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

Variational optimization in economics

by Robert McCann | University of Toronto
Time: 13:00  (Wednesday, Mar. 23, 2011)
Location: BA6183, Bahen Center, 40 St. George St.
Abstract:
In this talk I plan to discuss one of my recent research interests, which involves the application of mathematical techniques from the theory of optimal transportation to one of the central problems in economic theory: Optimal pricing facing informational asymmetry. The monopolist's problem of deciding what types of products to manufacture and how much to charge for each of them, knowing only statistical information about the preferences of an anonymous field of potential buyers, is one of the basic problems analyzed in economic theory. The solution to this problem when the space of products and of buyers can each be parameterized by a single variable (say quality X, and income Y) garnered Mirrlees (1971) and Spence (1974) their Nobel prizes in 1996 and 2001. The multidimensional version of this question is a largely open problem in the calculus of variations (see Basov's book "Multidimensional Screening".) I plan to describe recent work with A Figalli and Y-H Kim, identifying structural conditions on the value b(X,Y) of product X to buyer Y which reduce this problem to a convex program in a Banach space--- leading to uniqueness and stability results for its solution, confirming robustness of certain economic phenomena observed by Armstrong (1996) such as the desirability for the monopolist to raise prices enough to drive a positive fraction of buyers out of the market, and yielding conjectures about the robustness of other phenomena observed Rochet and Chone (1998), such as the clumping together of products marketed into subsets of various dimension. The passage to several dimensions relies on ideas from differential geometry / general relativity, optimal transportation, and nonlinear PDE.

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)