| August 2006 | September 2006 | October 2006 | November 2006 |
| January 2007 | February 2007 | March 2007 | April 2007 |
| Speaker: | Jason Cantarella |
| Title: | Computational Geometry |
| Speaker: | Cal Burgoyne |
| Title: | Quantum Mechanics |
| Speaker: | Dino Lorenzini |
| Title: | Algebraic Graph Theory |
| Speaker: | Dan Nakano |
| Title: | Lie Algebras |
| Speaker: | Elham Izadi |
| Title: | Algebraic Geometry |
| Speaker: | Malcolm Adams |
| Title: | Applied Dynamical Systems |
| Speaker: | Maxim Arap, University of Georgia |
| Title: | An Introduction to the Poincare Conjecture |
| Abstract: | The presentation is going to begin with the statement of Poincare conjecture. Afterwards, the presenter will try to introduce some of the topological notions which are needed to understand the statement of Poincare conjecture. Examples illustrating various concepts, definitions, and theorems will be provided. |
| Speaker: | Joe Rusinko, University of Georgia |
| Title: | Intro To Mirror Symmetry |
| Abstract: | String theory uses a particular type of manifold to describe the universe. Two such manifolds are called mirror symmetric if the universe they describe has the same physical properties. We'll explore some mathematical problems involved in mirror symmetry. |
| Speaker: | Ken Baker, Georgia Institute of Technology |
| Title: | Embedded surfaces and their boundaries |
| Abstract: | The genus of a compact orientable surface is defined in terms of its Euler characteristic and number of boundary components; all three are topological invariants of the surface. One may ``put'' (that is to say ``embed'') such a surface with boundary into R^3 in many different ways. The boundaries of various embeddings of various surfaces in R^3 are knots. Given a surface we'll explore what knots can arise as the boundaries of its embeddings. Given a knot we'll explore what surfaces it can bound. |
| Speaker: | Bree Ettinger, University of Georgia |
| Title: | Surrogate Models for a Simple Oil Reservoir |
| Abstract: | his VIGRE talk will be summary the Exxon Mobile TeamÕs findings from the IMA Math Modeling Workshop, in which we examined different algorithms to build surrogate models for a simple oil reservoir. Besides estimating NPV for certain high/low scenarios, we used surrogate models to find optimal producer well locations and to perform simple history matching of a 2D permeability field. |
| Speaker: | Tara Holm, Cornell University |
| Title: | The combinatorics of moment polytopes |
| Abstract: | I will discuss a problem that lies in the intersection of symplectic geometry and combinatorics. The symmetries of a symplectic manifold are reflected in its moment polytope. There is a dictionary translating the geometry into combinatorics, and vice versa. I will start with the definition of a polytope, describe enough symplectic geometry to motivate the moment polytope, and then I will discuss several of the dictionary entries. |
| Speaker: | Bobbe Cooper, University of Georgia |
| Title: | Tips for Surviving Graduate School |
| Abstract: | In this talk I will discuss strategies for managing your time and being productive in graduate school -- while keeping your sanity. We'll talk about balancing school and personal life, organizing office space, dealing with the multiple strains on your time, and getting motivation for long-term projects and day-to-day tasks. I'll also describe some nitty-gritty practical ways to start and continue mathematical research. This talk should be accessible to first-year graduate students. |
| Speaker: | David Pitts, University of Nebraska |
| Title: | Topology Meets Operator Algebras |
| Abstract: | A Banach algebra is a complete normed algebra, and one may consider topological properties of the group of invertible elements in any unital Banach algebra. For example, is the group of invertible elements arcwise connected? I will discuss this question for the class of infinite upper triangular matricies (relative to an orthonormal basis). This algebra can be viewed as a ``noncommutative analog'' of the Hardy algebra of all bounded analytic functions on the unit disk. The group of invertibles in the Hardy algebra is not arcwise connected, yet surpisingly, the question of whether the group of invertibles in the infinite upper triangular matricies is arcwise connected remains open. |
| Speaker: | Alexandra Shlapentokh, East Carolina University |
| Title: | On the non-existence of a general algorithm to determine whether an integer equation f(x_1,...,x_n)=0 has integer solutions (Hilbert's Tenth Problem). |
| Abstract: | At the beginning of the XX century the following question was posed by Hilbert: is there an algorithm that can determine whether an arbitrary polynomial equation in several variables and with integer coefficients has integer solutions? This problem became known as "Hilbert's Tenth Problem". In the early 1970's, Yurii Matiyasevich, building on the work by Martin Davis, Hilary Putnam and Julia Robinson showed that Diophantine sets and computably enumerable sets of integers were the same and thus showed that an algorithm sought by Hilbert did not exist. Matiyasevich's result immediately raised another question which proved to be even more vexing: is there an algorithm as described above but for the solutions in rational numbers? This problem is unsolved to this day. We will discuss the current state of this problem and other problems and conjectures which came out of attempts to solve HTP for rational numbers. |
| Speaker: | Caner Kazanci, University of Georgia |
| Title: | Analysis of Ecological Networks |
| Abstract: | In this talk, I will describe several mathematical problems arising in Ecology. One class of Ecological Models are stock-flow models, where systems of differential equations are used to simulate the flow of C, N, P, biomass or energy among compartments. Important ecosystem properties have been formulated based on these models. Properties such as dominance of indirect effects, network amplification, network cycling and network synergism provide insight into the behavior of the ecosystem as a whole. There has been examples of such approaches in other physical sciences, where higher order behavior of many interacting identities are described in simpler equations. While it is impossible to keep track of the locations and velocities of individual molecules, Navier-Stokes equation describes fluid dynamics in terms of averaged quantities, like temperature and pressure. Similarly, size distribution and grain boundary character explain some aspects of polycrystalline (metal) behavior. A very important question is the existence of such higher order properties and associated equations in ecology. There has been attempts to describe such ecosystem goal (or ecosystem health) functions. To tackle this important problem, we developed a stochastic simulation method, where each energy (or mass) packet is labeled and tracked in time as it flows through the network. This new method enables us to further investigate the existing and new quantitative ecological network properties and study their temporal and spatial evolution, which may lead to a PDE that describes ecosystem behavior. |
| Speaker: | Scott Dougan, University of Georgia |
| Title: | |
| Abstract: | Pattern formation is the fundamental question of developmental biology. In order to generate a living organism, a vast array of cell types must be generated from a single progenitor, the fertilized egg. In order to produce functional tissues and organs, these cell types must be organized in a highly precise manner. One mechanism by which this is accomplished is the formation of signaling centers, groups of cells which secrete molecules that provide positional information to surrounding cells. Cells respond to this information by adopting specific cell fates in a position dependent manner. A number of different types of molecules have been documented to provide positional information during embryogenesis. Morphogens are secreted proteins that act directly on cells at a distance and specify cell fates in a dose-dependent manner. Molecular clocks provide a mechanism to generate a reiterative pattern over time. Recently, bioengineers have attempted to build both types of patterning systems from scratch, using bacterial cultures as a starting material. The goal of this project is to analyze the mathematical f ormulas used to generate each system, and identify which variables could convert one type of information into another. Once those variables have been identified, we will test the hypothesis in zebrafish embryos by converting the morphogen Squint into a molecular clock. |
| Speaker: | Xuechao Li, University of Georgia |
| Title: | Edge coloring in Graph Theory |
| Abstract: | My talk includes introducing some basic concepts in Graph Theory, coloring problems in graph theory, conjectures on edge coloring and current results on those conjectures. |
| Speaker: | Jonathan Hanke, Duke University |
| Title: | How many ways can you write a number as a sum of 4 squares? |
| Abstract: | I hope to give a conceptual explanation of the formula for the number of ways to write a positive integer as a sum of 4 integer squares. In addition to philosophy, there will be lots of concrete computations with something for everyone. In particular, we will combine tools from seemingly unrelated areas of mathematics such as - Clock/modular arithmetic with prime numbers - Infinite sums, products, and transcendental numbers - Calculus and the geometry of 4-dimensional space to compute the number of ways of writing 1 and 2 as a sum of four squares. This talk should assume only undergraduate mathematics, and is meant to be a fun talk for first-year graduate students, who want to see something interesting in the land of number theory! |
| Speaker: | Ying Xu, University of Georgia (Institute of Bioinformatics) |
| Title: | TBA |
| Abstract: | |
| Speaker: | Shaying Zhao, University of Georgia (Institute of Bioinformatics) |
| Title: | Statistical Models for the Human Genome |
| Abstract: | We have been studying genomic changes during the human genome evolution as well as cancer development and progression. The comparison of the recently available genomic sequences of human and other mammals has indicated that mammalian genomes are heterogeneous, consisting of extensively rearranged sites and greatly conserved regions. Importantly, preliminary analyses indicate that many cancer-associated genomic abnormalities fall in the evolutionarily unstable sites. We are developing statistical models for an in-depth analysis. |
| Speaker: | Neil Lyall, University of Georgia |
| Title: | Additive patterns in the primes |
| Abstract: | Many classical questions concerning additive patterns in the primes remain unsolved; the twin prime conjecture and the Goldbach conjecture are two famous examples. Another long standing open problem, to show that the primes contain arbitrarily long arithmetic, was recently solved by Green and Tao (Tao received the Field's Medal in 2006 for this result). We hope to give an elementary overview of this seminal result as well as Gowers' revolutionary Fourier analytic proof of Szemer\'edi's theorem (Field's Medal 1998). |
| Speaker: | Matthew Ondrus, University of Arizona |
| Title: | Combinatorial Representation Theory of the Symmetric Group |
| Abstract: | Group theorists are often concerned with understanding the complex simple modules (i.e., irreducible representations) of a given group. It is well-known that the simple modules are in one-to-one correspondence with the conjugacy classes of the group, but it is not always easy to make this correspondence explicit. In the case of the symmetric group, however, there is a nice combinatorial rule for constructing the simple module corresponding to a particular conjugacy class. We will discuss this combinatorial construction and also look at what happens when the underlying field is changed to be a field of characteristic p. |
| Speaker: | Matt Mastin and Rachel Whitaker, University of Georgia |
| Title: | Calculating Ropelength of Composite Links |
| Abstract: | We will discuss work done this semester in the VIGRE Geometry group, as well as briefly discuss the application of the work to particle physics. Next, we give and overview of link properties, including symmetry and the connected sum operation. We then present the flow chart of the software suite used to compute the ropelengths. |
| Speaker: | No Meeting |
| Speaker: | Michael Guy, University of Georgia |
| Title: | A First Look at Moduli Spaces in Algebraic Geometry |
| Abstract: | Like other subjects, algebraic geometry has many "classification problems." I will give a beginner's first look at moduli spaces and their role in the classification and understanding of curves. This will be a completely elementary talk. |
| Speaker: | Dan Margalit, University of Utah |
| Title: | Introduction to moduli spaces |
| Abstract: | In topology, the surface of a donut is called a "torus". We can have a thick torus, like an inner tube, or a thin torus, like a hula hoop. In a sense, the most symmetric torus is very different from both of these. What does this space of donuts look like and what does it mean? We will give a gentle introduction and answer some of the basic questions, indicating directions for further study. |
| Speaker: | Jerry Hower, University of Georgia |
| Title: | An Introduction to Modular Forms and Maeda's Conjecture |
| Abstract: | I will first introduce modular forms and then discuss Maeda's conjecture. The latter states that certain polynomials associated to modular forms are in fact irreducible. |
| Speaker: | Jon Kujawa, University of Georgia |
| Title: | TBA |
| Abstract: | |
| Speaker: | Aaron Abrams, Emory University |
| Title: | Can you tile a square with an odd number of triangles of equal area? |
| Abstract: | Or how about this one: can you color each point of the plane with one of three colors, in a nontrivial way, such that no straight line contains points of all three colors? (What should ``nontrivial'' mean?) These questions and more will be answered. We will use a bit of topology, a bit of number theory, and a bit of magic. |
| Speaker: | Jacob Siehler, Washington and Lee University |
| Title: | Categories with Multiple Monoidal Structures |
| Abstract: | Categories with more than one multiplicative structure can serve as a bridge between algebraic topology and higher-dimensional category theory. We will illustrate the axioms of iterated monoidal categories by means of combinatoric examples involving tableaux shapes; sketch the connection to homotopy theory, and state a structure theorem for categories of operads in iterated monoidal categories. |
| Speaker: | Carrie Wright, University of Georgia |
| Title: | The Singled Out Game |
| Abstract: | Do you remember the game show "Singled Out" on MTV from the late 90's? Is there a strategy to winning the game? I will explain the basic premise of the game and then talk about whether there is a strategy to win the game of the 3 finalists. I will first break it down to what happens if there were only 2 finalists and then talk about the case when there are 3 finalists. Is the strategy the same as in the 2 person case? |
| Speaker: | Adrian Jenkins, Purdue University |
| Title: | Introduction to Complex Dynamics |
| Abstract: | I will talk about (discrete) dynamical systems in the local and global cases, of one and several complex variables. Complex dynamics is an interesting field of study, and very popular. All relevant definitions will be given, and proofs will be kept to a minimum. Basically, I would like to give an idea of some of the beauty of this field. |
| Speaker: | Bret Benesh, Harvard University |
| Title: | Maximal Subgroups of Sym(m) that are Isomorphic to a Symmetric Group |
| Abstract: | When is it possible for a symmetric group (denoted Sym(m)) to have a maximal subgroup that is isomorphic to another symmetric group (say, Sym(n))? One easy case is when m=n+1; for example, Sym(13) has a maximal subgroup that is isomorphic to Sym(12). However, there are other interesting and surprising ways in which this can happen. |
| Speaker: | Lloyd Reiber, University of Georgia |
| Title: | Rediscovering Gaming in Education: New Opportunities for Ancient Ideas |
| Abstract: | Games and education have enjoyed a long history together. Educational games are one of the earliest forms of instructional technology. The advent of computer technology, starting even as late as the introduction of the Apple educational games in K-12 and higher education classrooms. However, educators, administrators, and parents have long been ambivalent about gaming's use and role in education. Few people take a neutral stance on this issue. Proponents see games in education as the means of creating engaging and experiential learning experiences for students, whereas opponents see games as a mere diversion and a waste of precious class time. The advent of high-end sophisticated gaming environments over the past 5-10 years, such as those prevalent in the home entertainment market, has sparked a new and considerable interest in the use of games in education. Gamers devote immense intensity, commitment, passion, and time to games. The question of what educators can learn about this phenomenon in order to exploit it for educational purposes is finally being taken very seriously by scholars. This presentation will explore the general question of what makes games compelling from both intellectual and motivational points of view. It will focus on middle-tech and low-tech gaming technology and explore examples of gaming that any instructor can immediately begin to implement. The Internet houses thousands of small interactive games suitable for education that can be either downloaded or played online. The presentation will also discuss the educational opportunities of students building their own "Homemade PowerPoint Games". |
| Speaker: | Adam Speight, Georgia State University |
| Title: | Calibration of Recursive Models in One Shot |
| Abstract: | Formulating and solving well-posed, analytically intractable recursive models is a major challenge. Large models with many parameters are often given only superficial empirical treatment since most parameter estimation strategies require computing accurate numerical solutions a large number of times, which is often considered infeasible or impractical. I propose a numerical technique for simultaneously solving and calibrating a broad class of recursive models. The technique applies directly to local discretizations of continuous time dynamic programming problems and can be adapted to solve similar recursive models of competitive equilibrium, dynamic contracting, and dynamic games. The \emph{defect correction} principle used in Multigrid methods is extended and applied to simultaneously solve, calibrate, and identify the models I consider numerically. By coupling the empirical procedure into the model solver, I show heuristically that for a typical model, the solution, calibrated parameters, and sensitivity to changes in data can be computed at about three to four times the cost of solving the model a single time for a fixed set of parameters provided the model responds smoothly to parameter variations and is fully identified model. For over-identified models, the technique is readily extended to accommodate the Generalized Method of Moments and related techniques based on the Delta method. I illustrate and evaluate my technique by applying it to an infinite-horizon, continuous-time, portfolio choice problem discretized using finite-difference and Markov Chain approximations. I show how computational and analytical techniques from the Multigrid literature can be adapted to provide guidance for how to properly construct a multilevel algorithm and to predict and diagnose performance. |
| Speaker: | Joe Fu, University of Georgia |
| Title: | Geometric probability, continuous and discrete |
| Abstract: | Geometric probability is an old subject, built around Crofton's formula and its generalizations. The prototype Crofton problem is to compute the expected number of intersections of two curves placed in random positions in the sphere, but from this humble beginning the theory has taken off in a big way in recent years. Meanwhile, G.-C. Rota observed that the main classical ideas transfer readily to a number of discrete settings, the most elementary being the statistics of the number of points of intersection of two random subsets of fixed size in a finite set S. Here the basics were worked out by D. Klain in the '90s, but the time seems ripe to reexamine the subject in light of the recent developments in the continuous case. |
| Speaker: | Ed Azoff, University of Georgia |
| Title: | Measurable Dynamics |
| Abstract: | Let E be an equivalence relation on a set X. A _uniformization_ of E is a subset of X which meets each equivalence class determined by E in precisely one point. Finding "nice" uniformizations is a common mathematical goal. For example, Jordan canonical forms solve the uniformization problem for the relation of similarity on complex matrices. After some general remarks, we will specialize to the following setting. Given a bijection f on the interval [0,1), define x~y if and only if some (forward, backward, or neutral) iterate of f sends x to y. We will discuss classical work of Poincare, Denjoy and Glimm-Effros to the effect that the resulting equivalence relation is either very good or very bad. We will also examine some concrete examples illustrating how hard it can be to decide which alternative holds for a specific f. Along the way, we will catch glimpses into descriptive set theory (deining what "nice" means), ergodic theory (measures on [0,1) which are invariant under f), and dynamics (examining limit sets of orbits). My interest in this topic arose from joint work with Eugen Ionascu on a question from wavelet theory. |
| Speaker: | Efren Ruiz, University of Toronto |
| Title: | The Elliott Classification Program |
| Abstract: | The program to classify separable C*-algebra can be thought as a non-commutative version to the program to classify compact Hausdorff spaces. It turns out that invariants introduced in algebraic topology are complete invariants for certain classes of C*-algebras. The aim of this talk is to give an introduction to the program to classify separable C*-algebras. In particular, I will talk about the ground breaking work of George Elliott involving approximately finite dimensional C*-algebras. |