Graduate Student Seminar

Seminars in this series are for students to talk about something of  personal interest, or a professor to describe and explore their area of research.

The talks are at a very accessible level.

Free pizzas are a regular part  of this seminar series.

Further information on seminars can be found at the following link: http://www.math.toronto.edu/mgsa/seminar

Details

Self-referencing Recursions and Labeled Binary Trees

by Abraham Isgur | University of Toronto
Time: 13:00  (Wednesday, Feb. 10, 2010)
Location: BA6183, Bahen Center, 40 St. George St.
Abstract:
Self-referencing recursions (also called meta-Fibonacci or nested recursions) are those where the arguments in the recursion equation depend on previous recursion terms. For example, Q(n) = Q(n-Q(n-1))+Q(n-Q(n-2)), which with Q(1)=Q(2)=1 is Hofstadter's sequence, first mentioned in his book *Godel, Escher, Bach: An Eternal Golden Braid*.

Self-referencing recursions can be thought of as the discrete analogue of nonlinear differential equations in the same way that ordinary difference equations can be thought of as the discrete version of ODEs. As in the continuous case, there is no general approach to solving self-referencing recursions, and they are often classified into families exhibiting similar behavior.

The field of self-referencing recursions is very new (starting in 1979) and has many open problems. During the talk, I will discuss a few general notions about self-referencing recursions, and one of the major recent developments - a combinatorial interpretation in terms of labeled binary trees for solutions to some self-referencing recursions.

Dates in this series

· Thursday, Jan. 21, 2010: The Calderon Problem - From the Past to the Present (Leo Tzou)
· Wednesday, Feb. 03, 2010: Indecomposable characters on the group S(2) (Artem Dudko)
· Wednesday, Feb. 10, 2010: Self-referencing Recursions and Labeled Binary Trees (Abraham Isgur)
· Wednesday, Feb. 17, 2010: Introduction to the Well-posedness Theory of (Dispersive) PDEs (Hiro Oh)
· Wednesday, Mar. 03, 2010: Renormalization and universality in one-dimensional dynamics: critical circle maps (Michael Yampolsky)
· Wednesday, Mar. 10, 2010: The Dimer Model on a Planar Domain: From random domino tilings to limit shapes (Alex Bloemendal)
· Wednesday, Mar. 17, 2010: The Planar Dimer Model, continued (Alex Bloemendal)
· Thursday, Sep. 16, 2010: The calculus of Euler characteristic and some of its application (Dmitry Kerner)
· Thursday, Oct. 07, 2010: Equivalences of the Axiom of Choice (Mike Pawliuk)
· Thursday, Oct. 21, 2010: Covering arrays with row limit four (Nevena Francetic)
· Thursday, Oct. 28, 2010: Which groups are Lie groups? (Yevgeniy Likuomovich)
· Thursday, Nov. 04, 2010: All started with Weyl (Victor Ivrii)
· Thursday, Nov. 11, 2010: Sparse structures in Euclidean space (Dominic Dotterrer)
· Thursday, Nov. 18, 2010: A short introduction to curve singularities (Dmitry Kerner)
· Thursday, Nov. 25, 2010: Newton diagrams and applications (Dmitry Kerner)
· Thursday, Dec. 02, 2010: Convergence and smoothing properties of Steiner symmetrizations and other simple rearrangements (Almut Burchard)
· Tuesday, Jan. 11, 2011: TeXFreak (Victor Ivrii)
· Wednesday, Jan. 26, 2011: Two-sided chain condition in Leavitt path algebras (Pinar Colak)
· Tuesday, Feb. 01, 2011: SPECIAL GRADUATE SEMINAR -- How to classify algebraic varieties (Chenyang Xu)
· Wednesday, Feb. 02, 2011: Enrico Bombieri and the Prime Number Theorem (John Friedlander)
· Wednesday, Feb. 16, 2011: Basic Financial Derivatives and the Black-Scholes PDE (Ryan Donnelly)
· Wednesday, Mar. 09, 2011: Classical mechanics and symplectic geometry (Jonathan Fisher)
· Thursday, Mar. 17, 2011: On Computability of Julia sets (Artem Dudko)
· Wednesday, Mar. 23, 2011: Variational optimization in economics (Robert McCann)
· Wednesday, Mar. 30, 2011: Exact formulas in random growth and directed polymers (Jeremy Quastel)
· Wednesday, Apr. 06, 2011: Kitaev's quantum double model for topological quantum computation -- representations, higher categories and extended TQFTs (Lucy Zhang)
· Wednesday, Apr. 13, 2011: Tropicalization and Connection to Secondary Fans (Jihyeon Jessie Yang)
· Thursday, Sep. 29, 2011: Probabilistic Cauchy Theory and Invariant Measures for Hamiltonian PDEs (Geordie Richards)
· Thursday, Oct. 13, 2011: The cohomology ring of the GKM graph of a flag manifold (Yukiko Fukukawa)
· Friday, Nov. 04, 2011: Representations of the full group of a Bratteli diagram (Artem Dudko)
· Thursday, Nov. 10, 2011: How to Solve a Cubic Equation? (Askold Khovanskii)
· Thursday, Nov. 24, 2011: Rate of escape of random walks on groups (Balint Virag)
· Thursday, Dec. 01, 2011: Some aspects of geometric measure theory (Robert Jerrard)
· Thursday, Jan. 19, 2012: Bounded generation, congruence subgroups and the splitting of primes (Kumar Murty)
· Thursday, Jan. 26, 2012: How to solve a quintic polynomial? (Yuri Burda)
· Thursday, Feb. 02, 2012: Dynamics on the circle (Elio Mazzeo)
· Thursday, Feb. 09, 2012: How to keep a can from sliding down an incline (and make it roll instead) (David Li-Bland)
· Thursday, Mar. 15, 2012: Arithmetic graphs and the sum-product phenomenon (Brandon Hanson)
· Thursday, Mar. 22, 2012: Two Inverse Problems in Medical Imaging (Nicholas Hoell)
· Thursday, Mar. 29, 2012: Enveloping algebras of nonassociative structures (Marina Tvalavadze)
· Thursday, Nov. 08, 2012: Airy's rainbow and Stokes' mist: asymptotics through the prism of geometry (Brent Pym)
· Thursday, Dec. 13, 2012: C*-algebras and the Classification Program (Danny Hay)
· Thursday, Jan. 17, 2013: Why is the Riemann Hypothesis a big deal? (Asif Zaman)