The growth-optimal (Kelly) criterion almost surely leads to more capital in the long run and reaches levels of capital asymptotically faster than alternative strategies, but such outperformance may not be realized with high probability for an exceptionally long time. We will first demonstrate how the Kelly criterion arises in finance without first appealing to a logarithmic utility function, and then consider strategies based on alternative utilities that emphasize the probability of exceeding an underperforming benchmark faster than Kelly.

In 1950's Sierpinski asked whether there exists a linear order X isomorphic to its lexicographicaly ordered cube but not to its square. We will give some historical context and begin the proof that the answer is negative. More generally, if X is isomorphic to any of its finite powers X^n (n>1) then X is isomorphic to all of them.

I will talk about the construction of Kahler-Einstein metric under the assumption of negative holomorphic sectional curvature. This is based on the joint work with Yau.

We explore the structure of the singularities of Yang-Mills flow in dimensions n ≥ 4. First we derive a description of the singular set in terms of concentration for a localized entropy quantity, which leads to an estimate of its Hausdorff dimension. We develop a theory of tangent measures for the flow at such singular points, which leads to a stratification of the singular set. By a refined blowup analysis we obtain Yang-Mills connections or solitons as blowup limits at any point in the singular set. This is joint work with Jeffrey Streets