Colloquium and Seminar Schedule
The Mathematics Department colloquium series is usually held on Fridays from 4:10 - 5:00 p.m. throughout the quarter in Science North Building 53, Room 201. Refreshments are served before the colloquium from 3:30 - 4:00 p.m. in the Math Department Conference Room, 25-208B. All interested faculty, staff, students and visitors are welcome to join us and meet the speaker before the colloquium.
We also have colloquia on topics of particular interest to undergraduates during the quarter. These are scheduled on Thursdays from 11:10 - 12:00 noon, and the location varies. Check the posted flyers or this website for specific location. Refreshments are provided at the colloquia.
Please contact Francesca Fairbrother for more details.
Seminar Schedule
- Applied Mathematics Seminar
Anyone interested is welcome to attend. Please check link for meeting time/place and topic. - Geometry-Topology
Seminar
Anyone interested is welcome to attend. Please check link for meeting time/place and topic. - Operator Theory Seminar
Mondays, 11:10 a.m. - 12:00 noon in 25-208B.
Spring 2008 Colloquia
- Strengthening American Mathematics Education
and the Role of the University Mathematics Department
Speaker
Uri Treisman, University of Texas, Austin
Time
Friday, April 11, 2008, 4:10 - 5:00 p.m.
Place
Fisher Science 33, Room 286
Abstract
Professor Treisman will discuss ways in which the Dana Center, a component of the Mathematics Department at The University of Texas at Austin, works to strengthen mathematics education in Texas and across the nation. In particular, Professor Treisman will describe a series of new studies on the nature of innovation and mathematics teaching and learning.
About the Speaker
Philip "Uri" Treisman is professor of mathematics and of public affairs at the University of Texas at Austin. He is the founder and executive director of the Charles A. Dana Center, an organized research unit in the University's College of Natural Sciences. Uri chairs the steering committee of the Urban Mathematics Leadership Network--a coalition of 19 large urban districts seeking to improve PreK-12 mathematics teaching and learning. He is a member of the leadership team and chair of the design team of the Strategic Education Research Partnership, which is focused on creating new knowledge to solve urgent problems of American education. He is a founding board member of the National Center for Public Policy in Higher Education, a board member of the New Teacher Project, and an active advisor to many non-profit organizations committed to improving American education. He serves as an advisor to the Aspen Institute's Urban Superintendents Network and as a critical friend to many urban and state education leaders. He serves on the National Advisory Board of the Military Child Education Coalition (MCEC) and has served as Chief Juror for a Department of Defense-sponsored study of mobility in military families and its effects on education. From 1995 to 2004 he served as president of the board of the Consortium for Mathematics and its Applications (COMAP). From 2003 to 2007, he chaired the Chancellor's Advisory Panel for Mathematics in New York City.
Uri serves as advisor to the trustees of the Robert N. Noyce and Charles A Dana Foundations. He is active in creating support structures for volunteer-based and community-based organizations. He served as the vice-chair of the Governor's Commission for Volunteerism and Community Service under Texas Governor Richards and Governor Bush.
For his work on nurturing minority student high achievement in mathematics, he was named a MacArthur Fellow in 1992. In December 1999, he was named one of the outstanding leaders of higher education in the 20th century by the magazine Black Issues In Higher Education. In February 2006 he was named "2006 Scientist of the Year" by the Harvard Foundation of Harvard University for his outstanding contributions to mathematics. In all his work, he is an advocate for equity and excellence in education for all children. - Hadamard Products and Composition Operator Norms
Speaker
Linda Patton, Cal Poly
Time
Friday, April 25, 2008, 4:10 - 5:00 p.m.
Place
Science Building 52, Room A12
Abstract - Traveling Waves in a Viscoelastic Generalization of Burgers' Equation
Speaker
Jon Jacobsen, Harvey Mudd
Time
Friday, May 9, 2008, 4:10 - 5:00 p.m.
Place
Science North Building 53, Room 202
Abstract
We consider traveling wave phenomena for a viscoelastic generalization of Burgers equation. For asymptotically constant velocity profiles we find three classes of solutions corresponding to smooth wave solutions, piecewise smooth shock solutions, and piecewise constant shock solutions. Each solution type is possible for a given pair of asymptotic limits and we characterize the dynamics in terms of the relaxation time and polymer viscosity.
20 years ago this Fall Jon Jacobsen entered Cal Poly expecting to become a high school math teacher. - The Riemann Hypothesis
Speaker
Brian Conrey, Director of the American Institute of Mathematics
Time
Thursday, May 22, 2008, 11:10 a.m. - 12:00 p.m.
Place
Science North Building 53, Room 202
Abstract
The famous Riemann Hypothesis is nearly 150 years old. It was on Hilbert's list of 23 problems in 1900 and now it is on the Clay list of Millennial Problems, and has a one million dollar reward for its solution. Many people regard it as the most important unsolved problem in all of mathematics. In this talk we will explain exactly what the Riemann Hypothesis is and give some of the colorful history that has grown up around efforts to solve it.
Winter 2008 Colloquia
- Middle School Teachers' Formative Use of a Feedback Guide
Speaker
Jessica Strowbridge, Oregon State University
Time
Tuesday, January 8, 2007, 11:10 a.m. - 12:00 noon
Place
Science North Building 53, Room 202
Abstract
As part of a professional development program focused on mathematics problem solving, middle school teachers were introduced to a feedback guide intended to help them provide feedback to students and make instructional decisions. The teachers' use of this feedback guide is the focus of this talk. I will discuss the extent to which teachers use the guide reliably, as well as the evidence of the teachers' use of the feedback guide to inform follow-up instruction. Although the subjects of the study were middle school teachers, the discussion about instructional planning has implications for all levels of instruction.
Jessica Strowbridge is a candidate for a tenure-track position in the Mathematics Department. - Using Children's Thinking Activities:
Preservice Teachers' Perceptions
Speaker
Laura McLeman, University of Arizona
Time
Thursday, January 10, 2007, 11:10 a.m. - 12:00 noon
Place
Science North Building 53, Room 202
Abstract
In his 1985 AERA presidential address, Shulman discussed a knowledge base for teaching. Following this seminal idea, research has focused not only on what constitutes such a base but also on how teachers can acquire it. One area of focus in researching this acquisition is examining children's thinking through student-generated artifacts. In particular, some teacher educators use activities based on children's thinking as a way for preservice teachers to authentically engage with mathematical content. In doing so, preservice teachers can make their own mathematical discoveries and think more deeply about what children understand mathematically (Crespo, 2000; Crockett, 2002).
In this talk, I will share my dissertation research, which involves using three sets of children's thinking activities to understand preservice elementary teachers' perceptions in a mathematics for teaching course. Specifically, I will discuss the motivation for my dissertation study, some findings from a pilot study involving two case study students, and how these findings informed my subsequent dissertation work. Some samples of the data collected from the larger research project as well as conjectures of emerging themes will be shared.
Laura McLeman is a candidate for a tenure-track position in the Mathematics Department. - Students' Colloquial and Mathematical Discourses on Infinity and Limit
Speaker
Dong-Joong Kim, Michigan State University
Time
Tuesday, January 15, 2007, 11:10 a.m. - 12:00 noon
Place
Science North Building 53, Room 202
Abstract
This study will investigate and compare how native-English and native-Korean speaking university students, who received their education respectively in the U.S. and in Korea, think about the concepts of infinity and limit. Based on the communicational approach to cognition, according to which mathematics is a kind of discourse, the characteristics of students' discourse on the topics will be identified: words and their use, discursive routines, endorsed narratives, and mediators and their use. The intention of studying these two linguistically different groups is to illuminate the ways in which culture affects learning of mathematical concepts. Two groups of university students participated in the study. The comparisons of these two groups will be based on analyses of students' responses to a survey questionnaire and discourse analyses of paired interviews. I first analyzed and categorized about 120 university students' written responses to the survey within each group, and chose their representatives. Twenty representatives in each group were interviewed in pairs, and discourse analysis on those interview data will be conducted. The participants' discourse will be scrutinized with an eye to the common characteristics as well as culture- and education-related differences.
Dong-Joong Kim is a candidate for a tenure-track position in the Mathematics Department. - Predicting Sex/Gender Differences in
Performance on the SAT I Quantitative Section
Speaker
Bryan Nankervis, Texas State University, San Marcos, TX
Time
Friday, January 18, 2007, 4:10 - 5:00 p.m.
Place
Science North Building 53, Room 201
Abstract
This study, which is based on analyses of released National Assessment of Educational Progress (NAEP) items, measures the extent to which males and females exhibit differences in performance on certain varieties of mathematical problems and uses this information to predict performance gaps on the SAT I quantitative section. Further, this study demonstrates that the gaps are likely an artifact not only of the test's construction, but also of the environment of its administration and challenges the validity of the SAT as a predictor of college success. This research has far-reaching implications for the design and administration of high-stakes standardized mathematics tests, which have historically produced large achievement gaps between the sexes. Further, there are implications for the use of such exams in determining admission to colleges and the awarding of scholarships.
Bryan Nankervis is a candidate for a tenure-track position in the Mathematics Department. - Thesis Defense
Reduction of the Number of Quantifiers in Real Analysis Through Infinitesimals
Speaker
Raymond Cavalcante, Mathematics Graduate Student, Cal Poly
Time
Friday, January 25, 2008, 4:10 - 5:00 p.m.
Place
Science North Building 53, Room 201
Abstract
We construct the non-standard complex (and real) numbers using the ultrapower method in the spirit of Cauchy's construction of the real numbers. We show that the non-standard complex numbers *C are a non-archimedean, algebraically closed field, and that the non-standard real numbers *R are a totally ordered, real-closed, non-archimedean field. We explore the various types of non-standard numbers, and develop the non-standard completeness results (Saturation Principle, Supremum Completeness of Bounded Internal Sets, etc) for *R. We give non-standard characterizations for such usual topological objects as open, closed, bounded, and compact sets in terms of monads. We also consider such traditional topics of real analysis as limits, continuity, uniform continuity, convergence, uniform convergence, etc. in a non-standard setting. In both topology and real analysis we reduce (and in some cases eliminate) the number of quantifiers in the non-standard setting.
This is a defense of a Master's Thesis completed under the advisement of Todor Todorov. The talk is intended to be accessible to undergraduates and graduates alike, and we encourage their attendance. - Undergraduate Voices from an After-School Field Experience
Speaker
Ksenija Simic-Muller, University of Arizona
Time
Tuesday, January 22, 2007, 11:10 a.m. - 12:00 noon
Place
Science North Building 53, Room 202
Abstract
This talk is based on research in an after-school mathematics program (Math Club). Math Club was located in an elementary school in a primarily Mexican-American neighborhood of a Southwestern city, and was facilitated by undergraduate students, who differed culturally, linguistically, and/or in socioeconomic status from the students who attended the club. The program was project-based and community-oriented.
In the talk I will focus on experiences of two undergraduate facilitators, one of whom was a pre-service teacher at the time. I will demonstrate, through their own voices, how these students' ideas about teaching and learning mathematics to diverse populations changed through this experience: their field notes and comments in the focus group conducted at the end of the school year show that among other things, they learned to validate the students' everyday experiences and approaches they use to make sense of mathematics, and understood the need for a more engaging mathematics curriculum, since interactive, inclusive learning experiences are much less common for minority and low-income students.
This research was conducted as part of the Center for Mathematics Education of Latinos/as (CEMELA).
Ksenija Simic-Muller is a candidate for a tenure-track position in the Mathematics Department. - Lecture - Getting a Fair Share
Speaker
Ted Hill, Cal Poly Research Scholar in Residence
Time
Tuesday, January 29, 2008, 7:00 p.m.
Place
Kennedy Library, Room 510-B
Abstract
How does one fairly divide disputed territories, estates, votes, and cakes? Cal Poly Research Scholar in Residence, Ted Hill, will address those questions during his talk "Getting a Fair Share" scheduled for Tuesday, Jan. 29, at 7 p.m., in Room 510-B of the Kennedy Library. Hill's talk will highlight several mathematical devices developed in the last 50 years that offer elegant, practical, and often surprisingly simple solutions to fair-division problems that occur on a daily basis. A Professor Emeritus of Mathematics at the Georgia Institute of Technology, he has published extensively in the areas of probability theory and fair-division. For more information about the event, contact Cal Poly's Research and Graduate Programs office at 756-1508. - Multiscale Registration of Noisy Medical Images
Speaker
Dana Paquin, Kenyon College
Time
Friday, February 1, 2008, 4:10 p.m. - 5:00 p.m.
Place
Science North Building 53, Room 201
Abstract
Dana Paquin is a candidate for a tenure-track position in the Mathematics Department. - Secret Codes and Algebra: How to Use Curves to Take Over the World
Speaker
Stefan Erickson, Colorado College
Time
Monday, February 4, 2008, 4:10 p.m. - 5:00 p.m.
Place
Computer Science 14, Room 248
Abstract
Since ancient times, codes and ciphers have been used to transmit vital information without it falling into the wrong hands. The advent of the computer age has produced a strong demand for fast and secure cryptosystems. Today, cryptography is found in military, economic, and personal applications, including Internet commerce and digital signatures.
Most modern cryptosystems are based on computationally hard problems from mathematics, such as the factoring of the product of two large prime numbers in RSA. In 1985, Neal Koblitz and Victor Miller independently suggested that elliptic curves could serve as the basis of cryptosystems. After describing elliptic curves and motivating their use, we will demonstrate a variety of applications. We will also introduce hyperelliptic curves and describe a number of open questions related to their arithmetic and suitability for cryptography.
Stefan Erickson is a candidate for a tenure-track position in the Mathematics Department. - Generating Functions and Permutation Patterns
Speaker
Amanda Riehl, U.C. San Diego
Time
Wednesday, February 6, 2008, 4:10 p.m. - 5:00 p.m.
Place
Mott Physical Education Building 42, Room 205E
Abstract
We will discuss some historical results on the combinatorics of trig functions. We will show that extensions of these results give generating functions for certain statistics on permutations with given patterns. Various tools and techniques, particularly involving new symmetric function identities, will be outlined for different classes of patterns.
Amanda Riehl is a candidate for a tenure-track position in the Mathematics Department. - Mathematical Modeling of the Interactions Between Neurons and Glial Cells
Speaker
Anne Catlla, Duke University
Time
Friday, February 8, 2008, 4:10 p.m. - 5:00 p.m.
Place
Science North Building 53, Room 201
Abstract
Our brains are composed of networks of cells, including neurons and glial cells. While the significance of neurons has been established by biologists, the role of glial cells is less understood. One hypothesis is that glial cells facilitate neural communication in nearby neurons, while suppressing communication among more distant neurons via a reaction-diffusion process. I consider this proposed mechanism using partial and ordinary differential equation models. By analyzing the ordinary differential equation model, I can determine conditions for this hypothesis to hold. I then compare the results of this analysis with simulations of the partial differential equation model and discuss the biological implications.
Anne Catlla is a candidate for a tenure-track position in the Mathematics Department. - Hilbert Schemes and Balanced Metrics
Speaker
Morgan Sherman, California State University, Channel Islands
Time
Thursday, February 14, 2008, 11:10 a.m. - 12:00 noon
Place
Science North Building 53, Room 202
Abstract
In the study of the geometry of algebraic varieties (i.e. those defined by polynomial equations) one is led in particular to two fundamental questions: How do we classify all varieties of a given type? Given a variety what is its most natural embedding into projective space? We will consider an approach to each question -- borrowing tools from the diverse fields of algebra, combinatorics, and complex differential geometry -- and discuss recent developments.
Morgan Sherman is a candidate for a tenure-track position in the Mathematics Department. - Lost in Hyperbolic Space
Speaker
Vincent Bonini, McMaster University, Ontario, Canada
Time
Monday, February 18, 2008, 4:10 p.m. - 5:00 p.m.
Place
Computer Science Building 14 Room 248
Abstract
In Einstein's theory of General Relativity, asymptotically flat manifolds arise as space-like time slices of "realistic" space-time models of isolated gravitating systems. The positive mass theorem of Schoen and Yau then demonstrates a relation between local energy conditions of a space-time solution to Einstein's equations and the "mass" of an asymptotically flat manifold. In this talk we will discuss a purely Riemannian interpretation of these results and introduce some recent results on asymptotically hyperbolic manifolds, which can be interpreted as an attempt to generalize the above relations to Einstein's theory in the presence of a negative cosmological constant.
Vincent Bonini is a candidate for a tenure-track position in the Mathematics Department. - Applications of Nonstandard Analysis to Generalized Function Theory
Speaker
Hans Vernaeve, University of Innsbruck, Austria
Time
Monday, February 25, 2008, 4:10 p.m. - 5:00 p.m.
Place
Computer Science 14 Room 248
Abstract
After an introduction to generalized function theory, we will show how nonstandard analysis can be used to improve the properties of generalized functions, and give examples of problems in generalized function theory solved by nonstandard principles. Although generalized functions have their origin in the theory of partial differential equations and in applied mathematics (e.g., to describe shock waves), we will focus on the functional analytic aspects of the theory. We will also indicate some future directions of research.
Hans Vernaeve is a candidate for a tenure-track position in the Mathematics Department. - Automata and Wilf Equivalence in the Factor
Order
Speaker
Jeff Liese, University of California, San Diego
Time
Wednesday, March 5, 2008, 4:10 p.m. - 5:00 p.m.
Place
Mott Gym Building 42 Room 205E
Abstract
- The Ubiquity of Fluid Instability
Speaker
Professor Susan Friedlander, University of Southern California
Time
Friday, March 7, 2008, 4:10 p.m. - 5:00 p.m.
Place
Science North Building 53, Room 201
Abstract
We argue that in some appropriate sense almost all steady flows of an ideal fluid are unstable. However there are different kinds of instability, some of which could be called "slow" as opposed to "fast" instabilities associated with isolated unstable eigenvalues. We will discuss the behaviour of the Euler and Navier-Stokes equations in the context of fluid instability.
Professor Susan Friedlander is the Chief Editor of Bulletin of the American Mathematical Society. - Do The Locomotion: A Mathematical Model of a Locomoting Cell
Speaker
Kamila Larripa, University of California, Davis
Time
Tuesday, March 11, 2008, 11:10 a.m. - 12:00 noon
Place
Science North Building 53, Room 202
Abstract
Cell crawling is an important biological phenomenon because it underlies coordinated cell movement in morphogenesis, cancer, and wound healing. This phenomenon is based on protrusion at the cell's leading edge, retraction at the rear, contraction and graded adhesion powered by the dynamics of actin and myosin protein networks. We develop and numerically solve a 1-d model of a strip of the actin-myosin gel found in these cells.
Kamila Larripa is a candidate for a tenure-track position in the Mathematics Department.
Fall 2007 Colloquia
- Discrete Means and a Paradox of Social Choice
Speaker
Curtis D. Bennett, Mathematics Department Chair, Loyola-Marymount University
Time
Friday, September 28, 2007
4:10 p.m. - 5:00 p.m.
Place
Science North Building 53, Room 201
Abstract
Suppose you want to find the average person who owns 1.7 cars. Obviously, you cannot find one (unless you include mechanics that are building (or demolishing) cars). A discrete mean is a function that produces an integer "average" of sets of integers. In this talk we will briefly discuss the history of means of numbers, discuss the consequences of Kolmogorov's powerful theorem on means, and then classify all discrete means. From this we will derive a paradox of social choice. - Infinite-Dimensional Linear Algebra Motivated by Representation Theory
Speaker
Ivan Penkov, International University, Bremen
On sabbatical at U.C. Berkeley
Time
Friday, October 5, 2007, 4:10 - 5:00 p.m.
Place
Science North Building 53, Room 201
Abstract
For the purpose of representation theory we study the Lie algebra gl(\infty) each element of which is an infinite matrix with finitely many non-zero entries. More specifically, we are interested in analogs of the subalgebras of diagonal and upper triangular matrices in the Lie algebra of usual n times n matrices gl(n). This leads to new phenomena and new notions in pure linear algebra, which I plan to explain. The talk requires very little beyond a solid undergraduate linear algebra course. - Are There Infinitely Many Twin Primes?
Speaker
Dan Goldston, Mathematics Department, San Jose State University
Time
Friday, October 12, 2007
4:10 p.m. - 5:00 p.m.
Place
Science North Building 53, Room 201
Abstract
Twin primes are pairs of primes that are two apart, such as 3 and 5, or 29 and 31. Are there infinitely many twin primes? And can we prove it? This talk will provide a pretty convincing answer to the first question. As for the second question, up to now proofs have never been in sight (for mathematicians anyway), but recent work of the speaker with Pintz and Yildirim has maybe changed this situation. At present our method, while not producing twin primes, is able to prove that there are pairs of primes very close together compared to the average distance between consecutive primes. This talk will explain our knowledge of twin primes and discuss how the new method works. This work has had its share of media attention, and even generated a song on public television. I will show a few examples of this publicity and how mathematics is covered in the media. - From Patterns in Permutations to Patterns in Polyominoes and Back Again
Speakers
Don Rawlings, Mathematics Department, Cal Poly
Mark Tiefenbruck, Mathematics Department, Cal Poly
Time
Friday, October 19, 2007, 4:10 - 5:00 p.m.
Place
Science North Building 53, Room 201
Abstract
The three segmented pattern enumeration problems respectively associated with permutations, compositions, and words have long and separate, but parallel, stories. In contrast, ridge patterns in column-convex polyominoes have been all but ignored. With the twine provided by a sequence of serendipitous observations, we weave these four enumeration problems together as one. We then present two approaches for dealing with this class of problems.
Anyone with an interest in a good counting problem and a modest background in combinatorics will be able to appreciate this talk. - Preparing Prospective Secondary Teachers to Incorporate Technology in Mathematics Education
Speaker
Todd Grundmeier, Mathematics Department, Cal Poly
Time
Friday, October 26, 2007, 4:10 - 5:00 p.m.
Place
Science North Building 53, Room 201
Abstract
Prospective teachers should develop beliefs about the role of technology in the teaching of mathematics as state standards and national organizations suggest the use of technology as a teaching tool in mathematics classrooms. This talk will present the results of research that explored prospective teachers' views of the role of technology in mathematics education before, during, and after their experience in a mathematics class that focused on technology in mathematics education. Research results presented in the talk will focus on participants' views of how to utilize technology to teach mathematics and their views of the teacher's role in a classroom were technology is being used. The results of this research also led to the redesign of the course. This redesign and activities that have been developed to address weaknesses in the class that became evident from the research will also be discussed. - Finite Invariants of Infinite Free Resolutions
Speaker
Janet Striuli, University of Nebraska, Lincoln
Time
Thursday, November 1, 2007
11:10 a.m. - 12:00 noon
Place
Fisher Science Building 33 Room 287
Abstract
Free resolutions were introduced more than a century ago by Hilbert to answer questions from invariant theory. Since then, they have become a powerful tool for algebraists to study rings and modules.
In most cases, it takes an infinite number of steps to build a free resolution, so it is not obvious how to access and recognize the information it carries. In the talk, we will present some finite properties of infinite free resolutions. - Nonlinear Dynamics and Combinatorial Games: The Renormalization of Chomp
Speaker
Adam Landsberg, Physics Department, Claremont McKenna, Pitzer and Scripps Colleges
Time
Friay, November 2, 2007
4:10 p.m. - 5:00 p.m.
Place
Science North Building 53 Room 201
Abstract
Combinatorial games, which include Chess, Go, Checkers, Chomp, and Nim, have both captivated and challenged mathematicians, computer scientists, and players alike. Using the game of Chomp as a protoype, I will describe a methodology that reveals surprising connections between combinatorial games and some of the central ideas of nonlinear dynamics: scaling behaviors, complex dynamics and chaos, universality, and aggregation processes. Our central finding is that the game possesses an underlying geometric structure that "grows" (reminiscent of crystal growth), and we show how this growth can be analyzed using a renormalization procedure adapted from physics. Not only does this provide powerful insights into the game of Chomp (yielding a complete probabilistic description of optimal play and an answer to a longstanding question about the nature of the winning opening move in Chomp), but more generally it offers a mathematical framework for exploring this unexpected relationship between combinatorial games and modern dynamical systems theory. - A New Zero Divisor Graph
Speaker
Sandra Spirnoff
Time
Friay, November 9, 2007
4:10 p.m. - 5:00 p.m.
Place
Science North Building 53 Room 201
Abstract
A zero divisor graph of a ring R is a visual representation of the zero divisor activity in R. They have been studied by Beck, Anderson & Livingston, Mulay, and Wickham, to name just a few. We continue, using ideas of Mulay, to identify ring theoretic properties from these graphs. In particular, we are interested in the graph of equivalence classes of zero divisors. We will compare and contrast this graph with the original zero divisor graph and discuss some results involving the associated primes of the ring. - Hilbert Functions of Fat Points
Speaker
Susan Cooper, Mathematics Department, Cal Poly
Time
Friday, November 16, 2007, 4:10 - 5:00 p.m.
Place
Science North Building 53, Room 201
Abstract
Many algebraic ideas have been introduced in order to obtain information about finite point sets in projective space. In particular, the Hilbert function of a set of points has played a central role in many problems. The Hilbert function is simply a sequence of numbers that counts the polynomials vanishing on a point set degree-by-degree. It is known what the Hilbert function of a reduced set of points must look like. However, if we "fatten up" a set of points then such a general characterization is still an open problem. We'll give a numerical criterion under which these sequences are completely determined for some special fat points.
2006-2007 Colloquia
2005-2006 Colloquia
2004-2005 Colloquia
2003-2004 Colloquia
2002-2003 Colloquia
2001-2002 Colloquia
2000-2001 Colloquia
1999-2000 Colloquia
1998-1999 Colloquia