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Mathematics Department Talks 2013









MATH DEPARTMENT TALKS

2013

January 23rd, 3 pm, JMH 406
Math Club Talk
On the History of Number Theory
Dr. Michael Volpato (to be followed by a couple more talks)


January 30th, 3pm JMH 406
Math Club and FCRH Science Education Initiative talk on "Optimal Pentagonal Tilings"
Dr. Frank Morgan, Atwell Professor of Mathematics, Williams College
 
Abstract: Hales proved that the least perimeter way to tile the plane with unit areas is by regular hexagons. What is the least perimeter way to tile the plane with unit area pentagons? We will discuss some new results, examples, and open questions, including work by undergraduates.


The talk will be followed by a discussion on Undergraduate research experience at Williams College.


February 6, 3 pm, JMH 406
Math Club Talk
On the History of Number Theory II
Dr. Michael Volpato

Abstract: In this continuation talk, we delve into the history of elliptic curves. Taking our cue from Pierre de Fermat, who observed that integers which are the areas of rational right-triangles (i.e. "congruent   numbers") correspond exactly to points with rational coordinates on a certain elliptic curve first considered by Diophantus of Alexandria. We will see how Sir Isaac Newton, with his fledgling calculus, was able to create new rational points on an elliptic curve from old ones --- in a way very reminicent of how Diophantus found rational points on a circle! And how Norweigian mathematician Niels Henrik Abel, while  attempting to solve an integral with irrational denominator, showed how to take any two rational points on an elliptic curve and develop a third. Leading British mathematician Louis Mordell to prove (using ermat's method of infinite descent) that the rational points on an elliptic curve can all be generated (via the geometric methods of Newton and Abel) from a finite set of points. Understanding this finite set of generators of rational points on an elliptic curve still occupies much modern number-theoretic research! 


February 13, 3 pm, JMH 406
Math Club Talk
On the History of Number Theory III
Dr. Michael Volpato




February 27th
Math Dept/Math Club talk on " Hyperbolic Geometry, Toll Booths and Mathematics Education Reform"
Dr. Jane Gilman, Rutgers University


Abstract: We discuss some methods used in Mathematics Education Reform in undergraduate and graduate level courses. This includes a discussion of team teaching and using hands on constructions. We will demonstrate this with so called Hyperbolic Paper and explain the connection between Non-Euclidean Geometry and the world of borders between countries and tariffs. The speaker will chair a question and answer session about NSF programs for faculty and students at all levels engaged in either research or teaching.
1) Report on Geometry and the Imagination, CBMS Issues in Mathematics Education, 3,AMS, Providence, Rhode Island, (1993), 131-135. http://andromeda.rutgers.edu/~gilman/publications/46_Report.pdf.
2) Report on MSRI 1994 Summer Workshop on Hyperbolic Geometry and Dynamical Systems, (with D.B.A. Epstein and W.P. Thurston), Notices of the AMS 42 (12), (1995) 1520-1527 http://andromeda.rutgers.edu/~gilman/publications/48_MSRI.pdf


April 3, 3 pm, JMH 406
Math Club Talk
Title: Using representation theory to win a Nobel prize
Speaker: Dr. Jeff Breeding II

Abstract: Murray Gell-Mann noticed that when baryons and mesons were organized into octets they possessed a symmetry that looked similar to the representation theory of the Lie algebra su(3). If the representation theory of su(3) really did describe this symmetry, there should be another particle, which was previously unobserved, having certain properties predicted by this su(3) model. Gell-Man predicted the existence of this particle in 1962. In 1964, a particle that closely matched his predictions was discovered. This led to the theory of quarks and Gell-Man won the Nobel Prize in Physics in 1969 for his work in particle physics.


April 18, 1 pm, JMH 406
Math Club Talk
Title: Prime factorization, complex analysis, and applications to
arithmetic geometry
Speaker: Dr. Jim Brown, Clemson University

Abstract: Given a positive integer n, one knows from grade school that there is a unique prime factorization of n. However, in more general rings determining when one has unique factorization is a very difficult problem. As there are cases when one cannot factor elements uniquely into primes (try 6 in Z[\sqrt{-5}]), one would also like some way to measure how far away from having unique factorization a ring is. The class group of a ring is a group that measures the failure of unique factorization. We will discuss some results about the class group that relate back to Fermat's last theorem, before moving on to more delicate results on divisibility of class groups. We will use the case of class groups of number fields to motivate more general results dealing with modular forms and Galois representations. 


September 18, 3 pm, JMH 406
Math Club Talk
Title: Putnam Competition Information Session
Speaker: Dr. Jeff Breeding, Fordham University


Abstract: The William Lowell Putnam Mathematical Competition is an annual contest for college students established in 1938 in memory of its namesake.  The problems on the Putnam can be solved using only basic college level mathematics. This is a problem-solving exam, not an exam that tests for an encyclopedic knowledge of mathematics.

Each year on the first Saturday in December, over 2000 students spend 6 hours (in two sittings) trying to solve 12 problems. Individual and team winners (and their schools, in the latter case) get some money and some prestige. This year, the competition will be held on Saturday, December 7th.

In this information session, we will talk about how to register for the Putnam and how to get involved with Fordham's Putnam team and seminar.


September 25, 3 pm, JMH 406
Math Club Talk
Title: Undergraduate Research in Mathematics at Fordham
Speaker: Dr. Rolf Ryham, Fordham University


Abstract: Dr. Ryham will talk about how to get involved with undergraduate research in  Mathematics at Fordham. His students from this past summer will present their research at the end of the talk.


October 2, 3 pm, JMH 406
Math Club Talk
Title: Can you play a fair game of craps with a loaded pair of dice?, or What do the numbers 143 and 603 have in common?
Speaker: Dr. Ian Morrison, Fordham University


Abstract: This talk will recount the story of my work with Dr. Swinarski over the past year on the first question in the title. Most of the mathematics will be elementary and the talk will be accessible to students at all levels and even some faculty. My main goal is to illustrate how mathematical research projects evolve and to use our work to point out some strategies that are often useful in tackling them. Along the way, we'll learn a bit about the game of craps itself and touch on ideas from probability, geometry, algebra, number theory and combinatorics. The talk will conclude by answering the second question in the title by stating some elementary but mysterious open problems that Dr Swinarski and I invite you to work on.

October 16, 3 pm, JMH 406
Math Club Talk
Title: TBA
Speaker: Dr. Michael Volpato, Fordham University

Abstract: TBA


October 16, 4 pm, JMH 406
Math Club Talk
Title: Mathematica 9
Speaker: Andy Dorsett, Wolfram

Abstract: This talk will highlight new features of Mathematica 9, how
easy it is to get started with Mathematica, and subject-specific
applications with Mathematica in courses and research.


October 23, 3 pm, JMH 406
Math Club Talk
Title: Algebra, Computers, and Data: A summary in three acts
Speaker: Dr. Abe Smith, Fordham University

Abstract:  We all know that algebra and analysis apply as powerful
tools in the physical world of mechanics, but it is shocking how deep
of a role algebra and analysis play in the ephemeral world of virtual
online communication.  In this talk, I'll focus on three essential
algebraic ideas---equality, addition, and reflexivity---to examine
some of the key tools (and open problems) in computer science.

October 30, 2:45pm, JMH 406
Math Club Talk
Title: Heard on the Street: Brainteasers from Wall Street Interviews
Speaker: Dr. David Swinarski, Fordham University


Abstract: In this talk (titled after Tim Crack's popular book of the
same name), I'll discuss several short questions that I was asked when
I interviewed for internships in quantitative finance.  The questions
are puzzle-like in nature, and are accessible even to students who
have not taken probability or calculus.


November 13, 3:00pm, JMH 406
Math Club Talk
Title: Monsters and moonshine
Speaker: Dr. Jeff Breeding

Abstract: The classification of finite simple groups is one of the greatest achievements in group theory. By the Jordan-Hölder Theorem, finite groups can be decomposed uniquely into finite simple groups. So it is natural to ask for a complete classification of all finite simple groups. This allows us to understand the structure of all finite groups. The classification and proof of the classification occurred (mostly) in the years 1955--2004. Many mathematicians worked on this problem and their work is spread among many papers. Collected together, the proof of this result is estimated to be around 15000 pages! In this talk, we will review the history of the classification and describe a surprising connection of largest finite simple group, called the Monster group, to modular forms. 
 
 
December 4, 3:00pm, JMH 406
Math Club Talk
Title: A Blueprint for the Information Age
Speaker: Lihan Yao, Fordham University
 
Abstract: Claude Shannon’s 1948 landmark paper “A Mathematical Theory of Communication” binds previously disparate communication systems, such as the telegraph, AM Radio, television and telephone into a single theory of information. He presents the concept of information independent from a message’s meaning, as definite quantities based on physical considerations. With this new perspective, modeling information generation and understanding its transmission limitations is achieved. This talk focuses on discrete information and culminates in the Fundamental Theorem for a Discrete Channel with Noise.
 



MORE MATH TALKS COMING SHORTLY

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