# Seminar

# Complex Online Decision Making

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Suppose you want to find the least congested route in an ad hoc network. Each link's rate is unknown and stochastic, and each time you get to see the minimum rate (i.e., bottleneck) along any route you pick.

# On Testing Bent Functions

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A bent function is a Boolean function all of whose Fourier coefficients are equal in absolute value.

# Unbalanced Random Matching Markets

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We analyze large random matching markets with unequal numbers of men and women. We find that being on the short side of the market confers a large advantage.

# Leonid Gurvits's Proof of the Van der Waerden Conjecture

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The permanent of a doubly stochastic matrix is at least that of the matrix with each entry $1/n$ (the matrices are $n x n$).

# Some Mathematical Problems Arising in the Study of Chemical Reaction Networks

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Networks of chemical reactions have natural underlying combinatorial structure, allowing them to be represented as graphs or digraphs, perhaps with additional vertex or edge colourings/labellings.

# Split-width and the Verification of Concurrent Recursive Programs

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# A Bayesian Approach To Stochastic Root Finding

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A stylized model of one-dimensional stochastic root-finding involves repeatedly querying an oracle as to whether the root lies to the left or right of a given point $x$.

# Constructive and Non-constructive Aspects of the Lovasz Local Lemma

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In three talks, I will describe aspects of the Local Lemma that have recently been uncovered by Moser & Tardos, Pegden, and David Harris and myself.

# Constructive and Non-constructive Aspects of the Lovasz Local Lemma

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In three talks, I will describe aspects of the Local Lemma that have recently been uncovered by Moser & Tardos, Pegden, and David Harris and myself.