Date  Speaker  Title 

Introduction to Quantum Mechanics and Random Schrodinger Operators 

In this talk, I will introduce the basics of Quantum Mechanics and discuss the experimental and theoretical developments leading to Quantum theory.  
Elliptic Curves and Cryptography


Elliptic curves have been of theoretical interest to number theorists for a long time. However, more recently it was discovered that elliptic curves  
Shape Selection in NonEuclidean Plates Part II 

In nature there are many species of lifeforms, such as leaves, sea slugs, lichen, and fungi, that are examples of objects that closely resemble surfaces  
A free boundary problem for the heat equation and the waiting time phenomenon. 

We investigate a free boundary problem for the heat equation derived from combustion theory and study the development of the boundary, $\Gamma$.  
In this talk we will discuss
the basics of modern probability theory. We will introduce the
subject from its measuretheoretic framework and provide examples that give one better intuition. At the end, we will highlight more recent developments in the subject.  
MCMC, SA and PT for the TSP 

We
explore the potential of parallel tempering as a combinatorial
optimization method, applying it to the traveling salesman
problem. We compare simultaion results of parallel tempering with a benchmark implementation of simulated annealing, and study how different choices of parameters affect the relative performace of the two methods. We find that a strightforward implementation of parallel tempering can outperform simulated annealing in several crucial respects. When parameters are chosen appropriately, both methods yield close approximation to the actual minimum distance for an instance with 200 nodes. However, parallel tempering yields more consistently accurate results when a series of independent simulations are performed. Our results suggest that parallel tempering might offer a simple but powerful alternative to simulated annealing for combinatorial optimization problems.  
I will introduce piecewiseflat and
triangulated surfaces. In particular, I will discuss Delaunay
triangulations, which yield wellbehaved Laplacians which are defined based on the intrinsic geometry without an a priori choice of triangulation.  
Symmetries and Differential Equations  
How do we find an exact solution of a differential equation? In most differential equations courses, we were taught how to solve differential equations on  
The solution to a topology
exercise assigned in my first year showed up in a Salvador Dali
painting. Enough said. The talk will be accesible to
graduate students who have completed the core sequence in topology; however, it may provide a nice preview of algebraic topology for those who haven't finished the sequence yet.  
GTEAMS (Graduate Students
and Teachers Engaging in Mathematical Sciences) is a partnership
between the University of Arizona and local schools in the Tucson area. The program places graduate fellows, whose research interests lie in the mathematical sciences, in a K through 12 classroom to engage in a yearlong dialogue with a teacher and his/her students. The principal aim of this program is to help the fellow develop communication skills that work at both practical and research levels of mathematics. In this informal question and answer session, as past and current fellows, we give our combined perspectives on an amazing opportunity and experience available to all mathematics graduate students.  
Angel Chavez 

Tropical Geometry is a
blend of algebraic and polyhedral geometry. This talk will present
known methods of transforming an algebraic variety into its tropical counterpart. Examples will be emphasized.  
We will characterize the
automorphism groups of elliptic curves defined over the field of
complex numbers. The groups will be characterized as a semidirect product similar to the holomorph of the underlying group. Along the way we will learn about complex manifolds, Riemann surfaces, and moduli spaces of curves. The snacks will serve as an exciting visual aid throughout the talk.  
A Gröbner basis is a set of
multivariate polynomials that has nice algorithmic properties. In
particular, every ideal in a polynomial ring has a Gröbner basis, and from this basis we can determine geometric properties about the variety of the ideal. In this talk, I will give a brief overview of Gröbner bases and how they are useful. I will also discuss the Gröbner bases for the vanishing ideal of the cut vectors of a graph and the Gröbner fan associated with this ideal.  
Combinatorial geometry is the study of combinatorial problems in convex bodies. This talk will discuss two such problems: Borsuk's problem, which asks  
In this talk I will describe some geometric ideas for the study of finitely generated groups. We will begin with the basic tools: presentations, the word metric, and the Cayley graph. Afterward, we will discuss some applications of these ideas, including a solution to the word problem in hyperbolic groups and the role of (non) amenability in the BanachTarski theorem. 
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