250007 SE Seminar (Algebra) (2018W)

Lecturers

• Christian Krattenthaler

Classes (iCal) - next class is marked with N

Selection of potential topics for the Seminar "Algebra", WS 2018.

The members of the Algebra Research Area of the Faculty of Mathematics
offer in the upcoming winter term a joint seminar for Master students
addressing fundamental aspects of algebra. We propose here some topics
-- interested students are invited to contact directly the persons
mentioned in parenthesis.

(1) Minimum modulus problem for covering systems for congruences
(Arzhantseva)

(2) Lovasz' local lemma on probabilities of bad events (Arzhantseva)

(3) Integral bases of cubic and biquadratic number fields (Baxa)

(4) Hilbert's 10th Problem for rings of integral algebraic numbers in
number fields (Baxa)

(5) The Catalan Conjecture (Burde)

(6) Almost-inner derivations of Lie algebras (can you hear the shape of a
drum) (Burde)

(7) Maschke's Theorem about group-algebras (Carqueville)

(8) Elementary Morita-Theory (Carqueville)

(9) Hook-lengths formulas for "skew shapes": Naruse's formula and its
extensions (Fischer)

(10) Lecture Hall partitions (Fischer)

(11) André Weil's article about the group-theoretic analysis of the
marriage rules of an Australian Aborigines tribe (Grobner)

(12) Algebra of magic card tricks (Grobner)

(13) Resultants in several variables and elimination-theory (Hauser)

(14) Del Pezzo surfaces -- correspondences and categories (Katzarkov)

(15) The variety of conjugacy classes in the space of n x n Matrices
(Mahnkopf)

(16) Schur and Schubert polynomials (Mellit)

(17) Rook polynomials (Schlosser)

(18) Inverse relations and combinatorial identities (Schlosser)

(19) Pólya's theorem: An even polynomial taking only strictly positive
values can be multiplied with a polynomial of the form (1+x)^m to get a
polynomial with positive
coefficients (the polynomial 3x^2 - 3x + 1 already requires m=13) (Summerer)

(20) Szygmondy's theorem about the prime divisors of a^n - b^n (Summerer)

(21) Viennot's combinatorial theory of orthogonal polynomials (Krattenthaler)

(22) Complexity of (combinatorial) formulae (Krattenthaler)

• Monday 01.10. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
• Monday 08.10. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
• Monday 15.10. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
• Monday 22.10. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
• Monday 29.10. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
• Monday 05.11. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
• Monday 12.11. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
• Monday 19.11. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
• Monday 26.11. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
• Monday 03.12. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
• Monday 10.12. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
• Monday 07.01. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
• Monday 14.01. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
• Monday 21.01. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
• Monday 28.01. 13:15 - 14:45 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock