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Upcoming Events
All Talks will be at 3:00 in room 117 unless otherwise indicated.
April 10
Tathagata Sengupta
Past Events
September 6
First meeting of the year
Highlights: pizza and soda, of course. The Graduate Student Representatives were introduced: Rachel, Dawn, CJ, and Nate. Besides running this seminar, we attend faculty meetings and try to tell them what we want, and tell grad students what the faculty wants. Speaking of the seminar, you should give a talk! Or you should suggest a topic that you want someone to talk about.
September 20
Picnic!
There will be a Welcome Back cookout this Thursday for math graduate students and faculty. We'll begin cooking by 1:30, food should be available by 2:00 (hopefully sooner). Right now the forecast looks good, if it stays that way the cookout will be held in front of the 1st floor entrance. (If it rains, we'll be outside the second floor entrance.) We will have burgers, chicken, some garden burgers, along with potato salad, macaroni salad, cole slaw, chips, and soda.
October 11
Tathagata Sengupta
Birational geometry
The problem of birational classification of algebraic varieties is ancient: this is a fundamental problem we face in trying to understand algebraic equations. In this talk, we will try and figure out the beauty of one of the most fundamental geometric animals living on the algebraic varieties : the canonical bundle, and will hopefully see whats so "canonical" about it!
This will lead us to canonical models of varieties, and finally we might talk an insignificant bit about finite generation of the canonical ring, which is the crux of the minimal models program we hear everywhere nowadays.
October 18
Dong Wang
Applications of Multivariable
Integration in Multivariate Statistics
I am going to show some integrations techniques under the name "Random Matrix Theory." The only necessary background is Multivariable Calculus (Math 20A).
October 25
Alex Oster
Algebraic Number Theory and
Fermat's Last Theorem
Until the late 19th century, number theory consisted mostly of elementary calculations. Ernst Eduard Kummer was one of the first mathematicians to change this. In 1846, he invented his "ideal numbers", and laid down the foundation for a modern and abstract approach to various number theoretic problems.
This talk introduces the most basic notions and propositions of Algebraic Number Theory (number fields, Dedekind domains, primary decomposition, ideal class group, finiteness of the class number) and uses them to sketch Kummer's proof of Fermat's famous conjecture for regular prime numbers.
November 1
Mark Radosevich
Constructing 3-Manifolds
Progress in low dimensional topology is often accelerated by intelligent use of illustrations. I will attempt to illustrate several topological constructions of low dimensional manifolds, specifically Heegaard splittings, Dehn surgery, handlebodies, and open book decompositions.
November 8
Keefe San Agustin
Dessins d'Enfants
One of the more ambitious programs laid out by Alexander Grothendieck in his Esquisse D'un Programme is the complete characterization of the absolute Galois group over Q via its actions on topological spaces. The jumping-off point for this is the study of dessins d'enfants ("children's drawings") and this talk be an introduction to them.
Dessins are certain types of simple finite graphs drawn on Riemann surfaces - i.e., combinatorial objects that can be explicitly and concretely described. Now two remarkable things happen: each dessin is naturally defined over a number field and the absolute Galois group over Q acts faithfully on the set of dessins! This yields a simple bijection between a certain set of finite graphs and surfaces defined over the algebraic closure of Q. Following this thread of ideas leads to "combinatorial invariants of geometric Galois theory" and I'll try to explain both what is known and what is not in this still mostly unexplored terrain.
Keefe has also pioneered a series of talks on this topic. Contact him for details (syzygy@brandeis.edu).
November 15
Nate Stambaugh
From Special To General Relativity
Traditionally the transition from special relativity (no acceleration) to general relativity (arbitrary accelerations) is made by pretending there is a mass present, and that the presance of the mass causes the space to curve. In this talk, I will derive the Lorentz (length) contraction, and use it to show why an accelerating object would see its space as curved. This will be done using a backdrop of relatavistic circluar motion, and could potentially shed some light on Ehrenfest's Paradox, which is still not fully resolved. Ehrenfest's Paradox asks what will happen to rigid bodies (usually a disk) rotating at relatavistic speeds.
November 29
Dawn Nelson
The Dots and Boxes Game
This is a 2-player pencil and paper game. Begin with a rectangular array of dots (of any size). Take turns drawing vertical or horizontal segments connecting 2 adjacent dots. If a player draws the fourth side of a square the player initials the square and then must draw another segment. The winner is the player with the largest number of initialed squares.
If you come to this talk, I will show you how to beat anyone who doesn't come. Oh, and there may be some discussion of combinatorial game theory.
December 6
Florian Klössinger
The Arithmetic of Dedekind Extensions
Algebraic Number Theory arises mainly from the problem of determining integral solutions of diophantine equations. To do so it is easier to investigate the equations not in Z/ but in a "good" extension of it. To deduce useful information from this one needs to know how this extension behaves aritmetically with respect to Z/. So, a natural question is the following:
In my talk I want to introduce the basic notion of ramification theory in finite extensions and give a short outline of Hilbert's ramification theory.
January 17th and 24th
Keefe San Agustin
A vertex and an edge:
Something from Nothing
In the past ten years, there has been a flurry of results relating to the graph with one vertex and one edge. I'll give an over-view of what I know about this graph. No prior knowledge of Hall algebras, coherent or perverse sheaves, Kac-Moody Lie algebras, quantum groups, elliptic curves, or Calabi-Yau categories will be assumed, although by the end of the second talk I hope to convey some sense of how these topics are all related and why there is still a lot to be learned from such simple objects as finite graphs.
February 28
Aminul Huq
Dyck Paths and Counting
March 6 & 13
Matt Graham
Topos Theory