Theory and Its Applications (IWOTA), Williamsburg, VA, USA, July 22-26, 2008, talk: Invertibility for some classes of Toeplitz+ Hankel operators, and applications. 21. Workshop on Random Matrix Theory and Wireless Communication, Boulder, Colorado, USA, July 14-17, 2008, invited speaker, participation cancelled because of delayed VISA-issuance th KOTAC International Conference 2008 Operator Theory and its Applications, June 19-21, 2008, Seoul National University, South Korea, invited speaker Invertibility theory for some classes of Toeplitz+Hankel operators. 19. ICMS Workshop on Riemann-Hilbert problems and Toeplitz operators, Sept. 3-7, 2007, Edinburgh, UK, invited speaker Gap probabilities in Random Matrix Theory and determinants of Wiener-Hopf-Hankel operators. 18. AMS-IMS-SIAM conference on Interactions on Random Matrix Theory, Integrable Systems, and Stochastic Processes, June 24-28, 2007, Snowbird, UT, USA, invited speaker Asymptotics of the determinants of Wiener-Hopf Hankel operators with the sine-kernel. 17. Joint AMS and Mexican Math. Soc.-Meeting, Zacatecas, Mexico, May 24-26, 2007, invited to Special session on Operator Theory and Complex Analysis, talk: Szegö-Widom limit theorems for band-dominated operators with almost periodic coefficients.

7 16. AMS-Meeting, Tuscon, AZ, USA, April 23-26, 2007, invited to Special Session on New Developments and Directions in Random Matrix Theory, talk: Szegö-Widom limit theorems for band-dominated operators with almost periodic coefficients. 15. International Workshop on Operator Theory and Its Applications (IWOTA), Seoul National University, South Korea, July 31-Aug. 3, 2006, talk: Asymptotics behavior of some classes of Toeplitz-plus-Hankel determinants th ILAS Conference, Amsterdam, The Netherlands, July 18-21, 2006, talk: Asymptotics behavior of some classes of Toeplitz plus Hankel determinants. 13. Robert C. Thompson Matrix Meeting 2007, SFSU, Nov. 19, 2005, talk: Identities between Toeplitz and Hankel determinants. 12. ISAAC-Congress (International Society for Analysis, its Applications and Computation), Università di Catania, Italy, July 25-30, 2005, talk: The classical dimer model and block Toeplitz determinants. 11. Conference on Operator Theory, Function Spaces and Applications (OTFUSA), Universidade de Aveiro, Portugal, July 7-9, 2005, talk: Asymptotics of determinants of Wiener- Hopf-plus-Hankel operators with singular symbols. 10. Prelude of Mathematical Lectures on the occasion of the retirement of Prof. H. Bart, Erasmus Universiteit Rotterdam, The Netherlands, April 22-23, 2004, invited speaker, talk: Logarithmic residues in Banach algebras. 9. International Workshop on Operator Theory and Its Applications (IWOTA), Università di Cagliari, Italy, June 24-27, 2003, talk: Factorization theory for infinite Toeplitz plus Hankel matrices. 8. International Conference on Functional Analysis and Approximation Theory, Aqcuafredda di Maratea, Italy, September 22-28, 2000, talk: Invertibility of Toeplitz plus Hankel operators. 7. International Workshop on Operator Theory and Its Applications (IWOTA), Universidade do Algarve, Faro, Portugal, September 12-15, 2000, talk: Invertibility of Toeplitz plus Hankel operators. 6. Workshop on structured matrices, Technische Universität Chemnitz, Germany, January 6-7, 2000, talk: Asymptotic behavior of determinants of Toeplitz plus Hankel matrices. 5. Great Plains Operator Theory Symposium (GPOTS), Iowa State University, Ames, May 26-30, 1999, talk: Toeplitz determinants with several Fisher-Hartwig singularities. 4. International Workshop on Operator Theory and Its Applications (IWOTA), Rijksuniversiteit Groningen, The Netherlands, June 29 - July 3, 1998, talk Toeplitz determinants with several Fisher-Hartwig singularities.

8 3. International Workshop on Operator Theory and Its Applications (IWOTA), Indiana University, Bloomington, June 18-22, 1996, talk: Logarithmics residues and idempotents in Banach algebras. 2. Great Plains Operator Theory Symposium (GPOTS), Arizona State University, Phoenix- Tempe, May 22-26, 1996, talk: Logarithmics residues and idempotents in Banach algebras. 1. South Eastern Analysis Meeting (SEAM), University of Richmond (Virginia), March 15-17, 1996, talk: Toeplitz determinants with one Fisher-Hartwig singularity. Colloquium and seminar talks (since September 2003) 11. University of Colardo, Boulder, probability seminar talk: On the asymptotics of certain gap probabilities in Random Matrix Theory, March 17, UCSC, Graduate colloquium talk: From random matrices to Toeplitz matrices, and back, Jan 28, Seoul National University, Colloquium talk: Asymptotic behavior of Toeplitz+Hankel determinants, April 18, Johannes Gutenberg Universität Mainz, Colloquium talk: Asymptotisches Verhalten von Toeplitzdeterminanten, Dec. 15, Università di Cagliari, Italy, Seminar talk: Asymptotics of determinants of Wiener-Hopfplus-Hankel operators with singular symbols, July 21, Technische Universität Chemnitz, Germany, Seminar talk: Das klassische Dimer-Modell und Toeplitzdeterminanten, June 26, UCSC, Colloquium talk: A generalization of Pincus formula, March 1, San Jose State University, Colloquium talk: A generalization of Pincus formula, Febr. 16, Instituto Superior Técnico, Universidade de Lisboa, Colloquium talk: Factorization theory for singular integral operators with flip, March 26, Calif. Polytechnic State University, Colloquium talk: A generalization of Pincus formula, Sept. 26, Technische Universität Chemnitz, Colloquium talk: Factorization theory for Toeplitzplus-Hankel operators, Oct. 27, 2003.

9 TEACHING AND DEPARTMENT SERVICE Teaching at UCSC 2009/2010: Winter Math 205 Analysis II (Measure and Integration) Winter Math 105A Real Analysis Fall Math 103 Complex Analysis Spring 2008 Spring 2009: on leave 2007/2008: Winter Math 207 Complex Analysis Winter Math 103 Complex Analysis Fall Math 19B Calculus for Math, Sci, and Eng Fall Math 199 Independent Study 2006/2007: Spring Math 105B Real Analysis II Winter Math 105A Real Analysis I Fall Math 204 Analysis I (Topology) 2005/2006: Spring Math 206 Analysis III (Functional Analysis) Winter Math 117 Advanced Linear Algebra Winter Math 207 Complex Analysis Fall Math 19B Calculus for Math, Sci, and Eng 2004/2005: Spring Math 199 Independent Study Spring Math 105 B Real Analysis II Winter Math 105 A Real Analysis I Fall Math 103 Complex Analysis Service for UCSC Math Department Chair for the Mathematics Colloquium at UCSC from Fall 2006 until Winter 2008 Chair for the Analysis Preliminary Exam in Spring 2007, Winter 2008, and Winter 2010

10 Teaching at POSTECH, South Korea Spring semester 2009 Fall semester 2008 Spring semester 2008 Partial Differential Equations (graduate) Special Topics Course in Analysis (graduate) Mathematics I (undergraduate) Other: Co-organizer of a Math-Club, Fall 2008 and Spring 2009 Organizer of Mathematics Colloquium, POSTECH, Spring 2009 Teaching at Technische Universität Chemnitz Winter 2003 Summer 2003 Winter 2002 Winter 2001 Spectral theory of selfadjoint operators Number Theory II Number Theory I Operator Theory and Numerical Analysis Other: Tutoring of gifted high-school students on an irregular basis (approx. once every two weeks during teaching period) from Teaching problem session courses from for the following lectures: Analysis for Mathematicians I III (3 semester) Mathematics for Computer Scientists I III (3 semesters, 2 times) Partial Differential Equations (1 semester, 3 times) This is comparable to the duty of a TA (teaching assistant), however, it usually involves complete responsibility.