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Series: School of Mathematics Colloquium

Traditional Erdoes Magic (a.k.a. The Probabilistic Method) proves the existence of an object with certain properties
by showing that a random (appropriately defined) object will have those properties with positive probability. Modern Erdoes Magic analyzes a random process, a random (CS take note!) algorithm. These, when successful, can find a "needle in an exponential haystack" in polynomial time.
We'll look at two particular examples, both involving a family of n-element sets under suitable side conditions. The Lovasz Local Lemma finds a coloring with no set monochromatic. A result of this speaker finds a coloring with low discrepency. In both cases the original proofs were not implementable but Modern Erdoes Magic finds the colorings in polynomial times.
The methods are varied. Basic probability and combinatorics. Brownian Motion. Semigroups. Martingales. Recursions ... and Tetris!

Thursday, November 2, 2017 - 11:05 ,
Location: Skiles 006 ,
Joel Spencer ,
Courant Institute, New York University ,
Organizer: Lutz Warnke

Traditional Erdoes Magic (a.k.a. The Probabilistic Method) proves the existence of an object with certain propertiesby showing that a random (appropriately defined) object will have those properties with positive probability. Modern Erdoes Magic analyzes a random process, a random (CS take note!) algorithm. These, when successful, can find a "needle in an exponential haystack" in polynomial time. We'll look at two particular examples, both involving a family of n-element sets under suitable side conditions. The Lovasz Local Lemma finds a coloring with no set monochromatic. A result of this speaker finds a coloring with low discrepency. In both cases the original proofs were not implementable but Modern Erdoes Magic finds the colorings in polynomial times. The methods are varied. Basic probability and combinatorics. Brownian Motion. Semigroups. Martingales. Recursions ... and Tetris!

Series: Analysis Seminar

Monday, October 30, 2017 - 17:15 ,
Location: Skiles 005 ,
Spencer Bloch ,
University of Chicago ,
Organizer: Joseph Rabinoff

Monday, October 30, 2017 - 16:05 ,
Location: Skiles 005 ,
Bjorn Poonen ,
Massachusetts Institute of Technology ,
Organizer: Joseph Rabinoff

The function field case of the strong uniform boundedness conjecturefor torsion points on elliptic curves reduces to showing thatclassical modular curves have gonality tending to infinity.We prove an analogue for periodic points of polynomials under iterationby studying the geometry of analogous curves called dynatomic curves.This is joint work with John R. Doyle.

Series: Geometry Topology Seminar

Series: Combinatorics Seminar

Friday, October 27, 2017 - 15:00 ,
Location: Skiles 154 ,
Hassan Attarchi ,
Georgia Tech ,
Organizer:

This presentation is about the results of a paper by Y. Sinai in
1970. Here, I will talk about dynamical systems which resulting from the
motion of a material point in domains with strictly convex boundary,
that is, such that the operator of the second quadratic form is
negative-definite at each point of the boundary, where the boundary is
taken to be equipped with the field of inward normals. It was proved
that such systems are ergodic and are K-systems. The basic method of
investigation is the construction of transversal foliations for such
systems and the study of their properties.

Friday, October 27, 2017 - 13:00 ,
Location: Skiles 006 ,
John Etnyre ,
Georgia Tech ,
Organizer: John Etnyre

Notice the seminar is back to 1.5 hours this week.

In this series of talks I will introduce branched coverings of manifolds and sketch proofs of most the known results in low dimensions (such as every 3 manifold is a 3-fold branched cover over a knot in the 3-sphere and the existence of universal knots). This week we should be able to finish our discussion of branched covers of surfaces and transition to 3-manifolds.

Series: Stochastics Seminar

When considering smooth functionals of dependent data, block bootstrap methods have enjoyed considerable success in theory and application. For nonsmooth functionals of dependent data, such as sample quantiles, the theory is less well-developed. In this talk, I will present a general theory of consistency and optimality, in terms of achieving the fastest convergence rate, for block bootstrap distribution estimation for sample quantiles under mild strong mixing assumptions. The case of density estimation will also be discussed. In contrast to existing results, we study the block bootstrap for varying numbers of blocks. This corresponds to a hybrid between the subsampling bootstrap and the moving block bootstrap (MBB). Examples of `time series’ models illustrate the benefits of optimally choosing the number of blocks. This is joint work with Stephen M.S. Lee (University of Hong Kong) and Alastair Young (Imperial College London).