Past Events
I will begin by briefly recalling the relationship between complex projective algebraic geometry and symplectic topology, which goes through Kaehler manifolds. I will then survey results from the end of the last century, largely due to Seidel and McDuff, about the symplectic topology of…
Our speaker this week will be Persi Diaconis:
Title: Adding numbers and shuffling cards
Abstract: When ordinary integers are added in the usual way, 'carries' occur along the way. How do the carries go? They turn out to form an 'AMAZING matrix' (?). This same matrix occurs…
384I
Given a poset (P,≤), an antichain is a subset of pairwise incomparable elements of P. Let (P,w) be a graded, weighted poset. If the maximum weight of an antichain of P is equal to the weight of the largest rank of P, then P is said to be Sperner. In 1967, Rota conjectured…
Consider a diploid population (one in which each individual carries two copies of each gene) living in one spatial dimension. Suppose a particular gene appears in two forms (alleles) A and a, and that individuals carrying AA have a higher fitness than aa individuals, while Aa individuals have a…
Limit shape formation is a common feature of highly correlated statistical mechanical systems. On the macroscopic scale the random system settles into a deterministic limit often exhibiting fascinating arctic…
The Kardar–Parisi–Zhang (KPZ) equation is a fundamental stochastic PDE related to the KPZ universality class. In this talk, we focus on how the tall peaks and deep valleys of the KPZ height function grow as time increases. In particular, we will ask what are the appropriate scaling of the peaks…
Title: Complex cobordism and Hamiltonian fibrations
Abstract: I will discuss joint work with McLean and Smith, lifting the results of Seidel, Lalonde, and McDuff concerning the topology of Hamiltonian fibrations over the 2-sphere from rational cohomology to complex…
Abstract: In various areas of mathematics there exist "big fiber theorems", these are theorems of the following type: "For any map in a certain class, there exists a 'big' fiber", where the class of maps and the notion of size changes from case to case. We will discuss three examples…
We consider the standard L-function attached to a cuspidal automorphic representation of a general linear group. We present a proof of a subconvex bound in the t-aspect. More generally, we address the spectral aspect in the case of uniform parameter growth.
These results are…