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Series: Combinatorics Seminar

Series: Geometry Topology Seminar

Series: Combinatorics Seminar

Suppose we want to find the largest independent set or maximal cut in a sparse Erdos-Renyi graph, where the average degree is constant. Many algorithms proceed by way of local decision rules, for instance, the "nibbling" procedure. I will explain a form of local algorithms that captures many of these. I will then explain how these fail to find optimal independent sets or cuts once the average degree of the graph gets large. There are some nice connections to entropy and spin glasses.

Series: GT-MAP Seminars

TBA

Series: Stochastics Seminar

Series: Analysis Seminar

In
this talk, I will discuss some polynomials that are best approximants
(in some sense!) to reciprocals of functions in some analytic function
spaces of the unit disk. I will examine the extremal
problem of finding a zero of minimal modulus, and will show how that
extremal problem is related to the spectrum of a certain Jacobi matrix
and real orthogonal polynomials on the real line.

Wednesday, November 29, 2017 - 13:55 ,
Location: Skiles 006 ,
Anubhav Mukherjee ,
Georgia Tech ,
Organizer: Jennifer Hom

Series: PDE Seminar

Series: Combinatorics Seminar

Official School Holiday: Thanksgiving Break

Series: Algebra Seminar

Real-valued smooth differential forms on Berkovich analytic spaces were introduced by Chambert-Loir and Ducros. They show many fundamental properties analogous to smooth real differential forms on complex manifolds, which are used for example in Arakelov geometry. In particular, these forms define a real valued bigraded cohomology theory for Berkovich analytic space, called tropical Dolbeault cohomology. I will explain the definition and properties of these forms and their link to tropical geometry. I will then talk about results regarding the tropical Dolbeault cohomology of varietes and in particular curves. In particular, I will look at finite dimensionality and Poincar\'e duality.