Colloquium Schedule
Fall 2005 Colloquia
- Fejer's Inequality and Nilpotent Operators
Linda Patton, Mathematics Department, Cal Poly
Abstract - Sheafification of Matter, Space and Time
Goro Kato, Mathematics Department, Cal Poly
Abstract
We will focus on the foundations of quantum aspects of matter, space and time by sheafifying matter, space and time as we define the notions of a light cone and the equivalence principle and the general principles of covariance in terms of sheaf and category theories. We will begin with the duality and the EPR-type non-locality (entanglement), and then we will treat various notions with the concept of the category of presheaves over a site. - Paradox of Individuals and Formal Language of Analysis
Todor Todorov, Mathematics Department, Cal Poly
Abstract - Joint Mathematics/Statistics Colloquium
Secretary Problems
Ted Hill, Georgia Tech
Abstract
The subject of this talk will be so-called Secretary Problems, (also known as Marriage, Dowry, or Best-choice Problems), and more generally, Optimal-Stopping Problems. The basic framework is that a sequence of random variables (stock prices, offers on a house, "test scores" for job applicants [eg for a secretarial position]) is being observed, and the objective is to decide when to stop in order to maximize the reward. The classical "no-information" secretary problem and its solution will be reviewed, along with game-theoretic extensions, analogs for "full-information and "partial-information" stopping, a few counterintuitive surprises, and several basic unsolved problems. - An Undergraduate Research Project From Ancient Egypt
Andrew Hetzel, Tennessee Tech University
Abstract
Almost 3,600 years ago, Egyptians made use of expansions of rational numbers of the form 2/n as a sum of distinct so-called "unit fractions", that is, fractions of the form 1/m, where m is a positive integer. Moreover, what mattered to the ancient Egyptians was not that such rational numbers as 2/3 could be expressed as 1/3 + 1/3, but rather that 2/3 could be expressed as 1/2 + 1/6. Since that time, such expansions of positive rational numbers, termed "Ahmes expansions", have attracted considerable attention from the mathematical community and even form an area of active contemporary research. The speaker will talk about some of the history surrounding Ahmes expansions with an emphasis on some recent research in the area with which he has been personally involved. This research had its origins in the speaker's own undergraduate research project seven years ago. Motivated by this fact, the speaker will also discuss opportunities for undergraduates to participate in both formal and informal mathematical research programs.
This talk will be accessible to all undergraduates. Those with knowledge of introductory number theory may have a special appreciation for certain results that will be presented.
Winter 2006 Colloquia
- Filling Cusps and Subgroups: An Interaction
Between Topology, Geometry and Group Theory
Jason Manning, Cal Tech
Abstract
Dehn filling refers to the (topological) process of removing a torus cusp (an end homeomorphic to the product of a torus and a half-open interval) from a non-compact 3-manifold, and replacing it with a solid torus (the product of a disk with a circle). The 2 \pi Theorem of Gromov and Thurston asserts, roughly, that this can usually be done in a geometrically non-destructive way. This theorem can be interpreted and generalized in a number of differential geometric and group theoretic directions. I'll survey some of these, and close by describing some recent work which generalizes the notion of Dehn filling to relatively hyperbolic groups. Some applications to geometric group theory will be described. - The Linear Algebra of Internet Search Algorithms
Leslie Ward, Harvey Mudd College
Abstract
We often want to search the web for information on a given topic. Early web-search algorithms worked by counting up the number of times the words in a query topic appeared on each webpage. If the topic words appeared often on a given page, that page was ranked highly as a source of information on that topic. More recent algorithms rely on Link Analysis. People make judgments about how useful a given page is for a given topic, and they encode these judgments in the hyperlinks they choose to put on their own webpages. Link-analysis algorithms aim to mine the collective wisdom encoded in the resulting network of links. I will discuss the linear algebra that forms the common underpinning of three link-analysis algorithms for web search. I will also present some work on refining one such algorithm, Kleinberg's HITS algorithm. This is joint work with Joel Miller (HMC '00), Greg Rae (HMC '00), Fred Schaefer (HMC '00), Ayman Farahat, and Tom LoFaro. It originated in a Mathematics Clinic project at Harvey Mudd College. - Introduction to Non-Standard Analysis for Non-Logicians
Todor Todorov, Mathematics Department, Cal Poly
Abstract
The non-standard analysis (NSA for short) is a modern rigorous version of the old Leibniz-Euler infinitesimal calculus. It was invented by A. Robinson in the 1960s as a particular application of model theory (a branch of mathematical logic). It has numerous applications in different areas of mathematics, physics and mathematical economics. In this talk I will present an introduction to this theory in the framework of the usual (standard) real analysis and with minimum involvement of mathematical logic (this explains "for non-logicians'' in the title). The talk will be accessible to students who have taken a first course in real analysis. In my discussion I will focus mostly on the reduction of the quantifiers in this theory: NSA uses fewer quantifiers than the standard real analysis. For example, the usual standard definition of a limit of a function includes three (non-commuting) quantifiers. In contrast its non-standard counterpart includes only one quantifier. - The Conjugacy Problem in Dynamical Systems
John Alongi, Mathematics Department, Cal Poly
Abstract
Spring 2006 Colloquia
- Minimal Graded Betti Numbers and Related Observations
Ben Richert, Mathematics Department, Cal Poly
Abstract
It is easy to demonstrate that two non-isomorphic graded quotients of the polynomial ring R = k[x_1, ..., x_n] may have the same Hilbert function. To study how much information the Hilbert function suppresses, we pass to a finer invariant, the graded Betti numbers. The goal is to consider which sets of graded Betti numbers arise if we consider quotients with a fixed Hilbert function. There is a natural partial order on this set, which is is known to have a unique largest element, but which need not have a unique minimal element. The "middle" of this partial order can be studied by adding restraints to the quotients we consider. For instance, we might restrict to quotients with annihilators generated by monomials, or those with a certain self-duality property (Gorenstein quotients). One such restriction is to the quotients whose annihilators are squarefree monomials ideals. In this talk, I will discuss certain results obtained last summer during my NSF REU (for example, the existence of infinite families of partial orders, growing exponentially with degree, for which no unique minimal element exists), as well as considering how the constructions developed in that paper might turn out to be interesting in their own right. - The Power & Pitfalls of Probability
Ted Hill, Cal Poly Research Scholar in Residence
Abstract
During the past 75 years probability theory has blossomed into a powerful mathematical tool. This lecture will describe a few of the surprises and revelations of probability, with concrete real-life examples of strategies that DID beat lotteries and racetracks. On the other hand, common misperceptions about randomness allow casinos to flourish and the IRS to detect fabricated data in tax returns.
Dr. Hill's research in probability theory and fair division has been supported by grants from the Fulbright Commission, the National Science Foundations of the U.S. and the Netherlands, the Israel-U.S. Bi-National Science Foundation, and the German Academy of Sciences. He is currently supported by a research grant through Cal Poly from the National Security Agency. This talk is sponsored by the Robert E. Kennedy Library, the Cal Poly Honors Program, the College of Education, and Research and Graduate Programs. - Creating New Bijections From Old Ones
Tony Mendes, Mathematics Department, Cal Poly
Abstract
Suppose A and B are finite sets with the same number of elements. The relationship between A and B is best understood with an explicit 1-1 and onto function f : A -> B. However, many times it is difficult to find such a bijection. We will describe how to take old, boring bijections and combine them to create new, awesome bijections. Although these techniques are not difficult to understand, they have recently been used to solve open problems in combinatorics. - Special Interdisciplinary Colloquium
Professors Estelle Basor and Abrahim "Rami" Shani
Faculty and staff are invited to attend an interdisciplinary colloquium Wednesday, May 10, to honor the professional and creative work of Professor Estelle Basor, Mathematics Department, and Professor Rami Shani, Management area of the Orfalea College of Business. President Baker and interim provost Bob Detweiler, in association with the Academic Senate Research and Professional Development Committee will host the colloquium, from 3 to 5 p.m. in the Smith Alumni and Conference Center. Basor and Shani were the recipients of the 2005 Distinguished Research, Creative Activity and Professional Development Award. Basor will present "The Delight of Mathematics," Shani will discuss "Sustainable Work Systems: Emerging Challenges." A social hour will follow the presentations. Seating is limited; reservations are encouraged. Call ext. 6-2186 by May 5, or e-mail academicaffairs@calpoly.edu.
Colloquium Flyer - Finite Sections of Operators with Almost Periodic Diagonals
Bernd Silbermann, Technische Universitat Chemnitz, Germany
Abstract - The Limit Length of a Finitely Presented Group
Matthew E. White, Cal Poly
Abstract
In this talk, we will discuss a new object called the limit length of a group. This is a tool for studying the "complexity" of a finitely presented group. We will also look at some conjectures, including that for hyperbolic 3-manifolds the limit length of the fundamental group equals a certain constant multiple of volume. Work done by myself in conjunction with some REU students has shown this to be true for hyperbolic 2-manifolds. I have also proved one half of this conjecture using a theorem of Cooper to provide a lower bound for the limit length in terms of volume. - Beyond Delta-Epsilon:
How Math Majors Thrive in the Real World
Chris Sabbe, Dorado Corporation
Abstract
Ever wonder what you're going to do with your math degree if you're not interested in pursuing graduate school? Concerned the C you received in Math 412 will doom you to a life in the mail room? Ten years ago, questions like these ran through one Cal Poly math major's head. Armed with only a few Putnam exam points and a less than stellar GPA, he marched into the world of business and technology and would journey to places he never would have imagined - from Cape Town to Cairo to Botswana and back.
Ever wonder how to get hired for a job that doesn't require differentiation, linear algebra, or anything resembling that dastardly delta-epsilon proof? Come hear the tales of this math major's struggles to break into the first job interview, the pressures of running a multi-national software implementation, and how all those crazy proofs really do have a profound impact on how you think, work, and succeed in life after college.
Chris Sabbe is a Cal Poly Mathematics graduate. He works at Dorado Corporation in San Mateo, CA. Dorado is the top software company in the mortgage lending industry, serving 5 of the Top 10 banks in the country including Chase, Citibank, and Washington Mutual. - Promoting Equity in Mathematics Classrooms -
Successful Teaching Practices and Their Impact on Student Learning
Jo Boaler, Stanford University
Abstract
The low and inequitable mathematics performance of students in urban American high schools is a critical issue for our times. In this talk I will report the results from a four-year longitudinal study of approximately 700 students as they progressed through three high schools. One of the findings of the study was the incredible success of "Railside" school where students learned more, enjoyed mathematics more and progressed to higher mathematics levels. In the talk I will provide evidence of the students' understanding, show a video of some of the teaching, and provide detailed analyses of the ways that the teachers brought about high and equitable achievement.
2004-2005 Colloquia
2003-2004 Colloquia
2002-2003 Colloquia
2001-2002 Colloquia
2000-2001 Colloquia
1999-2000 Colloquia
1998-1999 Colloquia