Upcoming events
Wednesday, November 25, 2009 5-7 PM
Reminder: no meeting this week!
RLM 12.104
Just a reminder, there won't be a meeting.
Have a good Thanksgiving!
Saturday, December 5, 2009 12-12 AM
Putnam Exam
Past events
Wednesday, November 18, 2009 5-7 PM
The enigma of the equations of fluid motion: a survey of existence and regularity results by Professor Natasa Pavlovic
RLM 12.104 [poster]
The partial differential equations that describe the most crucial properties of the fluid motion are the Euler equations. They are derived for an incompressible, inviscid fluid with constant density. Some basic questions concerning Euler equations in 3 dimensions are still unanswered. For example, it is an outstanding problem to find out if solutions of the 3D Euler equations form singularities in finite time.
The equations that describe the most fundamental properties of viscous fluids are the Navier-Stokes equations. As with the Euler equations the theory of the Navier-Stokes equations in 3D is far from being complete. The major open problems are global existence, uniqueness and regularity of smooth solutions of the Navier-Stokes equations in 3D.
In this talk we will give a survey of some known results addressing existence and regularity of solutions to these equations.
Thursday, November 12, 2009 8-10 PM
Math Club Movie Night
RLM 12.104
- Thursday November 12th
- 8:30pm (I know it says 8:00 at the top; it's really 8:30
- RLM 12.104
- Donald Duck in Mathmagicland... and more!
Wednesday, November 11, 2009 5-7 PM
Knot Theory - the algebro-geometric way
RLM 12.104 [poster] [notes]
One way to gain insight into the topological structure of hyperbolic knot and link complements is through the existence of essential surfaces; surfaces which when embedded in the knot complement retain all of their topological information. How then does one detect essential surfaces in hyperbolic knot complements? It is through the algebro-geometric object called the character variety. Through discussing hyperbolic knot complements and describing their associated character varieties, the goal of my talk is to explain how topology and algebraic geometry come together.
The opening act for this talk will be Danny Fast fingers preforming my theme song for my character Emie-Lou-the-Math-Guru after Bill Nye the Science Guy.
Wednesday, November 4, 2009 5-7 PM
REU's and Summer Math Programs: an information session on mathematics programs for undergraduates
RLM 12.104 [poster]
Have you ever wondered what research in math is like? Have you ever wanted to know what it is that graduate students spend all of their time doing? If so then a math REU (Research Experience for Undergrads) or math program is a great way to try to spend your summer. This Wednesday, come learn everything you want to know about REU's. We'll have experienced graduate and undergraduate students to relay their knowledge and answer all your questions. Here's a list of REU's.
Some other summer programs include SPWM, PCMI, EDGE and a summer school at Carleton (ask Emily for more information).
Sunday, November 1, 2009 1-3 PM
Volunteers wanted for Math Adventure!
Austin Math Circle is looking for volunteers to help run its Math Adventure -- a day of fun, outdoor math games for local area high school and middle school students. No experience is required; anyone who would enjoy playing games with children on a Sunday afternoon is welcome.
The event will take place on Sunday, November 1st, from 1 PM to 3 PM.
Contact Dave Jensen if you are interested.
Wednesday, October 28, 2009 5-7 PM
Visualizing the Fourth Dimension, from 'Flatland' to 'Sphereland' and Beyond by Professor Thomas Banchoff from Brown University
RLM 12.166 [notes]
"How do mathematicians, artists, and philosophers try to comprehend geometry beyond our third dimension? Modern computer graphics approaches make it possible to see and interact with four-dimensional phenomena in ways never available before. With the aid of computer graphics images and animations I will discuss the 4th dimension.
Monday, October 26, 2009 4-6 PM
"Salvador Dali and the Fourth Dimension: A Mathematician's Personal Reflections" by Professor Thomas Banchoff of Brown University
ART 1.120 [poster]
Professor Thomas Banchoff of Brown University will be giving a lecture next Monday, Oct. 26 at 4:00 in the art building, ART 1.120. (The ART building is located at San Jacinto and 23rd, across from the stadium.)
Salvador Dali was fascinated by science and mathematics, and geometric objects in various dimensions are central to many of his paintings, for example 'Corpus Hypercubicus'. Where did Dali get his mathematical inspirations and how did he incorporate them into his painting? This talk will recount meetings with the artist over a ten year period, and it will be illustrated by computer graphics images and animations.
Professor Banchoff will also be giving a talk to the Math Club on October 28th.
Wednesday, October 21, 2009 5-7 PM
Phylogenetic Supertree Methods: tools for reconstructing the Tree of Life by Dr. Michelle Swenson
RLM 12.104
Estimating the Tree of Life, an evolutionary tree describing how all life evolved from a common ancestor, is one of the major scientific objectives facing modern biologists. This estimation problem is extremely computationally intensive, given that the most accurate methods (e.g., maximum likelihood heuristics) are based upon attempts to solve NP-hard optimization problems. Most computational biologists assume that the only feasible strategy will involve a divide-and-conquer approach where the large taxon set is divided into subsets, trees are estimated on these subsets, and a supertree method is applied to assemble a tree on the entire set of taxa from the smaller "source" trees.
Dr. Michelle Swenson will present supertree methods in a mathematical context, focusing on some theoretical properties of MRP (Matrix Representation with Parsimony), the most popular supertree method, and SuperFine, a new supertree method that outperforms MRP.
A video of Dr. Swenson's talk can be found here
Wednesday, October 21, 2009 5-7 PM
Phylogenetic Supertree Methods: tools for reconstructing the Tree of Life by Dr. Michelle Swenson
RLM 12.104 [poster]
Estimating the Tree of Life, an evolutionary tree describing how all life evolved from a common ancestor, is one of the major scientific objectives facing modern biologists. This estimation problem is extremely computationally intensive, given that the most accurate methods (e.g., maximum likelihood heuristics) are based upon attempts to solve NP-hard optimization problems. Most computational biologists assume that the only feasible strategy will involve a divide-and-conquer approach where the large taxon set is divided into subsets, trees are estimated on these subsets, and a supertree method is applied to assemble a tree on the entire set of taxa from the smaller "source" trees.
Dr. Michelle Swenson will present supertree methods in a mathematical context, focusing on some theoretical properties of MRP (Matrix Representation with Parsimony), the most popular supertree method, and SuperFine, a new supertree method that outperforms MRP.
A video of Dr. Swenson's lecture can be found here
Wednesday, October 14, 2009 5-7 PM
Mobius: The Original Invertebrate* by Nick Rauh
RLM 12.104 [poster]
An introduction to number-theoretic functions and the principle of Mobius inversion. A little group theory, some identities/applications, and a generalization to posets.
* Modern biology would likely classify Mobius as a vertebrate. Were he an invertebrate, even the claim to originality as such would be historically dubious, at best.
Wednesday, October 7, 2009 5-7 PM
Euler, Brouwer, Hopf: Topology by the Numbers, a talk by Dr. Vick
RLM 12.166 [poster] [notes]
We will explore three ways in which integers arise in topology -- the Euler number, the Brouwer degree, and the index of a singularity of a vector field -- and see how the relationships among them tell us important facts about surfaces and manifolds. No prior knowledge of the subject will be assumed.
Tuesday, October 6, 2009 5-7 PM
Pizza and Problem Solving
RLM 10.176
Starting Sept 29, the Putnam practice sessions (5PM on Tuesdays, 10.176 classroom) will include free food.
Putnam registration is due by October 13th.
Professor Sadun is organizing the Putnam exam for UT this year. The exam is on Saturday December 5th.
So if you are interested in taking the exam send an email ASAP with subject: Putnam registration; your name, year and EID.
If you have any questions please email Professor Sadun.
Tuesday, October 6, 2009 4-12 AM
"Salvador Dali and the Fourth Dimension: A Mathematician's Personal Reflections" by Professor Thomas Banchoff of Brown University
ART 1.120
Professor Thomas Banchoff of Brown University will be giving a lecture next Monday, Oct. 26 at 4:00 in the art building, ART 1.120. (The ART building is located at San Jacinto and 23rd, across from the stadium.)
Salvador Dali was fascinated by science and mathematics, and geometric objects in various dimensions are central to many of his paintings, for example 'Corpus Hypercubicus'. Where did Dali get his mathematical inspirations and how did he incorporate them into his painting? This talk will recount meetings with the artist over a ten year period, and it will be illustrated by computer graphics images and animations.
Professor Banchoff will also be giving a talk to the Math Club on October 28th.
Sunday, October 4, 2009 5-7 PM
Google calendar (the date has no meaning)
The Agenda tab has the information
Friday, October 2, 2009 12-1 AM
4-Dimensional Space with Jeff Weeks
RLM 12.104 [poster]
This will be an informal lunch session on 4-dimensional space. Jeff Weeks will start the discussion and then open the floor to questions.
There will be pizza from 11:40-12pm and the talk will start at noon.
Jeff Weeks is a great topologist and an amazing speaker. He has written the book "The Shape of Space", produced a SnapPea, a progam many topopogist use in their research, and programed torus games. As this is during lunch we will have some pizza.
Thursday, October 1, 2009 7-
RTG in Topology Public Lecture: The Shape of Space by Jeff Weeks
Thompson Conference Center 1.110
When we look out on a clear night, the universe seems infinite. Yet
this infinity might be an illusion. During the first half of the
presentation, computer games will introduce the concept of a
“multiconnected universe”. Interactive 3D graphics will then take
the viewer on a tour of several possible shapes for space. Finally,
we'll see how recent satellite data provide tantalizing clues to the
true shape of our universe. The only prerequisites for this talk are
curiosity and imagination. For middle school and high school
students, people interested in astronomy, and all members of the UT
and surrounding communities. Reception to follow.Wednesday, September 30, 2009 5-7 PM
Math Club meeting times update
RLM 12.104
There won't be a Wednesday Math Club this week, instead there will be Jeff Week's awesome talk on Thursday (Oct 1st)! He is also holding a session on Friday. Wednesday, September 23, 2009 5-7 PM
Equivalence Classes in Higher Math by John Meth
RLM 12.104 [poster] [notes]
We first encounter equivalence classes when we use fractions,
but rarely question the fundamental objects we are dealing with. I want to
explore a potpourri of examples of mathematical objects built out of
equivalence classes, and the relationships of these objects to each other.
We will see equivalence classes from most of the main branches of modern
mathematics.
A video of John Meth's talk can be found here
Wednesday, September 16, 2009 5-7 PM
How to Become a Mathematician in Just 5-7 Years
RLM 12.104 [poster] [notes]
Do you want to be a mathematician? Are you interested in going to graduate school? To address questions and concerns like these, we will be having a panel consisting of faculty members and graduate students from UT. We will go over things to think about as a math major, how to apply to graduate school, and we may even warn you about some signs that you may be turning into a mathematician.
Tuesday, September 15, 2009 5-7 PM
Weekly Putnam Problem Solving sessions start this week
RLM 10.176
They will be every Tuesday.
Professor Sadun will be running them.
Tuesday, September 15, 2009 2-4 PM
GRE study session
RLM 12.166
Contact Lucia for more information.
Tuesdays from 2-4 until Oct. 20!!
Book(s) and study material will be provided.
-Location may vary-
Sunday, September 13, 2009 6-8 PM
(Pi)cnic
Eastwoods/Harris Park
Math Club Picnic! There will be awesome food and even more awesome people to meet! Everyone is welcome.Wednesday, September 9, 2009 5-7 PM
Curvature, polyhedra, and modular origami by Professor Sadun
RLM 12.104 [poster] [notes]
What does curvature mean when you have a polygon, or a polyhedron, with corners? In answering this question, we'll see why there are exactly 5 regular (Platonic) polyhedra. Later on, we'll see how to fold variants of these shapes out of square pieces of paper.
A video of Professor Sadun's talk can be found here
Wednesday, September 2, 2009 5-7 PM
Circles, Rings, and Tractors: Clever Cleaving for Finding Formulas
RLM 12.104 [poster] [notes]
How do we discover the formulas for the areas of objects such as circles and annuli and the volumes of solids such as cones, pyramids, and spheres? In each case, an effective strategy involves dividing the object into small pieces and seeing how the small pieces can be re-assembled to produce an object whose volume or area is easier to compute. Some of these methods were devised thousands of years ago and some of them seem to be relatively new.Wednesday, May 6, 2009 5-7 PM
"Arithmetic Geometry: From Circles to Circular Counting" by Adriana Salerno
RLM 12.104
In this talk, I will show you a glimpse of one of the most exciting and accessible facets of research in modern number theory: arithmetic geometry. We will start with a (gentle) introduction to this area of research through some familiar examples. Then we will move on to a not so familiar example where we count solutions of equations mod p. I will end by answering two of the oldest and most mystifying questions in mathematics: how does this work fit into the bigger picture, and who cares?
Wednesday, April 29, 2009 5-7 PM
Student Talks
RLM 12.104
We will have the following talks this week, all given by UT students:
- Storm Search Modeling and the Constant Advection Equation by Nancy OkeudoIn
This talk we will discuss the meteorological background, physics, and numerics the Con-stant Advection equation, which is a simplified version of the 1-dimensional Shallow Water equations. In particular, we will focus on how the 1900 Galveston hurricane led to further study of storm surge modeling, the derivation of the Constant Advection equation, and the basic properties of numerical methods for its approximation.
- RSA: How It's Done by Christy Sheldon
In this talk I will develop background on RSA. After discussing all the elements used to encode a message, I will describe how to then decode the message using Fermat's Little Theorem.
- Folding Symmetries by Gilbert Bernstein
In this talk I will discuss the old mathematical topic of planar symmetries from a fresh point of view. Since at least 1924 (if not as far back as the Egyptians) it has been known that there are only 17 possible types of planar symmetry, sometimes called the Wallpaper groups. We will look at what happens when we "fold" up these wallpaper patterns along their symmetries.
- Erdos' Conjecture on Arithmetic Progressions by Michael Kelly
Arithmetic progressions of natural numbers are sequences whose consecutive terms are equally spaced. Erdos conjectured (still an open problem) that if some very simple data about the "density" of a set in the natural numbers is given, then the set will necessarily contain arithmetic progressions of any finite length. We will introduce these concepts and give a few examples.
- Multiplying Vectors and Determinants by Justin Hilburn
Have you ever wondered why the cross product only works in dimension 3? Or where the formula for the determinant came from? It turns out that both of these questions can be answered by looking at the exterior algebra.
Wednesday, April 22, 2009 5-7 PM
" Expanding graphs" by Matthew Stover
RLM 12.104
Expanders are families of graphs which are `sparse and highly connected'.
Conceptually, they represent very efficient communication networks, where
vertices are well-connected by few edges. However, explicit constructions
of expanders -- especially the `best possible' expanders, called Ramanujan
graphs -- were not found until the 80s. I will explain what expanders are,
then explain the history behind the first constructions, giving an idea of
the wide range of deep mathematical ideas required to build them.Wednesday, April 15, 2009 5-7 PM
"'Am I knotted?' A conversation between Neil Hoffman and Knestor the knot about the Jones polynomial" by Neil Hoffman
RLM 12.104
If you have a knot, one thing you might want to know is if that
knot is actually knotted or if it is the unknot. In the event you have a
knot that can talk back to you, it might just ask if it's knotted. We'll
see how the Jones polynomial can help us give a good partial answer.Wednesday, April 8, 2009 5-7 PM
"Lie groups, Lie algebras, and their "best" metrics: transforming transformation groups" by Dan Knopf
RLM 12.104
TBAThursday, April 2, 2009 5-7 PM
Talk by Professor Reichl
RLM 7.104
Part of the Math and Physics Lecture Series
TBAWednesday, April 1, 2009 5-7 PM
"On billiards and time irreversibility... The birth of Statistical Mathematical Physics" by Professor Gamba
RLM 12.104
Part of the Math and Physics Lecture Series
We will discuss the legacy of Ludwig Boltzmann in the connections between time irreversible stochastic processes and the theory of the Boltzmann Equation in the modeling of probabilistic dynamics of particle interactions modeled by elastic billiards, as well as connections to conservation laws and compressible fluid models.
Thursday, March 26, 2009 5-7 PM
"An Introduction to Anti-de-Sitter Space/Conformal Field Theory Correspondence" by Professor Distler
RLM 7.104
Part of the Math and Physics Lecture Series
TBAWednesday, March 25, 2009 5-7 PM
"An application of quantum field theory to group theory" by Professor Freed
RLM 12.104
Part of the Math and Physics Lecture Series
TBAWednesday, March 11, 2009 5-7 PM
"Enumerative Geometry - Learning to count all over again" by Brian Katz
RLM 12.104
Some of the most exciting mathematics is born from a connection
between two seemingly disparate ideas. For example, enumerative geometry
calls upon the tools of both combinatorics and algebraic geometry, and
each sheds light on the other. In my opinion, the major player in this
partnership is the idea of a moduli space. In this talk, I will flesh out
these claims and use the geometry of a few moduli spaces to answer
enumerative (counting) questions. If time allows, we will also parallel
these ideas for tropical algebraic geometry. Most of my examples will be
very familiar but viewed from a different perspective, so the majority of
the talk will be accessible to any student with a basic understanding of
linear algebra.Wednesday, March 4, 2009 5-7 PM
"Data, and what to do with it" by Martin Blom
RLM 12.104
Science tries to make models for what happens around us based on what
we see. In this talk I will give an introduction to probability and
Bayesian statistics, which is a mathematical framework for quantifying
our belief in different models, and rules for how we should change our
belief as new information becomes available.Wednesday, February 25, 2009 5-7 PM
"Complex Numbers and the Beauty of Mandelbrot Set" by Prof. Daniels
RLM 12.104
Some of the mathematics and properties behind one of the most intricate and
interesting shapes in Complex Analytic Dynamics, The Mandelbrot Set, will be explored in this presentation. Background topics presented will include the Quadratic Map, Orbit Analysis, and properties of The Julia Set in addition to Mandelbrot Set properties. All topics will be introduced from the standpoint of discrete deterministic Chaos. Finally, computer graphics will be used to visually illustrate some of the mathematics discussed including how to “count” and “add” on the Mandelbrot Set.Wednesday, February 18, 2009 5-7 PM
"The Jump to Light Speed" by Prof. Allcock
RLM 12.104
Everyone knows that when your starship jumps to light speed: you see the stars suddenly rush past, so that it looks like an explosion of stars in front of you. But this isn't what actually happens: really, they appear to all rush together in front of you. So it looks like an *implosion* instead. Really this is all about the boundary of hyperbolic 3-space. Find out what this means!Wednesday, February 11, 2009 5-7 PM
"Machines Reasoning about Machines" by Professor J. Moore
RLM 12.166
``Artificial intelligence,'' ``Lisp,'' ``theorem
proving,'' ``program verification,'' ``formal
methods,'' ... these are phrases that conjure up
conflicting images in many people. The basic idea
is this: Since (a) formal mathematical logic can
be used to specify precisely what a computer
program or piece of hardware is supposed to do,
and (b) software can be written to manipulate
formal mathematics to discover and check proofs,
therefore (c) machines can check whether software
and hardware designs do what they're supposed to.
But how realistic is it to specify hardware and
software precisely? Formally? What logic would
you use? How realistic is it to apply AI-based
theorem proving techniques to prove theorems about
hardware and software? Is this a pipe-dream or a
widely used industrial certification method or
something in between? In this talk I'll describe
38 years of work on the subject of applying
mechanized mathematics to hardware and software.
The system I'll discuss is often called ``the
Boyer-Moore theorem prover,'' which is actually a
description of a series of theorem provers for
pure Lisp dating back to 1971, written by Boyer,
Moore, and Kaufmann, and used by such companies as
AMD, IBM, Rockwell-Collins, and others. I'll
describe how we got to this interesting point in
history, where machines are sometimes able to
reason about other machines -- and themselves.Wednesday, February 4, 2009 5-7 PM
"Proof by Pictures: A Tour through Visual Mathematics" by Eric Katerman
RLM 12.104
How do you evert a sphere? What's left once you remove a knot from space? Does every sphere bound a ball in space? We'll watch some amazing videos that will help us answer these questions.
Wednesday, January 28, 2009 5-7 PM
"Quadratic Reciprocity and Weil Reciprocity" by Dr. Jacob Lurie (MIT)
RLM 12.104
I'll begin by reviewing the law of quadratic reciprocity over the ring of
integers, and then explain how it can be generalized to the setting of a
polynomial algebra over a finite field.Wednesday, December 3, 2008 5-7 PM
"Spherical Geometry: Methods and Magic" by Cody Patterson
RLM 12.104
If you passed high school geometry, you're familiar with how distances and
angles "work" in \mathbb{E}^2, the Euclidean plane. But how do these
concepts carry over to the unit sphere \mathbb{S}^2? Can we do trigonometry
on the unit sphere as effortlessly as we can in the Euclidean plane? I'll
show that the answer to this question is yes, and that in fact certain
aspects of spherical trigonometry are even more elegant than their
counterparts in Euclidean trigonometry. If you've ever wanted to know how
to find the area of a spherical polygon, this is the talk for you.Wednesday, November 19, 2008 5-7 PM
"The ABC Theorem and the ABC Conjecture" by Mark Rothlisberger
RLM 12.116
In many ways, the ring of integers is similar to the ring of polynomials over the real numbers. For the purposes of this talk, the main similarity is that both are universal factorization domains. Over the integers, prime numbers play a key role, mirrored in many respects by irreducible polynomials over the integers. We will first prove ABC theorem for polynomials, the main consequence of which is that if two polynomials with zeros of large multiplicity are added together, their sum can not have any zeros of large multiplicity. It is easy enough to formulate a corresponding conjecture over the integers; however the presence of counterexamples forces modifications. Furthermore, the absence of a key tool used in the proof of the ABC theorem means that over the integers, nothing has yet been proved. However, we will discuss the far-reaching implications of the ABC conjecture on other areas of number theory. Finally, I will introduce to you a way that you can help progress towards the solution of this important, yet elusive result at home, even while you're asleep!Wednesday, November 12, 2008 5-7 PM
"Down with sine and cosine!!! How these transcendental functions are holding you back from Geometry of a more Universal variety, and what you can do to stop them" by Sarah Rich
RLM 12.104
The talk will be based on a book called "Divine Proportions". The author
of the book devises a method for doing "rational trigonometry" over any
field, which leads to a concept of geometry over any arbitrary field of
characteristic not equal to two. I will discuss both the foundations and
some of the interesting results of his work, as well as possibly
contemplate its merits and limitations.
Wednesday, November 5, 2008 5-7 PM
"Knots and How to Color Them" by Brandy
RLM 12.104
How do we know when a knot is tricolorable? Namely, given a knot
projection and three colors, can we color each arc of the knot so that at
every crossing the arcs which meet there are either all the same color or
all different colors? After discussing some properties of knots, we will
talk about how to determine when knots are not just tricolorable but also
n-colorable.Wednesday, October 29, 2008 5-7 PM
"A Brief Introduction to the p-adic Numbers" by Keenan Kidwell
RLM 12.104
The set of real numbers is the completion of the set of rational numbers with respect to the familiar notion of distance furnished by the usual "Archimedean" absolute value; intuitively, this means that the reals consist of the rationals together with all the limits of sequences of rationals that ought to converge with respect to this absolute value but which fail to do so because of certain "holes." If p is any rational prime, then the set of p-adic rational numbers is an analogous object obtained by completing the rationals with respect to a different absolute value, the "non-Archimedean" p-adic absolute value, which measures the distance between two rationals based on the p-divisibility of their difference. Despite the fact that the sets of real and p-adic numbers both constitute completions of the rationals, the latter is a much more exotic object, both topologically and algebraically; for instance, every triangle in the p-adic world is isosceles, and any point of a ball is its center. We will encounter these and other peculiarities as we detail the construction of the p-adic numbers and explore some of their most interesting features.Wednesday, October 22, 2008 5-7 PM
"The Mathematics of Cancer Biology" by Nestor
RLM 12.104
This talk has two goals: one is to show how mathematics helps us understand cancer and the other is to present some important ideas from analysis. In the last couple of decades we have seen the emergence of several mathematical models for cancer. These models have drawn inspiration from field is such as classical fluid dynamics. It is the mathematics behind these models that will very likely allow scientists to understand the behavior of tumors at a deeper level. In this way, mathematics will potentially play a role in the development of reliable and effective cancer treatments. After providing some background in biology, I will present a particular model for tumors and explain a few of the techniques behind its study.Wednesday, October 15, 2008 5-7 PM
"Realizability of Polytopes" by Eric Katz
RLM 12.104
Given a polytope (a higher dimensional generalization of a polygon), one can write down the data of the faces and how they fit together. Can such a process be reversed? Given abstract data of faces that satisfy certain axioms, can one reconstruct the polytope or even be sure that one can find a polytope with that face data? This is the realizability question. It turns out that realizability plays host to all sorts of bizarre phenomena. There is face data for which one can find no polytope. There is also face data for which one can only find polytopes whose vertices have irrational coordinates. We will explore such odd behavior and give a method for generating all sorts of weird examples.Wednesday, October 8, 2008 5-7 PM
"Let's Meet at the Euler Characteristic" by Professor Gary Hamrick
RLM 12.104
The Euler Characteristic of surfaces provides a wonderful opportunity to see the interplay of geometry, algebraic topology, and analysis that does not require sophisticated knowledge to grasp. It is actually a very special case of the celebrated Atiyah-Singer Index Theorem, a result that touches on virtually all areas of mathematics.
In the last few decades mathematics has progressed in such a way that its various branches such as algebra, analysis, geometry, and topology are becoming ever more inextricably linked together. An early such development occurred in the 17th century with Descartes' invention of algebraic geometry via his introduction of Cartesian coordinates. But the process has accelerated tremendously in relatively recent times.
A spectacular example in Perelman's proving Thurston's Conjecture relating the geometry and topology of 3-dimensional manifolds by the use of partial differential equations (analysis). A small corollary is the Poincare' Conjecture, one of the $1,000,000 Clay Institute Problems.
Another such example is Andrew Wiles' proof of Fermat's Last Theorem the most famous problem in number theory. What Wiles actually proved was a result in algebraic geometry that had been known to imply Fermat's Last Theorem.
Wednesday, October 1, 2008 5-7 PM
"Surfaces, Tessellations and Hyperbolic Geometry" by Grant Lakeland
RLM 12.104
How does one find the shortest distance, and a path of that distance,
between two points on a torus? How about on other surfaces? In this talk,
I'll explain an answer to the first question involving tessellations of
the Euclidean plane, and how it leads us to study tessellations of the
hyperbolic plane to answer the second.Wednesday, September 24, 2008 5-7 PM
How to Become a Mathematician in Just 5-7 Years
RLM 12.104 [poster]
Do you want to be a mathematician? Are you interested in going to graduate school? To address questions and concerns like these, we will be having a panel consisting of faculty members and graduate students from UT. We will go over things to think about as a math major, how to apply to graduate school, and we may even warn you about some signs that you may be turning into a mathematician.Wednesday, September 17, 2008 5-7 PM
"Mobius inversion and colorings of graphs" by Dr. Nicholas Proudfoot (University of Oregan)
RLM 12.104 [poster]
A proper coloring of a graph is a way to label the vertices such that
adjacent vertices get different labels. (The famous Four Color
Theorem, proven in 1976, says that any graph that can be drawn on a
blackboard without edge crossings admits at least one proper coloring
with at most four different colors.) I'll discuss the beautiful
theorem of Mobius inversion for functions on posets, and explain what
it has to do with coloring graphs.Wednesday, September 10, 2008 5-7 PM
"Discrete Mathematics for Molecular Models", by Andrew Gillette
RLM 12.104 [poster]
A simplistic but useful model of a molecule treats its atoms as filled spheres of fixed radius with fixed relative position in space. In this talk, we will examine some of the discrete math concepts aiding such models, including Voronoi and Delaunay diagrams and their generalization known as power diagrams. If time permits, we will also discuss how such diagrams can be used to identify certain topological properties of the molecule. This talk assumes no background in biology and only a basic comfort with mathematical notions.Thursday, September 4, 2008 5-7 PM
What Is Actuarial Science? by Dr. Mark Maxwell
RLM 12.104
Wednesday, September 3, 2008 5-7 PM
The Pythagorean Theorem, Euclid's Parallel Postulate, and non-Euclidean Geometry by Braxton Collier
RLM 12.104 [poster]
In this talk I will explain a simple, visually intuitive proof of the Pythagorean theorem. Considerations of the ingredients that go into this deceptively simple proof lead to an examination of some basic questions concerning the foundations of geometry, and in particular the validity of Euclid's fifth, "parallel" postulate. Historically, attempts to prove this postulate from Euclid's other axioms led to the discovery of non-Euclidean geometry. Not only does non-Euclidean geometry play a vital role in modern mathematics, but it also features centrally in Einstein's description of gravity as a manifestation of space-time curvature.Wednesday, April 16, 2008 5-7 PM
Breaking the ice: The melting of ice caps and non-linear heat equations
RLM 12.104 [poster]
Wednesday, April 9, 2008 5-7 PM
Abelian Sandpiles and My Favorite Open Math Problem, by Geir Helleloid
RLM 12.104
The abelian sandpile model was invented by physicists to
study physical phenomena like avalanches, but the idea was quickly
co-opted by mathematicians who realized that they could do a lot of
fun mathematics with the model. In fact, playing around with the
model feels like playing a game, so it is sometimes called the
chip-firing game. I'll show you a lot of the math behind the model,
focusing on the group-theoretic aspects. You don't need to know
anything about group theory though; in fact, coming to this talk is a
good way to find out what a group is! Highlights will include crazy
and beautiful fractal-like images and simulations, the entire audience
standing up to physically compute sandpile addition, and my favorite
open math problem.
Wednesday, April 2, 2008 5-7 PM
Public Key Cryptography, by Brendan Younger
RLM 12.104
Public-key cryptography allows people to send encrypted messages to
each other without ever having to get together to share a common
secret. This makes it particularly attractive for performing secure
transactions over the internet or sending super-secret spy messages.
It's also rather intriguing in that it requires a "trap-door"
operation which is very easy to perform in one direction and very
difficult to perform the inverse of. In this talk, I will discuss the
RSA cryptosystem and some of the attacks against it. I will then try
to give an overview of elliptic curve cryptosystems and at least point
out the difficulties in choosing appropriate parameters. If time
permits, I will discuss cryptosystems based on the knapsack problem
and why those have failed.Wednesday, March 26, 2008 5-7 PM
The Music of the Spheres, by Alex Kahle
RLM 12.104
Exotic spheres, infinite spheres, hairy spheres... who the humble sphere had so many surprises?Friday, March 21, 2008 3-4 PM
Dean's Scholars presents computer scientist Ron Graham
ACES 2.302
There is no question that the recent advent of the modern computer has had a dramatic impact on what mathematicians do and on how they do it. However, there is increasing evidence that many apparently simple problems may in fact be forever beyond any conceivable computer attack. In this talk, Dr. Ron Graham will describe a variety of mathematical problems in which computers either have had, may have or will probably never have a significant role in their solutions.
Ron Graham was chief scientist at AT&T Bell Labs before taking a job at the University of California-San Diego in the Computer Science department. Dr. Graham is a former president of the American Mathematical Society. He has also been featured on Ripley's Believe It or Not as a talented mathematician, juggler, and trampolinist while also holding a spot in the Guinness Book of World Records for creating the worlds largest number used in a serious mathematical proof. He has produced over 300 papers, including several with his friend Paul Erdos, and won the annual Steele Prize for lifetime achievement from the American Mathematical Society in 2003. Without a doubt, Ron Graham is one of the world's foremost mathematicians in discrete mathematics.
Wednesday, March 19, 2008 5-7 PM
Tilings: a mathematical model for crystals and quasicrystals, by Natalie Frank
RLM 12.104 [notes]
Crystals are solids that have well-ordered, repeating atomic structures. Tilings of R^2, R^3, or even R^n are mathematical models of this structure. In the laboratory, scientists can measure the diffraction spectrum of a solid by shining x-rays through it. If the material is a crystal, the spectrum will have sharply defined brights spots known as Bragg peaks. Diffraction spectra can also be computed for a tiling, and if it is periodic, the spectrum will show Bragg peaks. Until the 1980's, it was thought that only crystals produce Bragg peaks. It was then that a new form of matter was discovered, one that had Bragg peaks in its spectrum, but could not have the well-ordered atomic structure of a crystal. This form of matter was named quasicrystal. We will discuss some of what is known about quasicrystals and their tiling counterparts.Wednesday, March 12, 2008 5-7 PM
Spring Break
RLM 12.104
No School!Wednesday, March 5, 2008 5-7 PM
Talk by Nick Rauh
RLM 12.104 [notes]
TBAWednesday, February 27, 2008 5-7 PM
Huh? Mathematicians study knots just for the sake of it?, by Emily Landes
RLM 12.104 [poster] [notes]
Take two ropes, loosely tie each into the same knot and fuse together the
two free ends of each strand. Drop both knots on the ground. There, they
each appear as a concoction of over and under crossings. Most likely,
these identical knots will fall differently. Now work backwards. Start
with two 2D concoctions of over and under crossings. When do they
correspond to the same 3D knot? How can we be sure?
The classification of knots involves a search for knot invariants, properties that remain unchanged under three specific perturbations called Reidemeister moves. One such invariant is the Khovanov homology of a knot projection. As the machinery behind this invariant requires significant development, I will use my talk to present the intuitive picture.
Wednesday, February 20, 2008 5-7 PM
The Million-Dollar Question: Is God a Geometer?, by Prof. Lorenzo Sadun
RLM 12.104 [notes]
Yang-Mills Theory is a way to cast fundamental physics in
geometric terms. One of the million-dollar "millenium" problems posted
by the Clay Institute is to rigorously construct a Yang-Mills theory in
4 dimensions and prove some properties about it. I'll go over the
history of geometric constructs in physics, and explain what the
Yang-Mills problem is all about.
Wednesday, February 13, 2008 5-7 PM
What are the possible shapes of space?, by Professor Dan Knopf
RLM 12.104 [poster] [notes]
Manifolds are objects (like curves, surfaces, and our
universe) that look like Euclidean space locally but whose global
picture may be much different. We'll discuss some of what interests
mathematicians when they study the topology and geometry of such
objects. For 2-dimensional manifolds, a strong connection between their
topology and geometry was known since the nineteenth century. For
3-dimensional manifolds, a similar connection has only recently been
verified. We'll talk about this connection and some of the big ideas
behind its proof. For 4-dimensional manifolds, we aren't even sure yet
what the right questions are. Maybe you will study these some day.
Wednesday, February 6, 2008 5-7 PM
Ramsey Theory and Distortion: Is Euclidean geometry inevitable?, by Professor Ted Odell
RLM 12.104 [poster] [notes]
An example of a Ramsey theorem is that if we have 17 red and
blue balls then there are at least 9 red balls or else 9 blue balls.
We will discuss some more dramatic extensions of this theorem and then
move on to different geometries in 2,3,4, or n- dimensional or even
infinite dimensional space. As we shall explain the Ramsey problem in this
setting is "Can you truly distort Euclidean space?"
Wednesday, January 30, 2008 5-7 PM
Confession of a Physicist to Mathematicians, by Professor Cecile DeWitt-Morette
RLM 12.104 [poster] [notes]
Listening to what mathematicians
say is sometimes good and sometimes bad.
Wednesday, January 23, 2008 5-7 PM
Knot Theory and DNA, by Professor Jennifer Mann
RLM 12.104 [poster] [notes]
In our daily lives we encounter tangling and knotting in long, flexible
objects such as extension cords and strings of Christmas tree lights.
Often this knotting is an annoyance, and sometimes it compromises the
function of the cord or string. Knotting also occurs in DNA. We will
discuss the biological consequences of DNA knots and how DNA knots are
resolved.
Wednesday, December 5, 2007 5-7 PM
Beyond Curves and Surfaces by Prof. Dan Freed
RLM 12.104 [poster]
Curves are 1-dimensional and surfaces 2-dimensional. Geometers
study shapes of arbitrary--even infinite--dimension. We will
explore this idea, how such shapes (called manifolds) arise, and
talk about some exciting recent work about 3-dimensional smooth
manifolds.
Wednesday, November 28, 2007 5-7 PM
Movie Night!
RLM 12.166 [poster]
Join us for another mathy movie: ENIGMA, starring Dougray Scott and Kate Winslet.
Wednesday, November 14, 2007 5-7 PM
Group Action for Science Nerds by Brian Katz
RLM 12.104 [poster]
In modern algebra, groups have become a very abstract idea, a
structure worth investigating for its own sake. But this is not how groups
came to be, and it's not how groups are used. Here's how you should think
about groups, and all you need to know to understand this talk:
GROUPS DO THINGS.
The quintessential example of a group is the symmetries of some physical object, the ways to transform the object in space that make it look the same, like rotating a square 90 degrees. In particular, the symmetries of a molecule tell us how it will react to light, and conversely, we can use light to predict the symmetry and shape of molecules (which are way too small to look at). Hopefully this talk will be interesting to both mathematics and chemistry students.
Wednesday, November 7, 2007 5-7 PM
Elliptic Curves: The Curves that keep on giving by Kim Hopkins
RLM 12.104 [poster]
Elliptic curves have been a subject of great interest for mathematicians from the 18th century to present day. They combine algebra, number theory, and geometry in order to address problems such as the congruent number problem, Diophantine equations, and Fermat’s Last Theorem. They also provide a useful approach to public-key cryptography. In this talk we will explain the basics of elliptic curves and explain how they can be applied in the areas described above.
Wednesday, October 31, 2007 5-7 PM
Show and Tell!
RLM 12.104
Today, a few members of the Math Club will show off some nifty mathematical tricks and treats, including mental divisibility tests and non-constructions using a straight-edge and compass. Spooky!Wednesday, October 24, 2007 5-7 PM
Info session: How to Use LaTeX
RLM 12.104 [poster]
Eric and Mark will give a demonstration of how to use LaTeX to produce beautiful mathematical documents. We will also provide a style sheet to get you started.
Wednesday, October 17, 2007 5-7 PM
Annual Women in Mathematics Reception
RLM 12.104 [poster]
Pizza and chocolate of some sort will be served. A group of faculty members and graduate students will talk about career options and choices.
Thursday, October 11, 2007 5-7 PM
Movie Night: {proof}
RLM 4.102 [poster]
Please note the special time/place of this week's Math Club meeting: Thursday night at 5pm in RLM 4.102, we will be watching {proof}, starring Gwyneth Paltrow, Anthony Hopkins, and Jake Gyllenhaal.
Professor Vick will give a brief introduction to the movie, and refreshments will be served before the movie starts. Invite your friends! All undergraduates are invited!
Wednesday, October 3, 2007 5-7 PM
The Mathematics of Juggling by Henry Segerman
RLM 12.104 [poster]
How do you write down a juggling pattern? I'll talk about a system of
notation that partially answers this question, and led to the
discovery of many previously unknown patterns, as well as some
interesting combinatorial problems. There will be many demonstrations.
No prior juggling experience required.
Wednesday, September 26, 2007 5-7 PM
Fixed points and stormy weather by Professor Michael Starbird
RLM 12.104 [poster]
"Somewhere on Earth at this very moment there are two antipodal
points (that is, points directly opposite from one another through the
Earth) where the temperatures are identical and the pressures are also
identical. This meteorological fact follows immediately from the theorem
in topology known as the Borsuk-Ulam Theorem. Also, at this moment there
is a point on the Earth where the wind is not blowing. This other
meteorological fact follows from the Hairy Ball Theorem. We'll see neat
proofs of these and other facts whose primary tool is a wrapping rope."
Michael Starbird is Professor of Mathematics and a University Distinguished Teaching Professor at The University of Texas at Austin. He strives to present higher-level mathematics authentically to students and the general public and to teach thinking strategies that go beyond the mathematics. With those goals in mind, he wrote, with co-author Edward B. Burger, The Heart of Mathematics: An invitation to effective thinking, which won a 2001 Robert W. Hamilton Book Award and which is now used in hundreds of colleges and universities nationally each year. His promises to be an exciting talk!
Wednesday, September 19, 2007 5-7 PM
The Evolution of a Mathematician: To Grad School, and Beyond!
RLM 12.104 [poster]
This week we will have a panel consisting of faculty members and graduate students from UT discussing various topics concerning what it means to become a mathematician. We will go over things to think about as a math major, how to apply to graduate school, and we may even warn you about some signs that you may be turning into a mathematician.
Wednesday, September 12, 2007 5-7 PM
Filters and Social Choice, by David Jensen
RLM 12.104 [poster]
"When a large group of people have to make a decision together, bad things can happen. For example, in a strict plurality election system, it is possible for the majority of people to prefer any other candidate to the one that actually wins the election. It seems, then, that the plurality election system is unfair. What could we do to make it fair? Which election systems are the most fair? What does "fair" mean, anyway? We will consider these questions from a mathematical perspective, and we will discover a surprising answer."
David is a graduate student at UT, and in the past, he has given talks on the mathematics of juggling, nonstandard analysis, and Ramsey theory. This past summer, he was a counselor at Math Camp, where he taught algebraic geometry to high-school students from around the world.