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University of Leipzig
Mathematical Institute
Group: Algebra
Neues Augusteum, Room 515
Augustusplatz 10
04109 Leipzig
Phone: +49-(0)341-97 32186
E-mail: Public Key

News

Starting October 2014, I will have a position at the Geometry Institute at TU Dresden.

Teaching

Algebraic Geometry, Summer Term 2014.
Geometry of Linear Matrix Inequalities, Summer Term 2014.
Gödel's Incompleteness Theorems (Student Seminar), Summer Term 2014.
Logic and Model Theory, Winter Term 2013/14.
Convexity (Student Seminar), Winter Term 2013/14.
Real Algebraic Geometry 2, Summer Term 2013.
Real Algebraic Geometry 1, Winter Term 2012/13.
Algebra 1, Winter Term 2012/13.
Elementary Algebra and Number Theory, Summer Term 2012.
Discrete Structures for Computer Scientists, Winter Term 2011/12.
Convexity 2, Winter Term 2011/12.
Convexity 1, Summer Term 2011.
Linear Algebra for Physicists, Winter Term 2010/11.

Preprints


Publications

  1. "How Fast Do Polynomials Grow on Semialgebraic Sets?"
    with Pinaki Mondal,
    to appear in Journal of Algebra.

  2. "Hyperbolic Polynomials and Generalized Clifford Algebras"
    mit Andreas Thom,
    Discrete and Computational Geometry (2014).
    doi:10.1007/s00454-014-9598-1

  3. "Smooth Hyperbolicity Cones are Spectrahedral Shadows"
    mit Raman Sanyal,
    Mathematical Programming, Series B, Special Issue "Lifts of Convex Sets" (2014).
    doi:10.1007/s10107-014-0744-6

  4. "Can You Compute the Operator Norm?"
    with Tobias Fritz and Andreas Thom,
    to appear in Proceedings of the American Mathematical Society.

  5. "Determinantal Representations and the Hermite Matrix"
    with Daniel Plaumann and Andreas Thom,
    Michigan Mathematical Journal 62 (2), 407-420 (2013).
    doi:10.1307/mmj/1370870379

  6. "Real Closed Separation Theorems and Applications to Group Algebras"
    with Andreas Thom,
    Pacific Journal of Mathematics 263 (2), 435-452 (2013).
    doi: 10.2140/pjm.2013.263.435

  7. "Polynomials with and without Determinantal Representations"
    with Andreas Thom,
    Linear Algebra and its Applications 437 (7), 1579-1595 (2012).
    doi:10.1016/j.laa.2012.04.043

  8. "Positivstellensätze for Real Function Algebras"
    with Murray Marshall,
    Mathematische Zeitschrift 270 (3-4), 889-901 (2012).
    doi:10.1007/s00209-010-0831-1

  9. "Positive Polynomials and Projections of Spectrahedra"
    with João Gouveia,
    SIAM Journal on Optimization 21 (3), 960-976 (2011).
    doi: 10.1137/100801913

  10. "On the Real Multidimensional Rational K-Moment Problem"
    with Jaka Cimpric and Murray Marshall,
    Transactions of the American Mathematical Society 363 (11), 5773-5788 (2011)
    doi:10.1090/S0002-9947-2011-05225-6

  11. "Closures of Quadratic Modules"
    with Jaka Cimpric and Murray Marshall,
    Israel Journal of Mathematics 183 (1), 445-474 (2011).
    doi:10.1007/s11856-011-0056-y

  12. "Tracial Algebras and an Embedding Theorem"
    with Andreas Thom,
    Journal of Functional Analysis 259, 2939-2960 (2010).
    doi:10.1016/j.jfa.2010.08.010

  13. "Representation and Approximation of Positivity Preservers"
    Journal of Geometric Analysis 20 (3), 751-770 (2010).
    doi:10.1007/s12220-010-9126-3

  14. "On Semidefinite Representations of Non-closed Sets"
    Linear Algebra and its Applications 432, 3072-3078 (2010).
    doi:10.1016/j.laa.2010.02.005

  15. "Exposed Faces of Semidefinitely Representable Sets"
    with Daniel Plaumann and Markus Schweighofer,
    Siam Journal on Optimization 20 (4), 1944-1955 (2010).
    doi:10.1137/090750196

  16. "Positive Polynomials and Sequential Closures of Quadratic Modules"
    Transactions of the American Mathematical Society 362, 2619-2639 (2010).
    doi:10.1090/S0002-9947-09-05001-6

  17. "Stability of Quadratic Modules"
    manuscripta mathematica 129 (2), 251-271 (2009).
    doi:10.1007/S00229-009-0258-3

  18. "An Elementary Proof of Schmüdgen's Theorem on the Moment Problem of Closed Semi-Algebraic Sets"
    Proceedings of the American Mathematical Society 136, 529-537 (2008).
    doi:10.1090/S0002-9939-07-09087-9

  19. "A Note on the Representation of Positive Polynomials with Structured Sparsity"
    with David Grimm and Markus Schweighofer,
    Archiv der Mathematik 5, 399-403 (2007).
    doi:10.1007/s00013-007-2234-z

  20. "SOS Approximations of Nonnegative Polynomials via Simple High Degree Perturbations"
    with Jean B. Lasserre,
    Mathematische Zeitschrift 256 (1), 99-112 (2007).
    doi:10.1007/s00209-006-0061-8


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