Algebra and Geometry Seminar

The seminar is devoted to classical and modern questions of algebra and geometry. Most talks are two-hour informal talks. Comments and discussions are highly encouraged.


Topological approach to Klein's resolvent problem

by Yura Burda | University of Toronto
Time: 12:00 — 14:00  (Tuesday, Oct. 18, 2011)
Location: BA6180, Bahen Center, 40 St. George St.
Klein's resolvent problem asks whether by means of a rational substitution y=R(z,a_1,...,a_n) one can reduce an algebraic equation z^n+a_1 z^n-1+...+a_n=0 to an algebraic equation on y depending on a small number of algebraically independent parameters. We will talk about the history of the problem and see how topological considerations allow one to obtain some lower bounds in it. We will see that the analogue of Klein's resolvent problem for algebraic functions unramified over the algebraic torus can be solved completely using topological considerations, but they solve the original problem only for n<7. Case n=7 has been solved recently by A. Duncan and for n>7 the problem is wide open.

Dates in this series

· Monday, Jan. 11, 2010: On rational functions invertible in radicals  (Yuri Burda)
· Wednesday, Apr. 21, 2010: Dynamical foliations (Tanya Firsova)
· Friday, Mar. 11, 2011: NEW MINI-COURSE: Inifinitesimal Hilbert 16th problem: inside the proof (Dmitry Novikov)
· Friday, Mar. 25, 2011: Inifinitesimal Hilbert 16th problem: inside the proof - 2nd meeting (Dmitry Novikov)
· Friday, Apr. 01, 2011: Inifinitesimal Hilbert 16th problem: inside the proof II (Dmitry Novikov)
· Friday, Apr. 08, 2011: Algebraic Geometry and Convex Geometry (Askold Khovanskii)
· Tuesday, Apr. 19, 2011: Algebraic Geometry and Convex Geometry II (Askold Khovanskii)
· Tuesday, Oct. 11, 2011: On two classical invariants of singularities (Dmitry Kerner)
· Tuesday, Oct. 18, 2011: Topological approach to Klein's resolvent problem (Yura Burda)
· Thursday, Nov. 10, 2011: Folding polynomials as examples of discrete algebraically integrable systems (Yuri Burda)
· Tuesday, Nov. 15, 2011: Folding polynoimals as examples of discrete integrable systems (Yuri Burda)
· Tuesday, Jan. 17, 2012: Some parameter spaces of curves on toric surfaces, their tropicalizations, and applications (Jessie Yang)
· Tuesday, Jan. 24, 2012: Hermite's form of a quintic equation and geometry of cubic surfaces (Yuri Burda)
· Tuesday, Jan. 31, 2012: Obstructions to the local approximation of tropical curves in planes (Kristin Shaw)
· Tuesday, Feb. 07, 2012: Constructing the 17-gon with a ruler and a compass (Liudmyla Kadets)
· Tuesday, Mar. 27, 2012: Discriminant of transversal singularity type (Dmitry Kerner)
· Tuesday, Apr. 10, 2012: Discriminant of transversal singularity type (Dmitry Kerner)
· Thursday, Jun. 28, 2012: Folding polynomials and cutting cakes (Yuri Burda)
· Monday, Oct. 01, 2012: Radon and Fourier transforms for differential forms (Theodore Voronov )
· Tuesday, Oct. 09, 2012: Multiplicity in generic families of maps (Gal Binyamini)
· Tuesday, Oct. 23, 2012: Weil reciprocity law and Newton Polygons (Lucy Kadets)
· Tuesday, Oct. 30, 2012: Newton polyhedra theory and Bernstein--Kushnirenko theorem (Askold Khovanskii)
· Tuesday, Nov. 06, 2012: Universal Grobner basis of an ideal (Askold Khovanskii)
· Tuesday, Nov. 13, 2012: One more time about universal Gröbner bases (Askold Khovanskii)
· Tuesday, Nov. 20, 2012: Introduction to tropical bases (Kristin Shaw)
· Tuesday, Nov. 27, 2012: Combinatorics of affine birational maps (Ilya Karzhemanov)
· Monday, Dec. 10, 2012: Arithmetic properties of Chebyshev polynomials (Yuri Burda)
· Wednesday, Jan. 30, 2013: Geometry of numbers and finiteness of ideal class group (Kiumars Kaveh)
· Wednesday, Feb. 06, 2013: Geometry of numbers and finiteness of ideal class group (part II) (Kiumars Kaveh)
· Tuesday, Mar. 19, 2013: Stringy invariants of p-cyclic quotient singularities and weighted counts of Artin-Schreier extensions of the power series field (Takehiko Yasuda)