Seminars and Colloquia by Series

Infinite volume limit for the Nonlinear Schrodinger Equation and Weak Turbulence

Series
PDE Seminar
Time
Tuesday, December 2, 2014 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Pierre Germain – Courant Institute
Abstract: the theory of weak turbulence has been put forward by appliedmathematicians to describe the asymptotic behavior of NLS set on a compactdomain - as well as many other infinite dimensional Hamiltonian systems.It is believed to be valid in a statistical sense, in the weaklynonlinear, infinite volume limit. I will present how these limits can betaken rigorously, and give rise to new equations.

The Range of the Rotor Walk

Series
Combinatorics Seminar
Time
Tuesday, December 2, 2014 - 13:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Laura Florescu – Courant Institute, NYU
In a "rotor walk" the exits from each vertex follow a prescribed periodic sequence. On an infinite Eulerian graph embedded periodically in $\R^d$, we show that any simple rotor walk, regardless of rotor mechanism or initial rotor configuration, visits at least on the order of t^{d/(d+1)} distinct sites in t steps. We prove a shape theorem for the rotor walk on the comb graph with i.i.d.\ uniform initial rotors, showing that the range is of order t^{2/3} and the asymptotic shape of the range is a diamond. Using a connection to the mirror model and critical percolation, we show that rotor walk with i.i.d. uniform initial rotors is recurrent on two different directed graphs obtained by orienting the edges of the square grid, the Manhattan lattice and the F-lattice. Joint work with Lionel Levine and Yuval Peres.

Geometric homogeneity in disordered spatial processes

Series
Job Candidate Talk
Time
Tuesday, December 2, 2014 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Eviatar Procaccia – University of California, Los Angeles
Experimentalists observed that microscopically disordered systems exhibit homogeneous geometry on a macroscopic scale. In the last decades elegant tools were created to mathematically assert such phenomenon. The classical geometric results, such as asymptotic graph distance and isoperimetry of large sets, are restricted to i.i.d. Bernoulli percolation. There are many interesting models in statistical physics and probability theory, that exhibit long range correlation. In this talk I will survey the theory, and discuss a new result proving, for a general class of correlated percolation models, that a random walk on almost every configuration, scales diffusively to Brownian motion with non-degenerate diffusion matrix. As a corollary we obtain new results for the Gaussian free field, Random Interlacements and the vacant set of Random Interlacements. In the heart of the proof is a new isoperimetry result for correlated models.

Physics Colloquium - The Intelligent Physics Student's Guide to Pricing and Hedging

Series
Other Talks
Time
Monday, December 1, 2014 - 15:00 for 1 hour (actually 50 minutes)
Location
Howey Building - Room L2
Speaker
Emanuel Derman – Columbia University

Please Note: Predrag Cvitanovic, School of Physics

The syntax of theoretical physics and modern finance is deceptively similar, but the semantics is very different. I present a short introduction to the principles of modern finance, and compare and contrast the field to physics.

Structure-preserving numerical integration or ordinary and partial differential equations

Series
Applied and Computational Mathematics Seminar
Time
Monday, December 1, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Raffaele D'Ambrosio – GA Tech
It is the purpose of this talk to analyze the behaviour of multi-value numerical methods acting as structure-preserving integrators for the numerical solution of ordinary and partial differential equations (PDEs), with special emphasys to Hamiltonian problems and reaction-diffusion PDEs. As regards Hamiltonian problems, we provide a rigorous long-term error analyis obtained by means of backward error analysis arguments, leading to sharp estimates for the parasitic solution components and for the error in the Hamiltonian. As regards PDEs, we consider structure-preservation properties in the numerical solution of oscillatory problems based on reaction-diffusion equations, typically modelling oscillatory biological systems, whose solutions oscillate both in space and in time. Special purpose numerical methods able to accurately retain the oscillatory behaviour are presented.

Homology three-spheres and surgery obstructions

Series
Geometry Topology Seminar
Time
Monday, December 1, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Tye Lidman – University of Texas, Austin
The Lickorish-Wallace theorem states that every closed, connected, orientable three-manifold can be expressed as surgery on a link in the three-sphere (i.e., remove a neighborhood of a disjoint union of embedded $S^1$'s from $S^3$ and re-glue). It is natural to ask which three-manifolds can be obtained by surgery on a single knot in the three-sphere. We discuss a new way to obstruct integer homology spheres from being surgery on a knot and give some examples. This is joint work with Jennifer Hom and Cagri Karakurt.

Alexander's Theorem

Series
Geometry Topology Student Seminar
Time
Wednesday, November 26, 2014 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Eric Sabo – Georgia Institute of Technology –

Please Note: This is a project for Prof. Margalit's course on Low-dimensional Topology and Hyperbolic Geometry.

I will present a modern proof of Alexander's Theorem using Morse Theory and surgery.

Some Classic Puzzles of Martin Gardner, The Best Friend Mathematics Ever Had

Series
Other Talks
Time
Tuesday, November 25, 2014 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Colm Mulcahy – Spelman College

Please Note: Colm Mulcahy is a professor of mathematics at Spelman College, in Atlanta, where he has taught since 1988. He's currently on leave in the DC area. Over the last decade, he has been at the forefront of publishing new mathemagical principles and effects for cards, particularly in his long-running bi-monthly Card Colm for the MAA. Some of his puzzles have been featured in the New York Times. His book Mathematical Card Magic: Fifty-Two New Effects was published by AK Peters/CRC Press in 2013. Colm is a recipient of MAA's Allendoerfer Award for excellence in expository writing, for an article on image compression using wavelets.

Martin Gardner was best known for his 300 "Mathematical Games" columns in Scientific American, in which he introduced thousands of budding mathematicians to topics such as RSA cryptography, fractals, Penrose tiles and Conway's game of Life, as well as elegant puzzles which still lead to "Aha!" moments today. In his centennial year we'll survey some of what he achieved and in particular the puzzle legacy he leaves behind.

Everywhere differentiability of viscosity solutions to a class of Aronsson's equations

Series
PDE Seminar
Time
Tuesday, November 25, 2014 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Changyou Wang – Purdue University
For a $C^{1,1}$-uniformly elliptic matrix $A$, let $H(x,p)=$ be the corresponding Hamiltonian function. Consider the Aronsson equation associated with $H$: $$(H(x,Du))x H_p(x,Du)=0.$$ In this talk, I will indicate everywhere differentiability of any viscosity solution of the above Aronsson's equation. This extends an important theorem by Evans and Smart on the infinity harmonic functions (i.e. $A$ is the identity matrix).

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