- The research group
- ERC Starting Grant
- Sofja Kovalevskaja project
- DFG priority programme project
- Schavan professorship

- Maxim Derevyagin, Ph.D. (orthogonal polynomials, complex analysis, operator theory)
- Alex Dyachenko, Ph.D. student (fluid mechanics, complex analysis)
- Volha (Olga) Kushel, Ph. D. (total positivity and its generalizations)
- Michal Wojtylak, Ph. D. (matrix theory, perturbation theory)
- Galina Yuferova, Ph. D. (classical real and complex analysis, inequalities)

- Diego Dominici (orthogonal polynomials, special functions, asymptotic methods). currently an associate professor at CUNY New Paltz.
- Anders Jensen (commutative algebra, symbolic computations); currently at Aarhus University.
- Sadegh Jokar (approximation theory, wavelets and splines, compressive sensing, discretizations of PDEs); currently working in industry.
- Matthias Lenz (commutative algebra, geometry and combinatorics); currently a Junior Research Fellow at the University of Oxford.
- Luca Moci (commutative algebra, toric geometry), currently a postdoc at Institut de MathÃ©matiques de Jussieu (Paris 7).
- Nenad Moraca (linear algebra, combinatorics, probability); currently at the Novyi Sad University, Serbia.
- Ipek Savun (differential equations, stability); currently a high school teacher in Cyprus.
- Oded Schwartz (complexity theory, analysis of algorithms); currently a postdoc at UC Berkeley.
- Mikhail Tyaglov (classical real and complex analysis, stability and hyperbolicity); currently a special researcher at Shanghai Jiao Tong University.
- Zhiqiang Xu (approximation theory, splines, combinatorics); currently an associate professor at the Academy of Mathematics and Systems of the Chinese Academy of Sciences.

- classical analysis,
- operator theory,
- mathematical physics.

**Publications:**

- Alexander Dyachenko,
**Total nonnegativity of infinite Hurwitz matrices of entire and meromorphic functions,**Apr 2013. arXiv version. - Maxim Derevyagin,
**On the relation between Darboux transformations and polynomial mappings,**Dec 2012. arXiv version. - Matthias Lenz,
**Interpolation, box splines, and lattice points in zonotopes,**Nov. 2012. arXiv version. - Maxim Derevyagin, Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov,
**Bannai-Ito polynomials and dressing chains,**Nov 2012. arXiv version. - Mikhail Tyaglov,
**On the spectra of Schwarz matrices with certain sign patterns,**Electron. J. Linear Algebra 24 (2012), Special issue for the 2011 Directions in Matrix Theory Conference, 215-236. arXiv version. - Maxim Derevyagin, Olga Holtz, Sergey Khrushchev and Mikhail Tyaglov,
**Szego's theorem for matrix orthogonal polynomials,**J. Approx. Theory, 164 (2012), no. 9, 1238-1261 arXiv version.

**AIM Workshop:**

**Accurate and efficient linear algebra and related algorithms:**computational complexity and numerical stability of sequential and parallel linear algebra algorithms, stability of multivariate polynomial evaluation in floating point arithmetics.**Publications:**- Grey Ballard, James Demmel, Olga Holtz and Oded Schwartz,
**Graph expansion and communication costs of fast matrix multiplication,**J. ACM 59 (2012), no. 6, Art. 32, 23 pp. arXiv version. - Grey Ballard, James Demmel, Olga Holtz and Oded Schwartz,
**Minimizing communication in numerical linear algebra,**SIAM J. Matrix Anal. Appl. 32 (2011), no. 3, 866-901. arXiv version. - Olga Holtz and Noam Shomron,
**Computational complexity and numerical stability of linear problems,**European Congress of Mathematics, 381-400, Eur. Math. Soc., Zurich, 2010. arXiv version. - Grey Ballard, James Demmel, Olga Holtz and Oded Schwartz,
**Communication-optimal parallel and sequential Cholesky decomposition,**SIAM J. Sci. Comput. 32 (2010), no. 6, 3495-3523. arXiv version. - James Demmel, Ioana Dumitriu, Olga Holtz and Plamen Koev,
**Accurate and efficient expression evaluation and linear algebra,**Acta Numerica, 17 (2008), 87-145. arXiv version. - James Demmel, Ioana Dumitriu and Olga Holtz,
**Fast linear algebra is stable,**Numer. Math., 108 (2007), 59-91. arXiv version. - James Demmel, Ioana Dumitriu, Olga Holtz and Robert Kleinberg,
**Fast matrix multiplication is stable,**Numer. Math., 106 (2007), no. 2, 199-224. arXiv version

- James Demmel, Ioana Dumitriu and Olga Holtz,
**Toward accurate polynomial evaluation in rounded arithmetic,**Foundations of Computational Mathematics: Santander 2005 (L. Pardo et al, eds.) Cambridge University Press, 2006, pp. 36-105. arXiv version

- Grey Ballard, James Demmel, Olga Holtz and Oded Schwartz,
**Direct and inverse problems of core linear algebra:**The inverse eigenvalue problem for nonnegative matrices and its variants, eigenvalue localization of special matrix classes, Markov chains, other related problems and probability and combinatorics.**Publications:**- Olga Holtz, Volker Mehrmann and Hans Schneider,
**Matrices that commute with their derivative. On a letter from Schur to Wielandt,**arXiv version - Gautam Bharali and Olga Holtz,
**Functions preserving nonnegativity of matrices,**SIMAX, 30 (2008), no.1, 84-101. arXiv version

- Nenad Moraca,
**Bounds for norms of the matrix inverse and the smallest singular value,**Linear Alg. Appl., 429 (2008), no.10, 2589-2601. - Olga Holtz and Bernd Sturmfels,
**Hyperdeterminantal relations among symmetric principal minors,**J. Algebra, 316 (2007), no.2, 634-648. arXiv version

- Olga Holtz, Volker Mehrmann and Hans Schneider,
**Root localization and asymptotics of polynomials:**matrix criteria for stability and root location, applications to probability and theoretical computer science, connections with scalar- and matrix-valued orthogonal polynomials, including their asymptotics.**Publications:**- Olga Holtz and Mikhail Tyaglov,
**Structured matrices, continued fractions, and root localization of polynomials,**SIAM Rev. 54 (2012), no. 3, 421-509. arXiv version. - Yury S. Barkovsky, Mikhail Tyaglov,
**Hurwitz rational functions,**Linear Algebra Appl. 435 (2011), no. 8, 1845-1856. arXiv version. - Vladimir Kostov, Boris Shapiro, Mikhail Tyaglov,
**Maximal univalent disks of real rational functions and Hermite-Biehler polynomials,**Proc. Amer. Math. Soc. 139 (2011), no. 5, 1625-1635. arXiv version. - Mikhail Tyaglov,
**On the number of real critical points of logarithmic derivatives and the Hawaii conjecture,**J. Anal. Math. 114 (2011), 1-62. arXiv version. - Mikhail Tyaglov,
**Generalized Hurwitz polynomials,**May 2010. arXiv version. - Diego Dominici,
**Fisher information of orthogonal polynomials I,**J. Comput. Appl. Math. 233 (2010), no. 6, 1511-1518. arXiv version. - Diego Dominici,
**Polynomial solutions of nonlinear integral equations,**J. Phys. A 42 (2009), no. 20, 205201, 8 pp. arXiv version. - Diego Dominici,
**Asymptotic analysis of the Bell polynomials by the ray method,**J. Comput. Appl. Math. 233 (2009), no. 3, 708-718. arXiv version. - Yury Barkovsky (translated by Olga Holtz and Mikhail Tyaglov),
**Lectures on the Routh-Hurwitz problem,**Feb 2008. arXiv version.

- Olga Holtz and Mikhail Tyaglov,
**The algebra of box splines and zonotopes:**connections between polynomial spaces, polynomial ideas, constant-coefficient PDEs, multivariate difference equations, multivariate polynomial interpolation, tilings and integer points in zonotopes, combinatorics of hyperplane arrangements, and various counting functions on graphs.**Publications:**- Matthias Lenz,
**Matroids and log-concavity,**Jun 2011. arXiv version. - Matthias Lenz,
**Hierarchical zonotopal power ideals,**European J. Combin. 33 (2012), no. 6, 1120-1141. arXiv version. - Olga Holtz, Amos Ron and Zhiqiang Xu,
**Hierarchical zonotopal spaces,**Trans. Amer. Math. Soc. 364 (2012), no. 2, 745-766. arXiv version. - Bernd Sturmfels and Zhiqiang Xu,
**Sagbi bases of Cox-Nagata rings,**J. Eur. Math. Soc. (JEMS) 12 (2010), no. 2, 429-459. arXiv version. - Olga Holtz and Amos Ron,
**Zonotopal algebra,**Adv. Math. 227 (2011), no. 2, 847-894. arXiv version.

- Matthias Lenz,
**Interplay between approximation theory and other fields:**connections between approximation theory, classical geometry and analysis, algorithms, and probability theory.**Publications:**- Olga Holtz, Fedor Nazarov and Yuval Peres,
**New coins from old, smoothly,**Constr. Approx. 33 (2011), no. 3, 331-363. arXiv version. - Shaowei Lin, Bernd Sturmfels and Zhiqiang Xu,
**Marginal likelihood integrals for mixtures of independence models,**J. Mach. Learn. Res. 10 (2009), 1611-1631. arXiv version.

- Olga Holtz, Fedor Nazarov and Yuval Peres,

**Compressive sensing:**new algorithms for matrix and PDE problems based on compressive sensing ideas, constructions of good compressive sensing matrices, complexity and numerical performance analysis of compressive sensing algorithms, applications to other fields of mathematics.**Publications:**- Olga Holtz,
**Compressive sensing: a paradigm shift in signal processing,**Dec 2008. arXiv version.

- Olga Holtz,

**Applications of algebra to analysis and vice versa:**linear algebra applied in analysis, analysis applied to linear algebra, commutative algebra and number theory, orthogonal polynomials, Jacobi matrices, Nevanlinna-type problems, total positivity, its generalizations and applications.- Olga Kushel,
**Generalized Brouncker's continued fractions and their logarithmic derivatives,**Jan 2013. arXiv version. - Olga Kushel,
**Cone-theoretic generalization of total positivity,**Linear Algebra Appl. 436 (2012), no. 3, 537-560. arXiv version. - Maxim Derevyagin, Luc Vinet, Alexei Zhedanov,
**CMV matrices and little and big -1 Jacobi polynomials,**Constr. Approx. 36 (2012), no. 3, 513-535. arXiv version. - Olga Kushel, P. Sharma,
**Generalized even and odd totally positive matrices,**Linear Algebra Appl. 435 (2011), no. 11, 2722-2730. arXiv version. - Maxim Derevyagin, Vladimir Derkach,
**Darboux transformations of Jacobi matrices and Pade approximation,**Linear Algebra Appl. 435 (2011), no. 12, 3056-3084. arXiv version. - Maxim Derevyagin,
**Inverse problems for periodic generalized Jacobi matrices,**J. Math. Anal. Appl. 384 (2011), no. 2, 444-452. arXiv version. - Maxim Derevyagin,
**The Jacobi matrices approach to Nevanlinna-Pick problems,**J. Approx. Theory 163 (2011), no. 2, 117-142. arXiv version.

**Publications:**