# USF Mathematics Colloquium

### Spring 2014

#### Wednesday, April 16, 2014: 3.30-4.30pm in Lo Schiavo 103

#### Wednesday, April 16, 2014: 3.30-4.30pm in Lo Schiavo 103

*Preceded by Math Tea in the hallway outside Lo Schiavo 209, 3pm*

Brian Conrey, American Institute of Mathematics**T itle:** Primes and Zeroes, a Million Dollar Mystery

**Abstract: **More than 150 years ago Riemann proposed a way to understand how the prime numbers are distributed. But still to this day we have not been able to complete Riemann's program. This talk will focus on the colorful history of people and their attempts to prove Riemann's Hypothesis.

**Wednesday, May 7, 2014**

**Wednesday, May 7, 2014**

Pi Mu Epsilon Colloquium

Time and Location to be Announced ** **

Past talks

**Connect the dots!****Henri Picciotto (Urban School, Emeritus)****Wednesday, April 2, 2014****Abstract:**We will explore some interesting problems on a lattice. They cover a wide range. Some lead to a hands-on approach to secondary school topics such as slope, the Pythagorean theorem, and simplifying radicals. Some are currently unsolved and are fun to think about. Some fall somewhere in between.

**Eigenvalues of Toeplitz Matrices****Bin Shao (Univ. of San Francisco)**

Wednesday, March 19, 2014**Abstract:**Problems about abstract eigenvalue distributions, in general, are of interest because of their applications in physics. They are also fascinating from a purely mathematical point of view. A host of mathematicians and physicists have been attracted to such problems since the early 1900’s. In this talk, I will present one of the old and elegant results in this area; namely, a 1917 theorem of Gabor Szego’s which tells how the eigenvalues of Toeplitz matrices are distributed as their size grows to infinity. The purpose of this talk is to present an account of Szego’s result at the level accessible to undergraduates who have had a basic real analysis course or a calculus sequence course, and a basic linear algebra course.

*The Diagonal Harmonics and*n*Capricious Wives*Angela Hicks (Stanford University)Wednesday, March 5, 2014**Abstract:**In 1966, Konheim and Weiss told the mathematical story of*n*dutiful husbands driving down a one way street and parking in the first available space upon receiving the command from their*n*(independently) capricious wives. We will discuss the now famous combinatorial object that results from the story--the parking function--and a few of the reasons for its study. In particular, we'll discuss a space of multivariate polynomials called the diagonal harmonics and their conjectured connection to the parking functions. We'll discuss open problems in the area, and time permitting, a connection to the Catalan numbers. This talk will assume basic familiarity with partial derivatives and some familiarity with linear algebra (especially the concept of dimension of a space) but no deeper background will be assumed.

*Working for a National Laboratory in Operations Research--*

‘The Science of Better’**Carol Meyers**(Lawrence Livermore National Labs)Wednesday, February 19, 2014**Abstract:**Are you curious as to the kind of work that is done at a national laboratory? Have you heard of the field of operations research, or are you interested in learning about it and how it is applied to real problems? In this talk I will describe the kinds of math I use in my job at Lawrence Livermore National Laboratory, as well as giving an introduction to the discipline of operations research. The talk will focus primarily on two projects I have worked on. The first of these involves using optimization techniques to assess policy options for downsizing the US nuclear weapons stockpile.We discuss consolidation of the weapons complex in general, and our implementation of a mixed-integer linear programming model that is currently being used to evaluate policy alternatives. The second topic addresses using supercomputers to help solve energy grid planning problems, based on ongoing work with energy stakeholders in the state of California. With the increased introduction of renewable resources into the grid, planning models must account for increased intermittency of generation, which leads to larger and more complex optimization problems. We demonstrate how such problems can be solved much more quickly via the use of supercomputing.

*Wednesday, December 4***Pi Mu Epsilon Colloquium, featuring USF student research****Title**: Ranking NBA Players Using Linear Algebra**Speaker**: Milica Hadzi-Tanovic (Advisor: Professor Steve Devlin)**Abstract**: We introduce a network structure on NBA players where individuals are connected when they play against each other during a period of time in an NBA game. Using readily available play-by-play data, we give weights to the network edges to allow for head-to-head comparisons between players based on in-game performance. Using this network structure, we formulate and solve a graph diffusion process to produce a ranking of players. We then compare and contrast the diffusion ranking with existing player rankings such as Player Efficiency Rating and Adjusted Plus-Minus, as well as with similar network based ranking systems used in other contexts including the methods of Keener and Colley, and Google PageRank.

**Title**: New Insights into Stock Returns through Clustering**Speakers**: Jared Rohe, Paul Hundal (Advisor: Professor David Uminsky)**Abstract**: Spectral clustering techniques use properties of the spectrum of the similarity matrix of a collection of data in order to reduce the dimen-sionality reduction. We apply spectral clustering techniques promulgated by Shi and Malik (2000), as well as other clustering techniques, to analyze the log-returns of the constituents of the Standard and Poor's 500 Index for the 2007-2013 period. We use two different measures to diagnose the number of clusters that are latent in the collection of stock returns. The resulting clusters are closely aligned with the sectors associated with the two-digit Standard Industrial Classification (SIC) codes maintained by the Occupational Safety and Health Administration.

*Freedom for the Clones***Zvezdelina Stankova (Mills College)****Wednesday, November 13****Abstract:**The talk is based on a famous simple game with pebbles, rumored to have been proposed by a Russian teenager Maxim Kontsievitch for the Moscow Olympiads back in the 1980's. The game can be understood and played by anybody without any technical background. Yet, as we will see during the talk, solving the game will plunge us into the imaginative and creative realm of invariants, geometric series, and questioning whether it is possible to prove that something is impossible, as well as extensions of the game that involve the golden ratio and other problem-solving wonders. Meanwhile, the teenager Maxim grew into a world-famous mathematician, who won the most prestigious math award, the Fields Medal, partly for his research as faculty at UC Berkeley. No technical background is necessary for the talk: just bring your curiosity for the unknown and enthusiasm for discovering beautiful and powerful mathematics.

*An Introduction to the Binomial Options Pricing Model*

Jeff Hamrick (USF)**Wednesday, October 30, 2013****Abstract:**We aim to give an elementary introduction to the binomial options pricing model, which was first developed by Cox, Ross, and Rubinstein in 1979. In the process of pricing a simple contingent claim, we will connect the following ideas: the no-arbitrage condition, discounted risk-neutral expectations, and the replicating portfolio associated with a contingent claim. We will conclude the talk with a set of ideas: the extension of the binomial model to popular continuous-time models in finance, the valuation of exotic options, and the situation of this particular topic in the broader agenda of a typical upper-division elective in mathematical finance. We will also talk about graduate opportunities in mathematical finance (which is, distractingly, also called "financial engineering" or "financial mathematics").

* *

*Chromatic Numbers and Other Geometric Combinatorics Delights*(San Jose State University)

Tatiana Shubin**Wednesday, October 16, 2013****Abstract:**Geometriccombinatorics

(Santa Clara University)*An Introduction to Learning to Rank, with Applications to Predictive Policing*George Mohler**Wednesday, October 2, 2013****Abstract:**In this talk we will give an introduction to "learning to rank" problems that often arise in information retrieval. A learning to rank problem might involve ranking the relevance of urls returned by a search engine or ranking potential movies for a person based upon their user history and demographics. We will discuss some of the basic building blocks of algorithm design such as data munging, constructing base learners, ensemble learning, and then show how these ideas can be applied to ranking crime hotspots in a city.

*A Mathematician Displays Self Knowledge*(Saint Mary’s College)

Jim Sauerberg

Wednesday, September 18, 2013**Abstract:**Completing the sentence "This sentence contains exactly ___ e's, ___ i's, and ___ s's" appears easy, until one realizes that putting "5" into the first blank is correct but not satisfactory, while putting in "five" is satisfactory but incorrect. We will look at the mathematics that arises from trying to find correct and satisfactory completions.

(Santa Clara University)*Generalized Barycentric Coordinates: An Introduction and an Application to Algebraic Geometry*

Corey Irving

Wednesday, September 04, 2013**Abstract:**Barycentric coordinates allow one to express points of a polygon as convex combinations of the vertices. For triangles these coordinates are uniquely defined and well-known. However, for n-gons with n>3, they are not unique and less well-known. These generalized barycentric coordinates are used in a variety of applications ranging from the finite element method in differential equations to computer animation.

For the first part of the talk we discuss various ways to define barycentric coordinates for general n-gons. The second part will focus on one type of barycentric coordinates, Wachspress coordinates, which are rational functions on the polygon, and we examine an algebraic variety they define.

__Past talks (2010–Spring 2013)__

__Past talks (2010–Spring 2013)__