The Graduate Student Seminar is put on by the Mathematics Graduate Student Association . GSS meets approximately every other Monday.
All talks are at 4:15 in HH231 (Fall)/ HH229 (Spring) unless otherwise noted.
To volunteer to give a talk, or for anything else regarding the seminar, contact Justin Hilyard.
|Monday, September 3||Juan Migliore||A modern algebraic view of a classical geometric result|
|Monday, September 17||Martha Precup||The Geometry of Hessenberg Varieties|
|Monday, October 1||Melissa Davidson||Where did THAT come from?|
|Monday, October 22||Quinn Culver||The Recursion Theorem|
|Monday, November 5||Joshua Lioi||When Zombies Attack!|
|Monday, November 19||Victor OcasioGonzalez||Classic Nintendo games are (NP-) Hard|
|Monday, December 3||N/A||N/A|
|Monday, January 28||John Harvey||The classification of G-spaces, with a new Slice Theorem|
|Monday, February 11||Brian Shourd||Applications of Category Theory to Functional Programming|
|Monday, March 4||N/A||N/A|
|Monday, March 18||Alexander Diaz||Representations of Coxeter Groups and Hecke Algebras|
|Monday, April 8||Santosh Kandel||Infinite determinants of Hilbert space operators|
|Monday, April 29||John Holmes||N/A|
Pascal's theorem says that if a hexagon is inscribed in a conic, the three points of intersection of pairs of opposite sides of the hexagon are collinear. This turns out, in the end, to be a simple but surprising application of a modern algebraic theory (liaison theory). We'll start off looking at how many points we expect two plane curves to meet in, look at a result about cubic curves commonly called the Cayley-Bacharach theorem but actually due to Chasles, and then apply this to Pascal's situation. Then we'll see how Chasles' theorem is a special case of "the Hilbert function for linked sets of points," and see that results of that sort are easy to obtain.
Lie theoretic tools can be used to answer geometric questions about Hessenberg varieties, a family of subvarieties of the flag variety associated to an algebraic group G. We will show that structure of these varieties, including some open questions about connectedness, singularities, and irreducible components, is related to the root space decomposition of the Lie algebra 𝔤 corresponding to G.
Have you ever looked at a theorem or equation and wondered how on earth somebody ever thought of it? Today's your lucky day! We will trace the history of a specific solitary wave equation. Starting from the deep depths of time, we will travel through the eras and meet Pythagorus, Euler, and many others. Our journey will end with the Ostrovsky equation. This talk assumes you know how to spell your first name on a math exam. No other math is required.
Behold ye! I am the self-referentialator,
Empowering would-be quine creators.
Proof simplificator, mystificator.
I am the virus propagator,
The vanguard of the supreme trick logical,
The point-fixer of all functions computable.
Lean upon me for intelligence artificial,
And as a bulwark against escapes diagonal.
I, too, charge you that you make preparation
to be worthy to meet me, by your creation
in any language of a computation
that outputs its own instructions.
Though a fine messenger Q. might be,
This lecture stems from me, is of me.
Nay! I'm neither Turing nor Kleene,
Though they are both patres mihi.
The impending zombie apocalypse has been well documented in film, television, books, and video games. If we are to survive, we will need to be prepared. How better to prepare ourselves than with mathematics? Differential equations are a useful tool in the realm of applied mathematics. They can be used to study the spread of disease in a population, and might be our best hope for determining a strategy for dealing with this undead threat.
What does an mushroom-loving Italian plumber, a banana-hoarding ape, young swordsman clad in green tunic, a female space bounty hunter, and wandering teenager with a pocket full of monsters have in common? They've all had (NP-) hard lives! Join me as I navigate through computer science jargon and discover how to make our heroes lives just a little bit more difficult. My only assumption is that you're cool enough to know what the previous references are for!
The theory of classifying spaces for principal G-bundles is very widely known, but it seems that Palais' construction of classifying spaces for more general G-spaces is not so familiar to many mathematicians. In this talk, I will explain Palais' classifying theory, demonstrate a minor refinement, and apply it to prove a new and useful form of the Slice Theorem in the context of Alexandrov geometry.
In this talk, I will discuss some of the ways that category theory can be applied to programming, specifically to functional programming using the language Haskell. No prior knowledge of functional programming (or really of programming at all) is required or expected. We'll discuss how functors, monoids, and monads (what's a monad?) can be used to create and reason about purely functional code. "Abstract Nonsense?" - nonsense!
In the 1980's, David Kazhdan and George Lusztig were looking to decompose a complicated space of functions into irreducible representations of a group. In that quest, they found that this is equivalent to decomposing the regular representations of Hecke algebras. In this talk, I will construct such algebras and talk about all of the things they stumbled across in their mission (including the Kazhdan-Lusztig polynomials). My only assumption is that you took a basic algebra course.
I'll talk about a way to generalize the determinant of operators in finite dimensional Hilbert spaces to the determinant of operator on infinite dimensional Hilbert spaces. I will also talk about a regularized determinant of a class of operators and depending on the time constraint I'll give a quick application these regularized determinants.