Reine und angewandte Algebra

Seminarfolge, Sommer- und Windersemester 2007

Kursleiter: Olga Holtz

DiMi 14:15-16:00, MA 313

Sprechstunden: DiMi 16:00-17:00, MA 378

Geplanter Inhalt des Kurses

Verschiedene algebraische Themen:

Graphen und dazu gehoerige lineare Algebra
Kombinatorik von strukturierten Matrizen
Kommutative Algebra von Boxsplines
Zonotopen und hyperebene Arrangements
Matroiden und Modelle aus statistischer Physik
Algebra und Analyse von stabilen Polynomen

Jedes Seminar wird unabhaengig von den anderen sein. Entsprechende mathematische Fakte werden nach Bedarf vorgestellt. .

Vortraege

16. Apr - "Matrix inequalities", Olga Holtz
18. Apr - "Matroids and some physics models", Olga Holtz
24. Apr - "Eigenvalues of stochastic matrices", Nenad Moraca
25. Apr - "Generalizations of Perron-Frobenius", Hans Schneider
02. Mai - "Eigenvalues of stochastic matrices, II", Nenad Moraca
09. Mai - "Fast matrix multiplication", Olga Holtz
15. Mai - "Stability of polynomials", Mikhail Tyaglov
16. Mai - "Notions related to stability", Mikhail Tyaglov
21. Mai - "Mixing of Markov chains and matrix inequalities", Yuval Peres
23. Mai - "Eigenvalues of stochastic eigenvalues: Karpelevich's work", Nenad Moraca
29. Mai - "Basics of matroid theory", Moritz Schmitt
30. Mai - "Combinatorial matrix problems", Raphael Loewy
05. Jun - "Extensions of stability concepts to linear DAEs", Volker Mehrmann
12. Jun - "Generalized Hurwitz polynomials and related topics", Mikhail Tyaglov
13. Jun - "Motivating lattice gas models: a foray to statistical mechanics", Jerry Gagelman
19. Jun - "Open problems on stable and hyperbolic polynomials", Olga Holtz
20. Jun - "Perron-Frobenius theorem for matrix pencils", Elena Virnik
26. Jun - "A proof of the Hawaii conjecture", Mikhail Tyaglov
27. Jun - "Compressive sensing: the restricted isometry property", Sadegh Jokar
03. Jul - "Compressive sensing: exact recovery of sparse signals", Olga Holtz
04. Jul - "Compressive sensing: best k-term approximation and Gelfand widths", Olga Holtz
10. Jul - "Compressive sensing: geometric functional analysis and probability", Olga Holtz
11. Jul - "Stable rational functions", Mikhail Tyaglov
17. Jul - "The joy of solving equations", Bernd Sturmfels
13. Aug - "Markov chains, birth and death processes, and matrix-valued orthogonal polynomials, I", Alberto Gruenbaum
14. Aug - "Markov chains, birth and death processes, and matrix-valued orthogonal polynomials, II", Alberto Gruenbaum
21. Aug - "Groebner fans", Anders Jensen
22. Aug - "Univariate orthogonal polynomials", Diego Dominici
28. Aug - "Zonotopal algebra: linear-algebraic preliminaries", Olga Holtz
29. Aug - "Zonotopal algebra: commutative-algebraic preliminaries", Olga Holtz
30. Aug - "Hawaii (conjecture) revisited", Mikhail Tyaglov
4. Sep - "Zonotopal algebra: least polynomial interpolation", Olga Holtz
5. Sep - "Central zonotopal algebra", Olga Holtz
11. Sep - "Tropical warm-up", Bernd Sturmfels -- a lead-in to
12. - 16. Sep - Tropical Workshop, Bernd Sturmfels
18. Sep - "Exterior zonotopal algebra", Olga Holtz
19. Sep - "Interior zonotopal algebra", Olga Holtz
25. Sep - "A gentle introduction to frames", Olga Holtz
26. Sep - "Frames and compressive sensing", Sadegh Jokar
02. Okt - "Issues in multivariate polynomial interpolation I", Carl de Boor
04. Okt - "Issues in multivariate polynomial interpolation II", Carl de Boor
09. Okt - "Multivariate splines and polytopes", Zhiqiang Xu
10. Okt - "Eigenvalue perturbation analysis", Michael Karow
16. Okt - "Introduction to wavelets I", Sadegh Jokar
17. Okt - "Introduction to wavelets II", Zhiqiang Xu
23. Okt - "Introduction to triangulations in geometry", Anders Jensen
24. Okt - "On the BMV conjecture", Mikhail Tyaglov
31. Okt - "On some open problems from probability", Olga Holtz
07. Nov - "Bounding norms of inverses of H-matrices", Nenad Moraca
14. Nov - "More open problems from probability", Olga Holtz
21. Nov - "Short recurrences for Krylov subspace bases", Joerg Liesen
27. Nov - "Hyperbolic and Minkowski-type polynomials I: simple proofs and generalizations of Falikman-Egorychev and Schijver lower bounds", Leonid Gurvits
28. Nov - "Hyperbolic and Minkowski-type polynomials II: the mixed volume analogues of Falikman-Egorychev and Schijver lower bounds and their algorithmic applications", Leonid Gurvits
04. Dez - "Toric dynamical systems", Anne Shiu
05. Dez - "On complexity of deciding on switching stability of continuous time linear inclusions", Leonid Gurvits
11. Dez - "A short introduction to hardness of approximation", Oded Schwartz
12. Dez - "On the complexity of approximating some NP-hard problems", Oded Schwartz
18. Dez - "Relations among principal minors of a matrix", Shaowei Lin
19. Dez - "Powers of linear forms", Bernd Sturmfels
29. Jan - "Solving polynomial equations over the Puiseux series field algebraically, I", Anders Jensen
31. Jan - "Solving polynomial equations over the Puiseux series field algebraically, II", Anders Jensen
05. Feb - "Asymptotic analysis of differential-difference equations, I", Diego Dominici
07. Feb - "Asymptotic analysis of differential-difference equations, II", Diego Dominici
12. Feb - "R-functions and related problemsi, I", Mikhail Tyaglov
14. Feb - "R-functions and related problems, II", Mikhail Tygalov
20. Feb - "Orthogonal polynomials, discriminants, and electrostatic equilibrium problems", Mourad Ismail
21. Feb - "Monotonicity of eigenvalues of matrices", Mourad Ismail
26. Feb - "The reverse search property of Groebner fans", Anders Jensen
28. Feb - "Refinement equations with non-integer dilations", Zhiqiang Xu
04. Mar - Closed meeting of the Kovalevskaja group
05. Mar - "Integer linear and non-linear optimization", Matthias Koeppe
11. Mar - "A short introduction to expanders", Oded Schwartz
13. Mar - "An elementray construction of constant-degree expanders", Oded Schwartz

Teilnahme von Studenten

Studenten, die Interesse haben, einen Vortrag zu machen, muessen das im Voraus besprechen. Ihnen werden verschiedene Moeglichkeiten vorgeschlagen, z.B. ein Paper vorzustellen oder ueber eigene Forschung zu sprechen.

Mailingliste

Es gibt eine Mailingliste fuer diesen Kurs. Kurze Ankuendigungen ueber die Themen und die Sprecher werden jede Woche an die Liste geschickt. Wollen Sie auf die Liste, dann senden sie eine Nachricht an holtz@math.