# Seminars & Colloquia Calendar

## On-Line Algorithms and Reverse MathematicsĀ

#### Seth Harris (Cornell)

Location: ** Hill 705**

Date & time: Monday, 16 April 2018 at 5:00PM - 6:00PM

Abstract: Consider a two-player game (played by Alice and Bob) in which Alice asks a sequence \(\bar{a}\) and Bob responds with a sequence \(\bar{b}\) with no knowledge of Alice's future requests. A problem P is solvable by an on-line algorithm if Bob has a winning strategy in this game, where Bob wins the game if (\(\bar{a}, \bar{b}\)) constitutes a solution to P. For example, if we take P to be a graph coloring problem, Alice plays by adding a new vertex and edges connecting it to previous vertices; Bob chooses a color for that vertex. The graph is on-line colorable if Bob has a winning strategy in this game. Given a problem P, the corresponding sequential problem SeqP asserts the existence of an infinite sequence of solutions to P. We will show that the reverse-mathematical strength of SeqP is directly related to the on-line solvability of P, and we will exactly characterize which sequential problems are solvable in the axiom systems RCA\(_0\), WKL\(_0\), and ACA\(_0\).

This is joint work with Francois Dorais.

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Paul Feehan, Daniel Ketover, Natasa Sesum Organizer's webpage

Lev Borisov, Emanuel Diaconescu, Angela Gibney, Nicolas Tarasca, and Chris Woodward Organizer's webpage

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Lisa Carbone, Yi-Zhi Huang, James Lepowsky, Siddhartha Sahi Organizer's webpage

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Joel Lebowitz, Michael Kiessling

Yanyan Li, Haim Brezis Organizer's Webpage

Stephen D. Miller, John C. Miller, Alex V. Kontorovich, Alex Walker seminar website

Stephen D. Miller

Brooke Ogrodnik, Website

Organizers: Yanyan Li, Z.C. Han, Jian Song, Natasa Sesum

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