# 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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Quentin Dubroff Organizer's webpage

James Holland; Organizer website

Edna Jones Organizer's webpage

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Yanyan Li, Zheng-Chao Han, Jian Song, Natasa Sesum Organizer's Webpage

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Yanyan Li, Zheng-Chao Han, Natasa Sesum, Jian Song Organizer's Page

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

Simon Thomas website

Kasper Larsen, Daniel Ocone and Kim Weston Organizer's page

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

Yael Davidov Seminar webpage

Kristen Hendricks, Xiaochun Rong, Hongbin Sun, Chenxi Wu Organizer's page

Fioralba Cakoni Seminar webpage

Ebru Toprak, Organizer

Organizer's webpage: Organizer's webpage

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