Past Events
The Sylow theorems appear at the very start of group theory. If you look (and we will) you'll see that the proofs are 'just simple combinatorics'. This connection continues. In this talk I'll focus on the Sylow subgroups of the Symmetric group S_n. These have a simple description as 'chandelier…
Motivated by number theoretical results due to Montgomery,
Hejhal, Rudnick, and Sarnak, we study limiting distribution of k-tuple
smoothed counting statistics in circular ensembles of random matrices.
Some of the results were obtained in collaboration with…
We discuss the problem of distinguishing virtual transverse knots, equivalence classes of virtual braid closures modulo positive stabilization. Some of the most basic conjectures about these objects are surprisingly difficult to answer. We will define some state-sum invariants for virtual…
In the interchange process on a graph $G=(V,E)$, distinguished particles are placed on the vertices of $G$ with independent Poisson clocks on the edges. When the clock of an edge rings, the two particles on the two sides of the edge interchange. In this way, a random permutation $\pi_\beta:V\to…
We prove the infinitude of shifted primes $p-1$ without prime factors above $p^{0.2844}$. This refines $p^{0.2961}$ from Baker and Harman in 1998. Consequently, we obtain an improved lower bound on the distribution of Carmichael numbers. Our main technical result is a new mean value theorem for…
Abstract
Understanding the geometric and metric properties of harmonic measure is important for the solution of the Dirichlet problem for the Laplacian. In this talk I will survey the results obtained in recent years regarding the connection between harmonic measure, Hausdorff measures,…
We study the Continuum Directed Random Polymer (CDRP) which arises as a universal scaling limit of discrete directed polymers. In this talk, I will present some of the recent progress in understanding the geometry of the CDRP. In particular, I will show CDRP exhibits pointwise localization and…
Hacon-Kovács, Luo-Zhang conjectured that for a smooth complex projective variety of general type, the zero locus of any global holomorphic 1-form must be non-empty. In this talk, we will discuss about the proof by…
We will discuss the celebrated result of Kervaire and Milnor in the 1960s: the n-dimensional homotopy cobordism group is finite unless n=3. Further, we will investigate the interesting theorem of Gonzalez-Acuna in the 1970s: the n-dimensional homotopy and homology cobordism groups are isomorphic…