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:


Arithmetic graphs and the sum-product phenomenon

by Brandon Hanson | University of Toronto
Time: 13:10  (Thursday, Mar. 15, 2012)
Location: BA6183, Bahen Center, 40 St. George St.
The sum-product phenomenon is a quantitative way of saying that multiplication and addition in certain rings are more or less independent operations. Given a set A in a ring, its sum-set consists of all sums of two elements of A and its product-set consists of all products of two elements of A. Erdos conjectured that one of these sets must be substantially larger than A. Heuristically, if A has a small sum-set, A possesses some additive structure and its multiplicative structure is then quite random, or vice versa. A manifestation of this is expansion in graphs defined subject to arithmetic. We will survey some of these ideas on route to proving a sum-product estimate for finite fields via a beautiful proof of Solymosi.

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)