Calendar
- 01March 1, 2024
Richard P. Stanley Seminar in Combinatorics: A new lower bound for sphere packing
What is the maximum proportion of d-dimensional space that can be covered by disjoint, identical spheres? In this talk I will discuss a new lower bound for this problem, which is the first asymptotically growing improvement to Rogers’ bound from 1947. Our proof is almost entirely combinatorial and reduces to a novel theorem about independent sets in graphs with bounded degrees and codegrees.
This is based on joint work with Marcelo Campos, Matthew Jenssen and Marcus Michelen.
**Special Location**
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For more info, see https://math.mit.edu/combin/
- 01March 1, 2024
Gauge Theory and Topology Seminar: Sutured TQFTs and Floer homology
Science Center 5071 Oxford Street, Cambridge, MA 02138 USAThe bordered Floer homology of Lipshitz, Ozsvath, and Thurston was interpreted by Auroux as defining an element in the partially wrapped Fukaya category of a symmetric product of the boundary. We naturally expect that this assignment should be functorial; e.g. a cobordism between two manifolds with torus boundary should induce a morphism between the corresponding Lagrangians. I’ll describe a framework for thinking about functoriality in terms of sutured manifolds and describe what it looks like for Heegaard Floer homology.
- 04March 4, 2024
CMSA Colloquium: Strong bounds for arithmetic progressions
CMSA, 20 Garden St, G1020 Garden Street, Cambridge, MA 02138Suppose you have a set S of integers from {1,2,…,N} that contains at least N / C elements. Then for large enough N, must S contain three equally spaced numbers (i.e., a 3-term arithmetic progression)?
In 1953, Roth showed this is the case when C is roughly (log log N). Behrend in 1946 showed that C can be at most exp(sqrt(log N)). Since then, the problem has been a cornerstone of the area of additive combinatorics. Following a series of remarkable results, a celebrated paper from 2020 due to Bloom and Sisask improved the lower bound on C to C = (log N)^(1+c) for some constant c > 0.
This talk will describe a new work showing that C can be much closer to Behrend’s construction. Based on joint work with Zander Kelley.
- 05March 5, 2024
Probability Seminar: The Busemann process of (1+1)-dimensional directed polymers
Directed polymers are a statistical mechanics model for random growth. Their partition functions are solutions to a discrete stochastic heat equation. This talk will discuss the logarithmic derivatives of the partition functions, which are solutions to a discrete stochastic Burgers equation. Of interest is the success or failure of the “one force-one solution principle” for this equation. I will reframe this question in the language of polymers, and share some surprising results that follow. Based on joint work with Louis Fan and Timo Seppäläinen.
- 05March 5, 2024
CMSA General Relativity Seminar: High order WENO finite difference scheme for Einstein-Yang-Mills equations
In this talk, we will show the convergence analysis of the first-order finite difference scheme for static spherically symmetric $SU(2)$ Einstein-Yang-Mills (EYM) equations. We also construct a new WENO scheme for EYM.Zoom: https://harvard.zoom.us/j/7855806609
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