Juggling Mathematics and Magic

Professor Ronald Graham, one of the world’s best known mathematicians, computer theorists, and technology visionaries, will explain the math behind magic in his talk, “Juggling Mathematics and Magic”. Graham, who calls himself a “mathematician” will explore the mystery of magic and the art of juggling and their surprising links to mathematical concepts. 

Random potentials for pinning models with gradient and Laplacian interactions.

Speaker: 

Chien-Hao Huang

Institution: 

UCI

Time: 

Tuesday, November 27, 2012 - 11:00am

Location: 

RH 306

Abstract: We consider two models for bio-polymers, the gradient interaction and the Lacplacian one,
both with the Gaussian potential in the random environment. A random field φ : { 0, 1, ..., N } → R^d represents the position of the polymer path. The law of the field is given by exp( − ∑ i |∇ φi |^2 /2) where ∇ is the discrete gradient, and by exp( − ∑ i | ∆φi |^2 /2) where ∆ is the discrete Laplacian. For every Gaussian potential |·|^2 /2, a random charge is added as a factor: (1+βωi) |·|^2 /2 with P (ωi = ± 1) = 1/2 or exp(βωi) |·|^2 /2 with ωi obeys a normal distribution. The interaction with the
origin in the random field space is considered. Each time the field touches the origin, a reward ϵ ≥ 0 is given. Although these models are quite different from the pinning models studied in G. Giacomin (2011), the result about the gap between the annealed critical point and the quenched critical point stays the same.

Nonlinear Wave Equations With Damping And Supercritical Sources

Speaker: 

Yanqiu Guo

Institution: 

Weizman Institute

Time: 

Tuesday, January 8, 2013 - 2:00pm

Location: 

RH 340P

In this talk I will discuss the local and global well-posedness of coupled non- linear wave equations with damping and supercritical sources. Our interests lie in the interaction between source and damping terms and their influence on the behavior of solutions. I will introduce the method of using the monotone operator theory to obtain the local existence of weak solutions to our system. Also we extend a result by Brezis on convex integrals on Sobolev spaces, which allows us to overcome a major technical difficulty in the proof of the existence of solutions. 

 

Symplectic harmonic forms and the Federer-Fleming deformation theorem

Speaker: 

Yi Lin

Institution: 

Georgia Southern University

Time: 

Tuesday, March 5, 2013 - 4:00pm

Location: 

RH 306

Symplectic harmonic theory was initiated by Ehresmann and Libermann in 1940's, and was rediscoverd by Brylinski in late 1980's. More recently, Bahramgiri showed in his MIT thesis that symplectic harmonic representatives of Thom classes exhibited some interesting global feature of symplectic geometry. In this talk, we discuss a new approach to symplectic Harmonic theory via geometric measure theory. The new method allows us to establish a fundamental property on symplectic harmonic forms, which is a non-trivial generalization of Bahramgiri's result, and enables us to provide a complete solution to an open question asked by V. Guillemin concerning symplectic harmonic representatives of Thom classes.  This talk is based on a very recent work of the speaker.

J-holomorphic curves in a nef class

Speaker: 

Tian-Jun Li

Institution: 

University of Minnesota

Time: 

Tuesday, January 29, 2013 - 4:00pm

Location: 

RH 306

We investigate properties of reducible J-holomorphic subvarieties in 4-manifolds. We offer an upper bound of the total genus of a subvariety when the class of the subvariety is J-nef.

For a spherical class, it has particularly strong consequences: for any tamed J, each irreducible component is a smooth rational curve. We also completely classify configurations of maximal dimension. To prove these results we treat subvarieties as weighted graphs and introduce several combinatorial moves. This is a joint work with Weiyi Zhang.

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