Georgia Institute of Technology College of Sciences

The Scenery Reconstruction Problem consists in trying to reconstruct a coloring of the integers given only the observations made by a random walk. For this we consider a random walk S and a coloring of the integers X. At time $t$ we observe the color $X(S(t))$. The coloring is i.i.d. and we show that given only the sequence of colors $$X(S(0)),X(S(1)),X(S(2)),...$$ it is possible to reconstruct $X$ up to translation and reflection. The solution depends on the property of the random walk and the distribution of the coloring. Longest Common Subsequences (LCS) are widely used in genetics. If we consider two sequences X and Y, then a common subsequence of X and Y is a string which is a subsequence of X and of Y at the same time. A Longest Common Subsequence of X and Y is a common subsequence of X and Y of maximum length. The problem of the asymptotic order of the flucutation for the LCS of independent random strings has been open for decades. We have now been able to make progress on this problem for several important cases. We will also show the connection to the Scenery Reconstruction Problem.

Almost all models for complex fluids can be fitted into the energetic variational framework. The advantage of the approach is the revealing/focus of the competition between the kinetic energy and the internal "elastic" energies. In this talk, I will discuss two very different engineering problems: free interface motion in Newtonian fluids and viscoelastic materials. We will illustrate the underlying connections between the problems and their distinct properties. Moreover, I will present the analytical results concerning the existence of near equilibrium solutions of these problems.

The speaker has combined his two loves to create a dynamic presentation called "Mathemagics," suitable for all audiences, where he demonstrates and explains his secrets for performing rapid mental calculations faster than a calculator. Reader's Digest calls him "America's Best Math Whiz". He has presented his high energy talk for thousands of groups throughout the world. This event is free but reservations are required. The signup form will be available before 5pm on February 25. See details about the speaker.

Let a_1,...,a_k satisfy a_1+...+a_k=1 and suppose a k-uniform hypergraph on n vertices satisfies the following property; in any partition of its vertices into k sets A_1,...,A_k of sizes a_1*n,...,a_k*n, the number of edges intersecting A_1,...,A_k is the number one would expect to find in a random k-uniform hypergraph. Can we then infer that H is quasi-random? We show that the answer is negative if and only if a_1=...=a_k=1/k. This resolves an open problem raised in 1991 by Chung and Graham [J. AMS '91]. While hypergraphs satisfying the property corresponding to a_1=...=a_k=1/k are not necessarily quasi-random, we manage to find a characterization of the hypergraphs satisfying this property. Somewhat surprisingly, it turns out that (essentially) there is a unique non quasi-random hypergraph satisfying this property. The proofs combine probabilistic and algebraic arguments with results from the theory of association schemes. Joint work with Raphy Yuster