Hypatian Seminar

Organizational Meeting

The Hypatian Seminar organizational meeting will be held at 3:30 in South Hall 6635. We will be discussing ideas for the fall and winter quarters. Everyone is welcome--bring ideas!

Agenda:

1. Current amount of money available
2. NSF Grant progess Report
3. Filling in remaining slots in the Seminar
4. Outreach -- possible workshop with Girls Inc
5. Involving undergrads

Panel Discussion

Topic: : How to get a job/post-doc

Confirmed panelists: Emille Davie, Ilsenami Adeboye, Elizabeth Thoren. Bring questions!

Speaker: Marion Moore, UC Davis

Title: High Distance Heegaard Splittings

Abstract: Any 3-dimensional manifold can be decomposed into two simple pieces: a Heegaard splitting. A Heegaard splitting can be regarded as a pair of subcomplexes in the complex of curves of the Heegaard surface. It is possible to relate geometric and combinatorial properties of these subcomplexes with topological properties of the manifold and/or the associated splitting. One such property is the Hemple distance of a Heegaard splitting. I will define the Hemple distance and give examples of desirable characteristics of high distance splittings.

Speaker: Rena Levitt, Pomona

Title: Combinatorial Geodesics in Simplicial Complexes

Abstract: In his 1912 paper, Max Dehn posed three seminal problems in combinatorial group theory: the word problem, the conjugacy problem, and the isomorphism problem. While stated in terms of finitely presented groups, each problem arose naturally in Dehn's study of fundamental groups of $2$-dimensional surfaces. In this talk, I will discuss one method to solve the word problem by constructing a geometric space the group acts on, the Cayley Graph. Then I will discuss using metric conditions to show that groups acting on CAT(0) simplicial complexes are biautomatic, a condition that gives a positive solution to both the word problem and the conjugacy problem for these groups. This relies on looking at the structure of combinatorial geodesics in the spaces.

Speaker: Cindy Wyels, CSUCI

Title: Achievable pebbling numbers

Abstract: Graph pebbling arose in a search for a "natural" proof of a number-theoretic conjecture of Erdös and Lemke, and has since taken on a life of its own. Begin with a distribution of pebbles on the vertices of a graph G. A pebbling move consists of taking two pebbles from a vertex and moving one to any adjacent vertex (while discarding the second). We say the distribution is solvable if at least one pebble may be placed on any target vertex, via a sequence of pebbling moves (possibly of length 0). The pebbling number of G is the smallest integer for which every distribution with that many pebbles is solvable. The pebbling number of a graph of order n must lie between n and 2n-1. We ask which integers may be realized as the pebbling number of a graph of order n. We specify sufficient conditions for an integer to be realized as a pebbling number, identify where certain gaps among potential pebbling numbers must occur, and obtain improved upper bounds for pebbling numbers.

Speaker: Alissa Crans, LMU

Title: Higher-Dimensional Algebra: Weakening the notion of Equality

Abstract: A fundamental problem in mathematics consists of determining whether two given mathematical structures are 'the same'. For example, knot theorists are interested in knowing when knots are the same, while algebraists like to know when groups are the same. But what exactly do mathematicians mean when they say that two gadgets are the same? Often, they mean "sufficiently the same for our purposes," and that purpose naturally differs from field to field. Higher-dimensional algebra, which enables us to refine our notion of 'sameness', is the study of generalizations of algebraic concepts obtained by developing category-theoretic analogs of set-theoretic concepts. We will see how higher-dimensional algebra can be used to explore mathematical interpretations of being 'the same' by carefully examining the concept of equality and comparing it to weaker notions of sameness.

Short Talks

Speakers: Cynthia Flores and Arielle Leitner

Cynthia's Title: Manifolds with Nonnegative Ricci curvature
Abstract: I will present some interactions among the various concepts of curvature and the relatively new concept of isotropic curvature. I will show some of the known results about Betti numbers pertaining to certain compact manifolds of nonnegative isotropic curvature and generalize them for nonnegative isotropic Ricci curvature. The results are proved using the Weitzenbock Formula and Hodge Theory.

Arielle's Title: Factors Related to the Success of CSU Chico Students
Abstract: What is a better indicator of student success: High School GPA or SAT score? In this presentation, we will discuss the relation of High School GPA, SAT score, race, gender, parental education and other factors to student success; where success is measured in terms of graduating GPA and years to degree.

Speaker: Elizabeth Thoren, UCSB

Title: The Spectrum and Stability for PDEs

Abstract: The spectrum of a linear operator is a generalization of eigenvalues for a matrix. Just as with eigenvalues and their eigenvectors, the spectrum of an operator tells us how the operator stretches certain vectors. I'll start the talk with a gentle introduction to spectral theory for linear operators and then use spectral theory to define a good notion of linear stability for PDEs. This talk is for a general mathematical audience -- no familiarity with PDEs or functional analysis required.

Speaker: Mike Williams, UCSB

Title: Morse Theory on Surfaces

Abstract: Morse theory deals with the analysis of critical points of differentiable functions, as in the second derivative test from calculus. Some nice topological interpretations result from this theory. In this talk, I will give an introduction to Morse theory and a discussion of how this theory can be used to distinguish surfaces. Any student with knowledge of multivariable-calculus and linear algebra should be able to understand most of the talk.

Speaker: Alethea Barbaro, UCLA

TBA