Past Events

A pair of skew shapes are said to be (skew) equivalent if they admit the same number of semistandard tableaux of any weight; i.e. if their associated skew Schur functions are equal. A complete characterization is known for ribbon shapes (those with...

We describe a theorem due to Jianya Liu and Yangbo Ye (Pure and Applied Mathematics Quarterly, Volume 3, Number 2, 481-497, 2007) concerning the prime number theorem for automorphic L-functions. We state the theorem and review the strategy of the...

The PPSZ algorithm, due to Paturi, Pudlak, Saks and Zane, is currently the fastest known algorithm for the k-SAT problem, for every k>3. For 3-SAT, a tiny improvement over PPSZ was obtained by Hertli. We introduce a biased version of the PPSZ...

Peritrichously flagellated bacteria such as E. coli swim in a fluid environment by rotating motors embedded in the cell membrane and consequently rotating multiple helical flagella. We present a mathematical model of a microswimmer that can freely...

In its most well-known form, the Loewner equation gives a correspondence between curves in the upper half-plane and continuous real functions (called the “driving function” for the equation). We consider the generalized Loewner equation, where the...

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The concept of Hopf algebras originated from the theory of algebraic groups and algebraic topology in the mid 20th century. Hopf structures have numerous applications in many other mathematical branches, and now it is a familiar concept in...

The possibility that a discrete process can be fruitfully approximated by a continuous one, with the latter involving a differential system, is fascinating. Important theoretical insights, as well as significant computational efficiency gains may lie...

We use properties of modular forms to extend the Ramanujan-Mordell formula. Our result yields to formulas for representation numbers by the quadratic form ∑2ai=1x2i+∑2bi=1py2i, for all non-negative integers a,b and for all odd prime p. We obtain this...

Suppose two populations with different genetic types live close to each other and can interbreed, but hybrid offspring have a lower evolutionary fitness. The interface between such populations is known as a hybrid zone. We can model this situation...