Abstract:
Most mathematicians have heard of the sieve of Erastosthenes, but over the years, sieve methods have developed into a much larger area of research. I will give a brief introduction to sieve methods, specifically Selberg's sieve. Then we will use the sieve to prove that the sum of 1/p for p a twin prime is finite.
Friday, November 6th
Vidit Nandi, Rutgers University
"TBA"
Time: 1:40 PM
Location: Hill Grad Student Lounge
Friday, October 30th
Michael de Freitas , Rutgers University
"Uniqueness and Non-Uniqueness for Solutions to Ordinary Differential Equations"
Time: 1:40 PM
Location: Hill Grad Student Lounge
Abstract:
The first talk in the series "Indistinguishable Lectures in Analysis" is about the infamous Theorem of Existence and Uniqueness of Solutions for Ordinary Differential Equations. A typical statement would be that if f(x,y) is Lipschitz with respect to y then local existence and uniqueness of a solution would be guaranteed for the differential equation y' = f(x,y). Now does Lipschitz with respect to x alone also imply uniqueness for y' = f(x,y)? There are two possible answers to this question, depending on who you ask. Some people would say "no", while others would say "I don't care". Both are right. However the answer could turn to yes with surprisingly little added to the hypothesis, and it's remarkable that such a simple argument remained unnoticed until just about ten years ago. Some examples of nonuniqueness and its implications are also discussed.
Friday, October 23rd
Emilie Hogan, Rutgers University
"TBA"
Time: 1:40 PM
Location: Hill Grad Student Lounge
Abstract: TBA
Friday, October 16th
Arran Hamm, Rutgers University
"Borsuk, Ulam, and Combinatorics"
Time: 1:40 PM
Location: Hill Grad Student Lounge
Abstract:
The Borsuk-Ulam Theorem is a powerful topological theorem with no fewer than 6 statements. This talk will discuss applications of it to a couple of combinatorial problems. The first is the 'Thieves' Necklace Problem' where two thieves steal a necklace and attempt to divide the spoils in a fair way. The second is finding the chromatic number of the an infinite family of graphs called the Kneser graphs.
Friday, October 9th
Andrew Baxter, Rutgers University
"An Invitation to Permutation Patterns"
Time: 1:40 PM
Location: Hill Grad Student Lounge
Abstract: The talk will serve as a whirlwind tour of a very active subfield of combinatorics. Questions regarding permutation patterns have been considered since the 1980's, and the well of problems shows no signs of drying up soon. We will start with the basic definitions and varying viewpoints of the subject, move on to some of the cuter enumeration results, and finish with its connections to sorting algorithms (e.g. how hard is it to sort with a forklift).
Friday, October 2nd
Susan Durst, Rutgers University
"Bidding Games"
Time: 1:40 PM
Location: Hill Grad Student Lounge
Abstract:
Tic-tac-toe almost always ends in a tie. Everybody knows how the game works. It's played out. It's boring. But with a little tweaking, it can become an interesting game again. In bidding tic-tac-toe, the players don't take turns. Instead, they each have a number of bidding tokens, and bid for the right to move. In this talk, we'll discuss the structure and strategy of bidding games--how to turn any turn-based game into a bidding game, and how to calculate the optimal bids for finite bidding games.
Friday, September 25th
Chris Woodward, Amy Cohen, John Bryk, Rutgers University
"Career Development and Job Market"
Time: 1:40 PM
Location: Hill Grad Student Lounge
Abstract: [Panel Discussion] Professors and a recent graduate will discuss various aspects of getting ready for the job market, and
the different opportunities available. The discussion is meant for all students, not just for those applying this year.
Friday, September 18th
Bobby DeMarco Esq., Rutgers University
"Grasshoppers jumping over mines: A fun problem from the IMO and a look at mathematical blogging"
Time: 1:40 PM
Location: Hill Grad Student Lounge
Abstract: We will look at a problem from this past year's IMO (International Math Olympiad) about grasshoppers jumping over mines which was noted for its difficulty, with only a few of the 500 participants solving it. The problem is interesting not just because it is hard, nor because it has multiple pretty solutions which we will review, but also because of its connections to the world of mathematical blogging and polymath. Yay!
Friday, September 11th
Dan Staley, Rutgers University
"The Word Problem"
Time: 1:40 PM
Location: Hill Grad Student Lounge
Abstract: The word problem isn't what everybody used to hate back in fifth grade, but rather an interesting problem in group theory about when a word represents the identity element of a group. I'll talk about the word problem, it's history, and solutions for some types of groups. I'll also talk about group presentations in general, and, being a geometric group theorist, I'll discuss ways to visualize generators, relations, and cancellations.
This page was last updated on September 16, 2009 at 12:37 pm and is maintained by webmaster@math.rutgers.edu.
