Posted March 4, 2010
Last modified March 22, 2010
VIGRE@LSU: Student Colloquium Questions or comments?
3:40 pm – 4:30 pm Lockett 285
Barry Cipra
Barry Cipra is a freelance journalist who writes about mathematics in a very wide range of venues
SeVenn, EleVenn, and Beyond
The speaker will report on recent results on the existence of
rotationally symmetric Venn diagrams -- a problem first posed, by an
undergraduate, in the 1960s, and finally fully solved, by another
undergraduate, almost 40 years later. Many related open problems remain,
perhaps for yet another undergraduate to solve.
Posted March 4, 2010
Last modified March 9, 2010
VIGRE@LSU: Student Colloquium Questions or comments?
3:40 pm – 4:30 pm TBA
Barry Cipra
Barry Cipra is a freelance journalist who writes about mathematics in a very wide range of venues
Science Writing
Barry Cipra will be addressing the Communicating Math Class. All are welcome to attend.
Posted October 12, 2010
VIGRE@LSU: Student Colloquium Questions or comments?
10:40 am – 11:30 am Lockett 277
David Ross, Rochester Institute of Technology
Inferring Gibbs Free Energies from Light Scattering Data
Differences in free energies are the driving forces in chemical changes. The current project originated in our desire to understand phase changes in the protein mixtures in the lens of the human eye; such changes cause cataract disease. We are able to use a PDE to study the free energies as functions of the mixture composition, and we will formulate a well-posed problem for this equation with singular boundary conditions based on the Widom asymptotic form of the free energy.
Posted October 12, 2010
Last modified March 2, 2021
VIGRE@LSU: Student Colloquium Questions or comments?
2:40 pm – 3:30 pm Lockett 277
David Ross, Rochester Institute of Technology
ODEs in Industrial (and other) Applications
In this talk, we discuss several ODE problems from various areas of active research, such as MEMS (Micro-Electro Mechanical Systems) micro-energy harvesting, in which micro-machines built on computer chips glean energy from mechanical vibrations to power circuits, as well as topics in Osteoporosis research, Cataract research, Gear design and Ecological Economics.
Posted November 9, 2010
Last modified November 12, 2010
VIGRE@LSU: Student Colloquium Questions or comments?
2:40 pm – 3:30 pm Lockett 112
Rodolfo Torres, University of Kansas
Somewhere over the (mathematical) rainbow blue birds fly.... Why oh why are they blue?
Refreshments will be served from 2:00-2:30 pm in the Keisler lounge.
There are blue skies and blue birds over the rainbow as the song says, but not all blues are the same. The blue and green colors we see in birds, and even some of the ultraviolet that we cannot see, are produced by the way in which the light interacts with ordered microscopic structures in the tissues of the birds.
This order in the structures can be measured using Fourier analysis, a powerful mathematical tool. Like a prism that decomposes a beam of light into a rainbow of colors, Fourier analysis transforms the geometrical arrangements observed in electron microscope images of the tissues into a mathematical rainbow of basic components that quantify order or periodicities. We will illustrate how Fourier analysis processes the images and helps decipher the colors of birds and other animals. The talk will be accessible to all those who are curious about some of the mathematics and physics behind the bright blue and green colors found in nature.
Posted November 9, 2010
Last modified November 12, 2010
VIGRE@LSU: Student Colloquium Questions or comments?
12:40 pm – 1:30 pm Lockett 239
Rodolfo Torres, University of Kansas
Discrete decomposition techniques in Fourier analysis.
Refreshments will be served in the Keisler lounge from 12:00- 12:30.
Abstract: Decomposition techniques such as atomic, molecular, wavelet and wave-packet expansions provide a multi-scale refinement of Fourier analysis and exploit a rather simple concept: "waves with very different frequencies are almost invisible to each other". Many of these useful techniques have been developed around the study of certain operators called singular integral operators.
By breaking an operator or splitting the function on which it acts into non-interacting pieces, these tools capture subtle cancellations and quantify properties of an operator in terms of norm estimates in functions spaces. This type of analysis has been extensively used to study linear or multilinear operators with tremendous success.
In this talk we will give some background and motivation for some decomposition techniques and show some basic concepts about how they are used to study operators of interest in Fourier analysis.
Posted January 20, 2011
VIGRE@LSU: Student Colloquium Questions or comments?
4:10 pm – 5:00 pm Lockett 277
Andrei Zelevinsky, Northeastern University
Quiver representations and their mutations
A quiver is a finite directed graph, that is, a finite set of vertices some of which are joined by arrows. A quiver representation assigns a finite-dimensional vector space to each vertex, and a linear map between the corresponding spaces to each arrow. A fundamental role in the theory of quiver representations is played by Bernstein-Gelfand-Ponomarev reflection functors associated to every source or sink of a quiver. We discuss two recent modifications of these functors. The first (joint work with R.Marsh and M.Reineke) introduces decorated quiver representations and makes modified reflection functors act as isomorphisms of the corresponding Grothendieck groups. The second (joint work with H.Derksen and J.Weyman) extends reflection functors from sources and sinks to arbitrary vertices. This construction requires the quiver representations in question to satisfy relations of a special kind imposed by the framework of quivers with potentials. Motivations for this work come from several sources: superpotentials in physics, Calabi-Yau algebras and categories, clusteralgebras. However no knowledge is assumed in any of these subjects.
Posted April 26, 2011
Last modified May 2, 2011
VIGRE@LSU: Student Colloquium Questions or comments?
10:40 am – 11:30 am 276 Lockett Hall
Suzanne Lenhart, University of Tennessee
Optimal Harvesting in Fishery Models
We discuss two types of partial differential equation models of fishery harvesting problems. We consider steady state spatial models and diffusive spatial-temporal models. We characterize the distribution of harvest effort which maximizes the harvest yield, and in the steady state case, also minimizes the cost of the effort. We show numerical results to illustrate various cases. The results inform ongoing debate about the use of reserves (regions where fishing is not allowed), and are increasingly relevant as technology enables enforcement of spatially structured harvest constraints.
Posted April 26, 2011
Last modified May 2, 2011
VIGRE@LSU: Student Colloquium Questions or comments?
1:40 pm – 2:30 pm 276 Lockett Hall
Suzanne Lenhart, University of Tennessee
The power of optimal control: from confining rabies to improving CPR
Refreshments will be served in the Keisler Lounge from 1:00 to 1:30. This talk will present optimal control of two examples which are discrete in time. The first example involves difference equations that model cardiopulmonary resuscitation. The goal is to design an external chest and abdomen pressure pattern to improve the blood flow in the heart in standard CPR procedure. The second example is an epidemic model for rabies in raccoons on a spatial grid. The goal is to find the optimal distribution pattern for vaccine baits to slow the spread of the disease.
Posted September 20, 2011
VIGRE@LSU: Student Colloquium Questions or comments?
3:40 pm – 4:30 pm Wednesday, October 5, 2011 Lockett 243
Dan Cranston, Virginia Commonwealth University
The Search for Moore Graphs: Beauty is Rare
Abstract: A Moore Graph is k-regular, has diameter 2, and has k^2+1 vertices- that\'s the most vertices you could hope for in such a graph. These graphs are vertex-transitive and evoke a wonderful sense that \"everything fits just right.\" It\'s not hard to find Moore graphs when k is 2 or 3; they\'re the 5-cycle and the Petersen graph. But for larger k, they\'re very rare. In 1960, Hoffman and Singleton gave a beautiful proof that Moore Graphs can only exist when k is 2, 3, 7, or 57. For k equal to 2, 3, or 7, they showed that there exists a unique Moore Graph. When k is 57, nobody knows. I\'ll present Hoffman and Singleton\'s proof and take a wild stab at what they might have been thinking when they discovered it.
Dan Cranston is an invited speaker of the Student Colloquium Committee, which is funded by the VIGRE grant.
Posted September 20, 2011
VIGRE@LSU: Student Colloquium Questions or comments?
1:30 pm – 2:00 pm Keisler Lounge in Lockett HallRefreshments for the Student Colloquium Talk
We will be having refreshments during this time period leading up to Dan Cranston\'s talk.
Dan Cranston is an invited speaker of the Student Colloquium Committee, which is funded by the VIGRE grant.
Posted September 20, 2011
VIGRE@LSU: Student Colloquium Questions or comments?
2:00 pm – 3:00 pm Lockett 112
Dan Cranston, Virginia Commonwealth University
A Proof of Bertrand's Postulate
This talk is aimed at undergraduate students.
Abstract: Bertrand's Postulate states: For every positive integer n, there is some prime number p with n < p \\le 2n. This result was conjectured in 1845 by Joseph Bertrand, who verified it for all n < 3 \\times 10^6, and it was proved five years later by Chebyshev (nearly 50 years before the prime number theorem was proved). I'll present a beautiful proof of this result due to Paul Erd\"os.
Dan Cranston is an invited speaker of the Student Colloquium Committee, which is funded by the VIGRE grant.
Posted September 20, 2011
VIGRE@LSU: Student Colloquium Questions or comments?
3:40 pm – 4:30 pm Lockett 243
Dan Cranston, Virginia Commonwealth University
The Search for Moore Graphs: Beauty is Rare
This talk is aimed at graduate students.
Abstract: A Moore Graph is k-regular, has diameter 2, and has k^2+1 vertices- that\'s the most vertices you could hope for in such a graph. These graphs are vertex-transitive and evoke a wonderful sense that \"everything fits just right.\" It\'s not hard to find Moore graphs when k is 2 or 3; they\'re the 5-cycle and the Petersen graph. But for larger k, they\'re very rare. In 1960, Hoffman and Singleton gave a beautiful proof that Moore Graphs can only exist when k is 2, 3, 7, or 57. For k equal to 2, 3, or 7, they showed that there exists a unique Moore Graph. When k is 57, nobody knows. I\'ll present Hoffman and Singleton\'s proof and take a wild stab at what they might have been thinking when they discovered it.
Dan Cranston is an invited speaker of the Student Colloquium Committee, which is funded by the VIGRE grant.
Posted October 25, 2011
Last modified October 26, 2011
VIGRE@LSU: Student Colloquium Questions or comments?
1:30 pm – 2:30 pm Lockett 235
Loredana Lanzani, University of Arkansas
Practical Uses of Complex Analysis
This talk is primarily aimed at undergraduates.
In this talk I will quickly introduce the fundamental notion of conformal mapping for a planar (2-D) domain, which is one of the main ideas behind the classical subject of (one variable) complex analysis.
I will then proceed to present some of the applications of conformal mappings to real-life situations, including: cartography; airplane wing design (transonic flow); taxonomy; art (in particular, the work of M. C. Escher). No previous knowledge of complex analysis is required.
There will be a light lunch in the Keisler Lounge from 1:00-1:30.
Posted October 25, 2011
Last modified October 26, 2011
VIGRE@LSU: Student Colloquium Questions or comments?
3:30 pm – 4:30 pm Lockett 235
Loredana Lanzani, University of Arkansas
Several Complex Variables: the many joys (and occasional pains) of multivariable complex calculus
This talk is primarily aimed at graduate students.
In this talk I will discuss some of the main ideas behind the (relatively recent) research area of Several Complex Variables, which in many ways is strikingly different from its one-variable counterpart -- that is the classical (and much older) subject of complex analysis. A basic knowledge of multivariable calculus will be the main prerequisite for this talk.
There will be refreshments in the Keisler Lounge from 3:00-3:30.
Posted February 13, 2012
Last modified February 17, 2012
VIGRE@LSU: Student Colloquium Questions or comments?
1:40 pm – 2:30 pm Lockett 112
Kevin Knudson, Florida University
Fujimoto Approximation
This talk is primarily aimed at undergraduates.
If I hand you a strip of paper and ask you to fold it in half, or fourths, or 128ths, you can do it very easily. But what if I ask you to fold it into fifths, or sevenths, or 31sts? In this talk I'll show you Fujimoto's approximation method for folding into nths, where n is any odd number. A surprising cast of mathematical characters will show up along the way - binary decimals, discrete dynamical systems, and primitive roots of unity modulo n.
There will be a light lunch in the Keisler lounge at 1:00pm preceding the talk.
Posted February 13, 2012
Last modified February 17, 2012
VIGRE@LSU: Student Colloquium Questions or comments?
11:40 am – 12:30 pm Himes 253
Kevin Knudson, Florida University
Topological Data Analysis
This talk is primarily aimed at graduate students.
In this talk I will introduce the concept of persistent homology, a method to use techniques from algebraic topology to find nonlinear structures in large data sets. Several examples will be discussed including the space of natural images (analysis due to Carlsson, et. al.) and data sets built from human speech signals (joint with K. Brown). No detailed knowledge of algebraic topology will be assumed.
There will be refreshments in the Keisler lounge at 11:00am preceding the talk.
Posted April 4, 2012
Last modified April 16, 2012
VIGRE@LSU: Student Colloquium Questions or comments?
1:30 pm – 2:30 pm Lockett 239
Benson Farb, University of Chicago
Topology, dynamics, and geometry of surfaces (and their remarkable relationships)
This talk is primarily aimed at undergraduate students.
Surfaces can be considered from many different viewpoints: their
shape (i.e. topological structure), their geometry (e.g. curvature), and the
behavior of fluid flows on them. In this talk I will describe three
beautiful theorems, one for each of these aspects of surfaces. I will also
try to explain the remarkable fact that these seemingly completely different
perspectives are intimately related.
There will be a light lunch in the Keisler Lounge at 1:00pm.
Posted April 4, 2012
Last modified April 17, 2012
VIGRE@LSU: Student Colloquium Questions or comments?
11:30 am – 12:30 pm Lockett 239
Benson Farb, University of Chicago
The Mostow Rigidity Theorem: topology vs. algebra vs. geometry
The Mostow Rigidity Theorem changed geometry and topology. This talk, aimed at graduate students, will attempt to explain how and why.
There will be refreshments in the Keisler Lounge at 11:00am.
Posted October 24, 2012
Last modified October 30, 2012
VIGRE@LSU: Student Colloquium Questions or comments?
1:30 pm – 2:20 pm Lockett 232
Debra Knisley, East Tennessee State University
Graph-theoretic measures of biomolecular structures
In this talk I will present an overview of graph-theoretic models in molecular biology. We will see how graphs can be used to represent DNA structure, secondary RNA structure and protein structures. Techniques that attempt to numerically characterize biomolecular structure and function, using concepts from chemical graph theory, combinatorial graph theory and network science will be compared. Recent projects that utilize ideas from all of the above to model RNA and proteins will be presented as examples and the future of such applications will be a discussed. This is joint work with a number of students at ETSU, both undergraduate and beginning graduate.
This talk is primarily aimed at undergraduate students.
There will be a light lunch from 1:00-1:30 in the Keisler Lounge.
Posted October 24, 2012
Last modified October 30, 2012
VIGRE@LSU: Student Colloquium Questions or comments?
2:30 pm – 3:20 pm Lockett 232
Debra Knisley, East Tennessee State University
Vertex-weighted graph models of protein structure
In this talk I will present several graph based models of proteins. Our previous work on predicting changes in protein binding affinity due to mutations shows that graphical invariants coupled with data mining tools inherently combine primary sequential information, structural information and amino acid motif recognition. Misfolded proteins are responsible for a number of diseases, among them cystic fibrosis. The misfolding of a critical protein, the Cystic Fibrosis Transmembrane Conductance Regulator (CFTR) membrane protein, is the result of a single point mutation in the gene that encodes CFTR. We extend our previous findings to model CFTR with a nested vertex-weighted graph approach, defining novel measures of graphs from combinatorial concepts which we use as biomolecular descriptors. Our model is then used to perform virtual mutations of CFTR in order to numerically characterize the
consequences of each mutation on the structural features of the protein. We compare the results of eight of the most commonly occurring mutations of CFTR. This work is in progress and the findings are preliminary.
This talk is primarily aimed at graduate students.
There will be refreshments in the Keisler Lounge from 2:00-2:30.
Posted November 14, 2012
VIGRE@LSU: Student Colloquium Questions or comments?
2:30 pm – 3:20 pm Lockett 235
Renzo Cavalieri, Colorado State University
Counting factorizations in the symmetric group using graphs
Given a permutation x in the symmetric group and an integer r, we want to investigate the following question:
How many ways can I write x as a product of r transpositions?
This is a group theoretic question that can be answered in terms of representation theory of the symmetric group. In this talk I want to present a combinatorial approach, which provides the answer in terms of an appropriate weighted sum over certain decorated graphs which I suggestively call \"tropical covers\". This method comes from the study of an equivalent geometric question... but this is another story...
This talk is primarily aimed at undergraduate students.
There will be refreshments in the Keisler lounge from 2:00-2:30pm.
Posted November 14, 2012
VIGRE@LSU: Student Colloquium Questions or comments?
1:30 pm – 2:20 pm Lockett 235
Renzo Cavalieri, Colorado State University
A tale of Hurwitz theory
Hurwitz theory studies covers of algebraic curves by algebraic curves. It has been used as a tool for the study of the geometry of the moduli space of curves, and has appeared in the construction of toy models in string theory. Because of the \"multiple identities\" of algebraic curves (they are geometric objects, but they also are purely algebraic objects if you identify a curve with its field of functions), Hurwitz theory is by nature interdisciplinary.
In this talk I would like to present some aspects of Hurwitz theory, specifically the study of simple and double Hurwitz numbers, the connections to the geometry of the moduli space of curves, and the remarkable combinatorial structure that these numbers have.
This talk is primarily aimed at graduate students.
There will be a light lunch in the Keisler lounge from 1:00-1:30pm.
Posted January 22, 2013
Last modified January 25, 2013
VIGRE@LSU: Student Colloquium Questions or comments?
1:30 pm – 2:30 pm Lockett 237Sylvester's 4-point problem and straight line drawings of the complete graph $K_n$
Abstract: In the 1880's, Sylvester raised the following question: if we pick 4 points at random from the Euclidean plane, what is the probability that they make a convex quadrilateral? Equivalently, what is the probability that one point is inside the triangle formed by the other three? We will make this question more precise in the talk.
A problem in graph theory is to determine, over all sets of $n$ points in the plane, no three collinear, the smallest number $f(n)$ of crossings of the $\binom n2$ straight line segments joining all pairs of these $n$ points. It is easy to see that no crossings are required for $n\le 4$, $f(5)=1$, $f(6)=3$, $f(7)=9$.
In a beautiful paper, Scheinerman and Wilf show that the answer to Sylvester's question is $\lim_{n\to\infty} f(n)/\binom n4$. This will be the main content of this talk.
This talk is primarily aimed at undergraduate students. There will be a light lunch before the talk at 1:00pm in the Keisler Lounge.
Posted January 22, 2013
Last modified January 25, 2013
VIGRE@LSU: Student Colloquium Questions or comments?
3:30 pm – 4:30 pm Lockett 237
Bruce Richter, University of Waterloo
Embedding a Peano continuum in a surface
Abstract: It has been known since the 1930's that a Peano continuum (that is, a connected, compact, metric space) embeds in the sphere if and only if it does not contain the finite graphs $K_{3,3}$ and $K_5$ and two other particular continua $\mathfrak T_1$ and $\mathfrak T_2$. The spaces $\mathfrak T_i$ are closely related to the ``thumbtack space" consisting of a closed disc together with an line segment having one end at the centre of the disc, but otherwise disjoint from the disc. In this talk, we consider the same question for embedding a Peano continuum into a surface (that is, a connected, compact, 2-dimensional manifold).
The main result is that a Peano continuum $C$ embeds in a surface $\Sigma$ unless it contains one of:
1. A finite graph that does not embed in $\\Sigma$;
2. A surface of smaller genus than $\Sigma$;
3. The disjoint union of $\Sigma$ and a point; and
4. The continua $\mathfrak T_1$ and $\mathfrak T_2$.
This talk is primarily aimed at graduate students. There will be refreshments before the talk at 3:00pm in the Keisler Lounge.
Posted March 12, 2013
Last modified March 14, 2013
VIGRE@LSU: Student Colloquium Questions or comments?
12:30 pm – 1:20 pm Lockett 285
Michael Orrison, Harvey Mudd College
Generalizing the Condorcet Criterion
There will be a light lunch in the Keisler lounge from 12:00-12:30.
The Condorcet Criterion is relatively straightforward: In an election, if there is a candidate who would beat every other candidate in a head-to-head race, then that candidate should be declared the winner. In this talk, I\'ll describe a natural family of generalizations of the Condorcet Criterion that led us to some unexpected questions and answers concerning forbidden \"words of generalized Condorcet winners.\" This is joint work with Aaron Meyers, Jen Townsend, Sarah Wolff, and Angela Wu.
This talk is primarily aimed at undergraduate students.
Posted March 12, 2013
Last modified March 14, 2013
VIGRE@LSU: Student Colloquium Questions or comments?
3:30 pm – 4:20 pm Lockett 285
Michael Orrison, Harvey Mudd College
Doubly Adapted Bases for the Symmetric Group
There will be refreshments in the Keisler lounge from 3:00-3:30.
Abstract: Adapted bases play an important computational role in many applications of the representation theory of finite groups. In this talk, I will describe an interesting \"doubly adapted\" (with respect to the usual left action and right action) basis for the regular representation of the symmetric group. I will then explain why we think such bases might be the key to a new approach to creating fast Fourier transforms for finite groups. This is joint work with Mike Hansen and Masanori Koyama.
This talk is primarily aimed at graduate students.
Posted April 17, 2013
Last modified April 19, 2013
VIGRE@LSU: Student Colloquium Questions or comments?
12:30 pm – 1:30 pm Lockett 277
Mihaela Dobrescu, Christopher Newport University
Bee Hives, Pennies, Needles, and Harmonic Analysis - Part I
There will be a light lunch at 12:00 before the talk in the Keisler Lounge.
Analysis problems in general, and harmonic analysis problems in particular can lead to purely geometric problems, while geometric questions are often tackled via analytic methods. In these two talks, we will investigate some older and newer problems, some closed, some still open, in geometrical analysis and their connections with analysis and harmonic analysis, and other branches of mathematics.
This talk is primarily aimed at undergraduates. Prerequisites are only some multivariable calculus and geometric intuition.
Posted April 17, 2013
Last modified April 19, 2013
VIGRE@LSU: Student Colloquium Questions or comments?
3:30 pm – 4:20 pm Lockett 285
Mihaela Dobrescu, Christopher Newport University
Bee Hives, Pennies, Needles, and Harmonic Analysis - Part II
There will be refreshments at 3:00pm before the talk in the Keisler lounge.
Analysis problems in general, and harmonic analysis problems in particular can lead to purely geometric problems, while geometric questions are often tackled via analytic methods. In these two talks, we will investigate some older and newer problems, some closed, some still open, in geometrical analysis and their connections with analysis and harmonic analysis, and other branches of mathematics.
This talk will be primarily aimed at graduate students. However, undergraduates or anyone with a geometrical intuition are encouraged to attend.
Posted October 15, 2013
Last modified September 17, 2021
VIGRE@LSU: Student Colloquium Questions or comments?
12:30 pm – 1:20 pm Lockett 113
Tadeusz Iwaniec, Syracuse University and the University of Helsinki
Harmonic Mappings
There will be a light lunch before the talk from 12:00-12:30 in the Keisler lounge.
This talk is primarily aimed at undergraduate students.
Posted October 15, 2013
Last modified September 17, 2021
VIGRE@LSU: Student Colloquium Questions or comments?
3:30 pm – 4:20 pm Lockett 239
Tadeusz Iwaniec, Syracuse University and the University of Helsinki
p-Harmonic Equation
There will be refreshments in the Keisler lounge from 3:00-3:30 preceding the talk.
This talk is primarily aimed at graduate students.
Posted February 19, 2014
VIGRE@LSU: Student Colloquium Questions or comments?
2:30 pm – 3:20 pm Lockett 285
Satyan Devadoss, Williams College and Stanford University
Packings and partitions
This talk is primarily aimed at undergraduates.
Motivated by Kepler's study of cannonball packing, and Lord Kelvin's study of ether and foam, the quest to understand the packing and partitioning of space have lead to some of the most remarkable ideas in mathematics. We look at these puzzles, in 2D, 3D, and beyond, and show their stunning appearance in nature, architecture, and current unsolved problems.
There will be refreshments at 2:00pm in the Keisler lounge before the talk.
Posted February 19, 2014
VIGRE@LSU: Student Colloquium Questions or comments?
12:30 pm – 1:20 pm Lockett 241
Satyan Devadoss, Williams College and Stanford University
World of particle collisions
This talk is primarily aimed at graduate students.
Configuration spaces are not only fundamental objects in mathematics, but appear in numerous areas such as robot motion planning, DNA sequencing, sensor networks, surface reconstruction, and origami designs. Our story is motivated by the shape of the configuration space of particles moving and colliding on a circle, which is far more complicated than it seems. These novel spaces now appear across a broad spectrum of research, including geometric group theory, combinatorics, phylogenetics, and statistics. The entire talk is heavily infused with visual imagery.
There will a light lunch at noon in the Keisler lounge preceding the talk.
Posted March 24, 2014
VIGRE@LSU: Student Colloquium Questions or comments?
2:30 pm – 3:20 pm Lockett 232
Arkady Berenstein, University of Oregon
Cluster recursions
This talk is primarily aimed at undergraduate students. There will be refreshments in the Keisler lounge at 2:00pm preceding the talk.
In my lecture I will discuss a class of rational recursions that, rather surprisingly, turn out to be integer sequences. For example, the rational recursion
x_{k+1}=(x_k^2+1)/x_{k-1}
with x_1=x_2=1 gives x_3=2, x_4=5, x_5=13, x_6=34, ... (this is a half of the Fibonacci sequence).
The ultimate reason for the integrality is that each x_n is a Laurent polynomial over integers in x_1 and x_2. For instance,
x_5=x_1/x_2^2 + 2/x_1 + 2/(x_1^2 x_2^2) + x_2^4/x_1^3 + 3 x_2^2/x_1^3 + 3 x_2^4/x_1^3 + 1/(x_1^3 x_2^2)
which gives x_5=13 when x_1=x_2=1. This is an example of what cluster recursions are: rational recursions of order n with the property that each member of the sequence is a Laurent polynomial in x_1,...x_n with integer coefficients.
I will provide more examples of \"one-dimensional\" cluster recursions such as
x_{k+1}=(x_k^b+1)/x_{k-1}, where b is a positive integer,
x_{k+1}x_{k-3}=x_k x_{k-2}+x_{k-1}^2 (Somos-4 sequence),
some \"two-dimensional\" recursions like:
x_{i,j+1}x_{i,j-1} = x_{i+1,j}x_{i-1,j} + x_{ij}^2 (Q-system of type A)
and many others. The explanation of the integrality of these sequences and of the underlying Laurent Phenomenon is in the theory of cluster algebras introduced by S. Fomin and A. Zelevinsky in 2001. I will conclude the lecture with appropriate definitions of cluster mutations and will demonstrate how the above examples fit to the general cluster framework.
Posted March 24, 2014
VIGRE@LSU: Student Colloquium Questions or comments?
2:30 pm – 3:20 pm Lockett 232
Arkady Berenstein, University of Oregon
Quantum cluster algebras
This talk is primarily aimed at graduate students. There will be refreshments in the Keisler lounge at 2:00pm preceding the talk.
Cluster algebras have been introduced by Fomin and Zelevinsky in 2001
as an algebraic framework for total positivity and canonical bases in
representations of reductive groups. Now the theory of cluster algebras
is connected to many different areas of mathematics, for example, representation theory of finite dimensional algebras, Poisson geometry and Teichmuller Theory.
The goal of my talk (based on joint work with A. Zelevinsky) is to present the theory of quantum deformations of cluster algebras. While a cluster algebra corresponds to an integer skew-symmetrizable matrix B, its quantum version corresponds to a compatible pair of B with a skew-symmetric matrix Lambda responsible for the q-commutation relations and is, in many respects, a more natural algebraic object.
It turns out that all \"classical\" cluster structures can be carried over
(sometimes conjecturally) to the quantum world. For instance we conjectured 10 years ago that each quantum reductive or Kac-Moody group admits a quantum cluster structure. This has been recenly confirmed by Kenneth Goodearl and Milen Yakimov.
Ultimately, I will explain how to fulfill one of the original goals of the cluster project: construction of the canonical triangular basis in acyclic case.
Posted January 27, 2015
VIGRE@LSU: Student Colloquium Questions or comments?
1:30 pm – 2:20 pm Lockett 136
Thomas Lam, University of Michigan
Enumeration of Young tableaux
This talk is primarily aimed at undergraduates. Young tableaux are natural combinatorial objects that appear in combinatorics, representation theory, and algebraic geometry. I will talk about some old and some newer questions related to counting Young tableaux. These questions are closely related to some natural problems such as: how long is the longest increasing subsequence in a sequence of n random numbers? Refreshments will be served in the Keisler lounge at 1:00 pm.
Posted January 27, 2015
VIGRE@LSU: Student Colloquium Questions or comments?
2:30 pm – 3:20 pm Lockett 136
Thomas Lam, University of Michigan
Electrical networks and group theory
This talk is primarily for advanced undergraduates and graduate students. I will talk about electrical networks consisting only of resistors. These electrical networks satisfy certain \"relations\"; for example, two resistors in series (or two in parallel) can be replaced by a single resistor with a particular resistance. I will discuss an approach to studying electrical networks using generators and relations, where methods from (Lie) group theory might be applied. There will be refreshments in the Keisler Lounge at 2:00 pm
Posted February 4, 2015
VIGRE@LSU: Student Colloquium Questions or comments?
1:30 pm – 2:20 pm Lockett 136
Lihe Wang, University of Iowa
Mathematics, its origin, meaning, and applications
What is behind the common features of modern sciences? What is the driving force behind the modern productivity? What are the methods to discover information within random numbers? In this talk, we will try to present the miracle power of calculus with algebra and geometry and make clear the ubiquitous presence of mathematics throughout the discovery of calculus, linear algebra, and differential equations. A light lunch will be served in the Keisler lounge at 1:00 pm.
Posted February 4, 2015
VIGRE@LSU: Student Colloquium Questions or comments?
2:30 pm – 3:20 pm Lockett 136
Lihe Wang, University of Iowa
Regularity theory for elliptic equations
We will talk about a unified approach to the regularity theory of elliptic and parabolic equations. The introduction of Sobolev spaces, the meaning of embedding theorems, and the geometric and probabilistic meaning of some of the regularity and singularity theory will be discussed. Refreshments will be served in the Keisler lounge at 2:00 pm.
Posted March 3, 2015
Last modified March 4, 2015
VIGRE@LSU: Student Colloquium Questions or comments?
1:30 pm – 2:20 pm Lockett 138
Ben Webster, University of Virginia
Untying knots: topology, DNA, and coloring
I\'m sure you\'ve all seen a very tangled rubber band in your life. You know logically that it must be possible to untangle the band without breaking it but this can be hard to put this knowledge into practice. In fact, if your obnoxious roommate had cut the rubber band, tangled its ends together, and then carefully glued the ends together (isn\'t he always doing stuff like that?), how would you know? Of course, you\'d know you hadn\'t untangled it yet, but you can try every possible way.
Luckily, mathematicians have your back. They\'ve worried precisely this for a century (they can\'t trust their roommates either, apparently). Bacteria have worried about it a lot longer (with isomerase playing the role of the prankster roommate). I\'ll give a basic introduction to the theory of knots and their use in mathematics and biology. In particular, I\'ll show you how to wise up to your roommate\'s tricks (though it may take a while) .
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There will be a light lunch in the Keisler lounge at 1:00 pm.
Posted March 3, 2015
Last modified March 4, 2015
VIGRE@LSU: Student Colloquium Questions or comments?
2:30 pm – 3:40 pm Lockett 138
Ben Webster, University of Virginia
Symmetric Groups and Lie Algebras
I\'ll give an expository talk about the representation theory of symmetric groups over the rational numbers or finite field. While this is a very classical subject, it\'s one which is very rich, and where there is still a lot to say. I\'ll emphasize the connection to the emerging field of categorification, and explain in what sense a Lie algebra acts on the category of representations of S_n (for all n).
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There will be refreshments in the Keisler lounge at 2pm.
Posted March 9, 2015
VIGRE@LSU: Student Colloquium Questions or comments?
1:30 pm – 2:20 pm Lockett 138
Aaron Lauda, University of Southern California
Diagrammatic Algebra
In this talk we will introduce a calculus of planar diagrams that can be used to represent algebraic structures in a wide variety of contexts. We will start by introducing a diagrammatic framework for studying linear algebra. In this framework, familiar notions such as trace and dimension take on a diagrammatic meaning. We will see how the notion of duality transforms algebraic notions into intuitive manipulations of diagrams. Finally, we will see how this diagrammatic reformulation of linear algebra can be used to study invariants of tangled pieces of string (knot theory).
Refreshments will be served in the Keisler lounge at 1:00pm.
Posted March 9, 2015
VIGRE@LSU: Student Colloquium Questions or comments?
1:30 pm – 2:20 pm Lockett 138
Aaron Lauda, University of Southern California
From Ladder Diagrams to Knot Theory
The star of this talk will be an algebraic object called a quantum group. This is an algebraic object closely connected to Lie theory. We will review some basic facts about the representation theory of quantum groups before turning our attention to representations one can construct on certain planar diagrams called \'ladder diagrams\'. Our aim is to provide a hands-on introduction to representation theory by exploring how quantum groups impose structure on these ladder diagrams. Though this example may seem somewhat trivial, we will show that viewing ladder diagrams as representations of quantum groups allows us to construct diagrammatically defined knot invariants in an elementary way. Our aim is to demonstrate that using only the definition of the quantum group and one additional ingredient, one can produce a wealth of diagrammatically defined knot invariants including the Jones polynomial. We do not assume any previous background in topology or Lie theory. Refreshments will be served in the Keisler Lounge at 1pm.
Posted March 13, 2015
Last modified March 19, 2015
VIGRE@LSU: Student Colloquium Questions or comments?
1:30 pm – 2:20 pm Lockett 138
Peter Kuchment, Texas A&M
Tomography, mathematics of seeing invisible
Everyone has heard of CT, MRI, and Ultrasound medical scanners. Not many, though, know that mathematics plays a major role in obtaining the corresponding images. I will introduce basics of the mathematics of tomographic imaging. No prior knowledge of the subject is assumed. Refreshments will be served in the Keisler lounge at 1:00 pm.
Posted March 13, 2015
Last modified March 19, 2015
VIGRE@LSU: Student Colloquium Questions or comments?
2:30 pm – 3:20 pm Lockett 138
Peter Kuchment, Texas A&M
The Nodal Count Mystery
The beautiful nodal patterns of oscillating membranes, usually called by the (incorrect) name Chladny patterns, have been known for several centuries (Galileo, Leonardo, Hooke) and studied in the last hundred years by many leading mathematicians. In spite of that, many properties of these patterns remain a mystery. We will present the history and a recent advance in the area of counting the nodal domains. No prior knowledge of the subject is assumed. Refreshment will be served in the Keisler lounge at 2:00 pm.
Posted March 30, 2015
VIGRE@LSU: Student Colloquium Questions or comments?
1:30 pm – 2:20 am Lockett 235
Congming Li, Colorado State University
The maximum principle-from simple calculus to frontier research
In this talk, we present the following topics:
the calculus of the local maxima,
the maximum principle for partial differential equations, and
the method of moving planes.
We hope to help our students learn the frontier research on the method of moving planes from the very simple characteristics of local maxima:
f\'(x_0) = 0 and f\'\'(x_0) <= 0.
Refreshments will be served in the Keisler lounge at 1:00 pm.
Posted September 25, 2015
Last modified October 26, 2015
VIGRE@LSU: Student Colloquium Questions or comments?
2:30 pm – 3:20 pm Lockett 114
Clayton Shonkwiler, Colorado State University
15 Views of the Hyersphere
Abstract: The usual sphere in 3-dimensional space---meaning a hollow sphere, like a basketball--- is such a simple and familiar object that we don't really need to think about how to visualize it. The corresponding shape in 4-dimensional space, called the hypersphere, is a very natural mathematical object which is also important in general relativity and other areas of physics. Of course, it's a bit harder to visualize without 4-dimensional eyes, but I'll present 15 ways of thinking about the hypersphere which will hopefully make it a little more familiar and understandable. There will be lots of pictures and animations.
A light lunch will be served in the Keisler Lounge at 2:00pm.
Posted September 25, 2015
Last modified October 26, 2015
VIGRE@LSU: Student Colloquium Questions or comments?
3:30 pm – 4:20 pm Lockett 114
Clayton Shonkwiler, Colorado State University
A Geometric Perspective on Ranom Walks with Topological Constraints
Abstract: A random walk in 3-space is a classical object in geometric probability, given by choosing a direction at random, taking a step, and repeating n times. Random walks with topological constraints are collections of random walks which are required to realize the edges of some predetermined multigraph. The simplest nontrivial example is a random polygon, which is just a random walk which is required to form a closed loop.
Since random walks are used to mdoel polymers, random walks with topological constraints give models for polymer conformations with nontrivial topologies. Examples range in complexity from plasmids and viral DNA, which form simple closed loops, to rubbers and gels, which form large networks. Consequently, there is keen interest both in analyzing the geometric probability theory of such walks and in developing fast simulation algorithms.
In this talk I will describe some of the most exciting recent developments in the mathematics of random walks with topological constraints, focusing on the case of random polygons. These developments arise from a purely geometric understanding of the space of possible polygon configurations. Despite being based on rather deep theorems from symplectic/algebraic geometry, this geometric perspective is surprisingly elementary and has already yielded both exact theoretical statements and powerful new algorithms. This includes joint work with Jason Cantarella (University of Georgia) and Tetsuo Deguchi and Erica Uehara (Ochanomizu University, Tokyo).
Refreshments with be served in the Keisler Lounge at 3:00pm.
Posted September 25, 2015
Last modified November 13, 2015
VIGRE@LSU: Student Colloquium Questions or comments?
2:30 pm – 3:20 pm Lockett 134
Mark Goresky, Institute for Advanced Study
A glamorous Hollywood star, a renegade composer, and the mathematical development of spread spectrum communications
Abstract: During World War II Hedy Lamarr, a striking Hollywood actress, together with George Antheil, a radical composer, invented and patented a secret signaling system for the remote control of torpedoes. The ideas in this patent have since developed into one of the ingredients in modern digital wireless communications. The unlikely biography of these two characters, along with some of the more modern developments in wireless communications will be described. <\p><\p> A light lunch will be served in the Keisler Lounge at 2:00pm.
Posted September 25, 2015
Last modified March 2, 2021
VIGRE@LSU: Student Colloquium Questions or comments?
3:30 pm – 4:20 pm Lockett 114
Mark Goresky, Institute for Advanced Study
Modular forms and beyond
Several examples of the spectacular coincidences in number theory that can be "explained" using elliptic curves and modular forms will be described. A plan to find (and prove) higher dimensional generalizations of these phenomena was mapped out 40 years ago by Robert Langlands. Since then, Langlands "program" has occupied the attentions of hundreds of talented mathematicians in what surely must be one of the grandest mathematical gestures in history. Today, much of Langlands' plan is nearing completion, but many mysteries still remain. Some of the ingredients in this vast circle of ideas will be described.
Refreshments will be served in Keisler Lounge at 3:00pm.
Posted January 22, 2016
VIGRE@LSU: Student Colloquium Questions or comments?
2:30 pm – 3:30 pm Lockett 136
Tom Braden, University of Massachusetts, Amherst
Geometry of machines
Abstract:
One interesting kind of space whose geometry we can study is a configuration space: a space whose points represent possible states in a mechanism or other physical system. Navigating along a path inside the space is then represented by motions of the machine. Some quite complicated and high dimensional sdpaces which cannot be visualized directly can be explored very concretely in this way.
I will focus mainly on configuration spaces of planar bar-and-joint machines, which are two-dimensional machines made from rigid bars, hinges, and anchors. Amazingly, a theorem of Kapovich and Milson says roughly that any manifold can appear as (part of) the configuration space of such a machine.
A light lunch will be served in the Keisler Lounge at 2:00pm.
Posted January 22, 2016
VIGRE@LSU: Student Colloquium Questions or comments?
3:00 pm – 3:50 pm Lockett 232
Tom Braden, University of Massachusetts, Amherst
Deformations in topology and algebra
Abstract:
The idea of deformation appears all over mathematics. In its most basic form, one takes an object and fits it into a family of related objects parametrized by some auxiliary variables. When the family varies nicely enough, the entire family can have nicer properties than the original object did.
This talk will present a few interesting settings from topology and algebra in which this idea works nicely. In the realm of topology, the equivariant cohomology ring of a space with a torus action is a deformation of the ordinary cohomology ring. In algebra, one can view polynomial differential operators as a deformation of ordinary polynomial functions, and a useful way to study certain representations of Lie algebras is by deforming the action of a Cartan subalgebra. These ideas will be presented via concrete examples and a minimum of technical machinery.
Refreshments will be served in the Keisler Lounge at 2:30pm.
Posted February 26, 2016
VIGRE@LSU: Student Colloquium Questions or comments?
1:30 pm – 2:20 pm Lockett 114
Sara Billey, University of Washington
Trees, Tanglegrams, and Tangled Chains
Abstract: Tanglegrams are a special class of graphs appearing in applications concerning cospeciation and coevolution in biology and computer science. They are formed by identifying the leaves of two rooted binary trees. We give an explicit formula to count the number of distinct binary rooted tanglegrams with n matched vertices, along with a simple asymptotic formula and an algorithm for choosing a tanglegram uniformly at random. The enumeration formula is then extended to count the number of tangled chains of binary trees of any length. This includes a new formula for the number of binary trees with n leaves. We also give a conjecture for the expected number of cherries in a large randomly chosen binary tree and an extension of this conjecture to other types of trees. This talk is based on recent joint work with Matjaz Konvalinka and Frederick (Erick) Matsen IV posted at http://arxiv.org/abs/1507.04976 .
A light lunch will be served at 1pm.
Posted February 26, 2016
VIGRE@LSU: Student Colloquium Questions or comments?
3:30 pm – 4:20 pm Lockett 114
Sara Billey, University of Washington
Enumeration of Parabolic Double Cosets for Coxeter Groups
Abstract: Parabolic subgroups WI of Coxeter systems (W,S) and their ordinary and double cosets W/WI and WI∖W/WJ appear in many contexts in combinatorics and Lie theory, including the geometry and topology of generalized flag varieties and the symmetry groups of regular polytopes. The set of ordinary cosets wWI, for I⊆S, forms the Coxeter complex of W, and is well-studied. In this talk, we look at a less studied object: the set of all parabolic double cosets WIwWJ for I,J⊆S.
Each double coset can be presented by many different triples (I,w,J). We describe what we call the lex-minimal presentation and prove that there exists a unique such choice for each double coset. Lex-minimal presentations can be enumerated via a finite automaton depending on the Coxeter graph for (W,S).
In particular, we present a formula for the number of parabolic double cosets with a fixed minimal element when W
is the symmetric group Sn. In that case, parabolic subgroups are also known as Young subgroups. Our formula is almost always linear time computable in n, and the formula can be generalized to any Coxeter group.
This talk is based on joint work with Matjaz Konvalinka, T. Kyle Petersen, William Slofstra and Bridget Tenner.
Refreshments will be served at 3pm in the Keisler lounge.
Posted March 8, 2016
VIGRE@LSU: Student Colloquium Questions or comments?
2:30 pm – 3:20 pm Lockett 114
Tadele Mengesha, The University of Tennessee, Knoxville
Integration by parts, local and nonlocal
Abstract:
In this talk, I will review the impact of integration by parts on our understanding of the derivative of rough functions. Once a property of smooth functions, integration by parts can be used as a defining character of regular functions as well as their derivative in the broader sense. As a consequence, a renewed notion of solution to ordinary and partial differential equations, especially those with irregular source term or irregular coefficients can be formulated. I will discuss some frequently used spaces of functions that can be described with the new notion of regularity. Extension of the definition and application of integration by parts to integral equations, also know as, nonlocal equation will be presented.
A light lunch will be served in the Keisler lounge at 2:00 pm
Posted March 8, 2016
VIGRE@LSU: Student Colloquium Questions or comments?
3:30 pm – 4:20 pm Lockett 114
Tadele Mengesha, The University of Tennessee, Knoxville
Averaged directional difference quotients
Abstract: We study averaged directional difference quotients of vector fields and their continuity property over several function spaces. A third order tensor field will be used to distinguish appropriate directions in which slopes are averaged. The averaged directional derivatives will be shown to approximate classical notions of derivatives. We will use this approximation property to characterize vector fields in the space of Sobolev, bounded variation, and bounded deformation functions in a unified way.
Refreshments will be served in the Keisler lounge at 3:00pm
Posted March 31, 2016
VIGRE@LSU: Student Colloquium Questions or comments?
2:30 pm – 3:30 pm Lockett 136
Mark Reeder, Boston College
Understanding the Hypersphere
Abstract: A Hypersphere is a sphere in four dimensions. It controls motion in our three dimensional world. Though we feel the effects of the hypersphere, our brains cannot easily visualize the whole of it. In this talk, Algebra, Geometry and Topology will unite to help us understand the Hypersphere.
A light lunch will be served in Keisler Lounge at 2:00pm.
Posted March 31, 2016
VIGRE@LSU: Student Colloquium Questions or comments?
12:30 pm – 1:30 pm Lockett 136
Mark Reeder, Boston College
From the Hypersphere to E8
Abstract: This talk will be an introduction to compact groups G of continuous symmetries. We will see that Hyperspheres are the bricks in the construction of G, and also that G contains a \"principal hypersphere\" which knows way more than it should about the topology and group theory of G.
Refreshments will be served at 12:00pm in the Keisler Lounge.