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.

Details

On rational functions invertible in radicals

by Yuri Burda | University of Toronto
Time: 11:00  (Monday, Jan. 11, 2010)
Location: HU1018, 215 Huron St
Abstract:
J.F. Ritt in his works on equations solvable in radicals and on commuting rational functions has encountered a very special class of rational functions, possessing remarkable properties. These functions include the Tchebyshev polynomials and several families of rational functions, related to isogenies of elliptic curves. We will discuss these functions, present several characterizations of them, study their moduli, dessins d'enfants (when possible) and some multidimensional analogues.

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)