The Grothendieck Constant Is Strictly Smaller Than Krivine's Bound

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RE 102
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Host

Department of Applied Mathematics

Speaker

Yury Makarychev
Associate Professor, Toyota Technological Institute at Chicago / Department of Computer Science, University of Chicago
http://ttic.uchicago.edu/~yury/



Description

The speaker will talk about the Grothendieck Inequality, which was proved by Alexander Grothendieck in 1953. The Grothendieck inequality has numerous applications in analysis, quantum mechanics, and computer science. From the point of view of combinatorial optimization, the inequality states that the integrality gap of a certain semidefinite program is less than an absolute constant. The optimal value of this constant, called the Grothendieck constant KG, is unknown. In 1977, Krivine proved that KG ≤ π / (2 log(1+√2)) ∼ 1.782 and conjectured that his bound is optimal. In this talk, the speaker will disprove this conjecture and show that KG is strictly less than Krivine's bound.

Joint work with Mark Braverman, Konstantin Makarychev, and Assaf Naor.

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