Mathematics Department Events
Fall 2011
Congruences and Geometry
Alex Ghitza
Department of Mathematics
University of Melbourne
Abstract. We will discuss some of the (arithmetic) geometry that forms the modern framework for the study of congruences. The objective is to introduce and motivate some congruences conjectured by Harder, and which are the object of work in progress with Nathan Ryan.
Integer Relation Algorithms
Alex Ghitza
Department of Mathematics
University of Melbourne
Abstract. In "experimental mathematics," a basic problem is that of searching for small integer relations between given real numbers. We will describe two algorithms (PSLQ and LLL) that are widely used for solving this problem and compare them from the points of view of theoretical complexity and typical performance in practice.
(This talk should be accessible to ungraduates.)
- Student Colloquium Series: Thursday, February 9, 12:00 noon in 268 Olin Science
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The Mystic Hexagon Theorem: Polynomials and Geometry
Karen Chandler
Department of Mathematical Sciences
Susquehanna University
Abstract: Consider a hexagon as a six-sided figure with sides not necessarily of equal lengths. When Blaise Pascal (1623-1662) was sixteen, he exhibited an amazing fact on hexagons. We will see how this extends to concepts in algebraic geometry: comparing polynomials with the geometry of their (common) sets of solutions. In particular, we shall see how Pascal's theorem extends to the theorem of Etienne Bezout (1730-1783) on curve intersections. We will then examine precisely how to remove all mystery on hexagons "from scratch." I will then describe how these concepts relate to my own research.
PIZZA and DRINKS provided. All are welcome.
- Student Colloquium Series: Thursday, January 26, 12:00 noon in 268 Olin Science
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Sums of Squares: An Introduction to Quadratic Forms
Jodi Black
Department of Mathematics
Bucknell University
Abstract: The 2-square identity gives that products of sums of 2 squares are sums of 2 squares. More precisely:
(x12+x22)(y12+y22)=(x1y1-x2y2)2+(x2y1+x1y2)2
One of the nice properties of the expression above is that it is bilinear in the xi and yj. By 1898 bilinear 4-square and 8-square identities had been discovered and Hurwitz had shown that no other bilinear n-square identities exist. But what if we don't require bilinearity? For which positive integers n is a product of sums of n squares a sum of n squares? A complete answer would not come for more than half a century until Pfister's groundbreaking work on quadratic forms which not only resolved this longstanding open problem but also revolutionized the study of quadratic forms. We will discuss the sums of squares question as motivation for a brief foray into quadratic forms.
PIZZA and DRINKS provided. All are welcome.
- Student Colloquium Series: Thursday, November 17, 12:00 noon in 268 Olin Science
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Life and Death on an Infinite Grid
Chris Phan
Department of Mathematics
Bucknell University
Abstract: In 1970, mathematician John H. Conway introduced his Game of Life, a simulation with very simple rules that nevertheless gives rise to rich, complicated behavior. In my talk, I will discuss some of the phenomenon seen in Conway's Game of Life, as well as some other types of cellular automata.
PIZZA and DRINKS provided. All are welcome.
- Distinguished Visiting Professor Seminar: Wednesday, November 16, 4:00 pm in 372 Olin Science
- Distinguished Visiting Professor Colloquium: Monday, November 14, 4:00 pm in 372 Olin Science
- Student Colloquium Series: Thursday, November 3, 12:00 noon in 268 Olin Science
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Student Panel: What I did with my summer vacation
Leigh Arnold ’13 (Mathematics Education),
Matt Mizuhara ’12 (Mathematics Research), and
Lyndsay Shand ’12 (Statistics)
Mathematics students at Bucknell University
Abstract: What will you do this summer? For some ideas on what is available and what some of Bucknell's mathematics students have done in the past, come to the student panel to hear students talk about their past summer experience. Students will speak about research experiences at Bucknell and other institutions, teaching experiences, and internships they received. A question and answer period will follow the session.
PIZZA and DRINKS provided. All are welcome.
- Student Colloquium Series: Thursday, October 20, 12:00 noon in 268 Olin Science
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Statistics in Observational Astronomy
Katelyn Allers
Department of Physics and Astronomy
Bucknell University
Abstract: Experiments in observational Astronomy have, by nature, conditions that are not well controlled. Observational Astronomers rely on the detection of photons to infer the properties of astronomical objects. Two things are detected as a part of the process: signal and noise, and knowing how to separate them lies at the heart of having a reliable data set. We will review the statistics used by astronomers when reducing photometric and spectroscopic data. With data in hand, a major goal of astronomers is to then infer the underlying physical properties of the objects under scrutiny. This is usually done by performing a statistical comparison to other data sets or theoretical models, and we will discuss the statistical tests commonly used for this purpose.
PIZZA and DRINKS provided. All are welcome.
- Student Colloquium Series: Thursday, October 20, 12:00 noon in 268 Olin Science
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Moving faces to other places: Dice rolling, coat checking and facet derangements
Gary Gordon
Mathematics Department
Lafayette College
Abstract: Suppose you have a die sitting on a table. Now you pick it up and roll it so that it occupies the same place on the table it did before. How many ways could you have done this so that none of the 6 numbers are in the same place? What if you have an n-dimensional die? We relate these questions to a famous hat-check problem from combinatorics, and interpret the answer in terms of a coat-check problem. Along the way, we'll meet derangements -- permutations with no fixed points. We will do some counting, some calculus, some geometry and some group theory. It is possible we may also have some fun.
PIZZA and DRINKS provided. All are welcome.
- Student Colloquium Series: Thursday, October 6, 12:00 noon in 268 Olin Science
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A Mathematical Look at Approval Voting
Josh Garver
Department of Mathematics
Bucknell University
Abstract: Approval voting systems allow voters to approve or disapprove of a number of candidates or options simultaneously, unlike majority voting where each voter is allowed to make at most one choice. We will look at some examples of societies defined by the idea of approval voting, and use mathematical concepts to examine when we can have agreement between voters in these societies. In doing so we will find some connections to pure mathematics including Hellys Theorem.
PIZZA and DRINKS provided. All are welcome.
- Talk: Thursday, September 29, 12:00 noon in 268 Olin Science
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Finding Mathematics in Poetry
JoAnne Growney
Guest poet-mathematician JoAnne Growney will lead a poetry reading (with occasional commentary) of poems with mathematical connections from the anthology Strange Attractors: Poems of Love and Mathematics (2008) and from her blog (Intersections -- Poetry with Mathematics). Contributions from audience members will be welcomed as time permits.
JoAnne Growney is co-editor of Strange Attractors: Poems of Love and Mathematics (A K Peters, 2008) and author of a chapbook of mathematical poems, My Dance is Mathematics (Paper Kite Press, 2006). Her 2010 collection, Red Has No Reason (Plain View Press), also contains a selection of poems with mathematical structure and imagery. Growney was a professor of mathematics at Bloomsburg University before moving to Maryland where her primary activity is poetry. She proselytizes for poetry-with-mathematics in her blog, http://poetrywithmathematics.blogspot.com.
PIZZA and DRINKS provided. All are welcome.
- Student Colloquium Series: Thursday, September 22, 12:00 noon in 268 Olin Science
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The Goluptious Gamma Function
Karl Voss
Department of Mathematics
Bucknell University
Abstract: The gamma function dates from the first few decades after the invention of calculus. Euler is traditionally assigned credit for creating the gamma function and we will discuss what brought him to consider this remarkable function. The gamma function appears in a variety of different mathematical contexts. In particular, it can be used to solve an interesting problem related to the volume of the unit sphere.
PIZZA and DRINKS provided. All are welcome.
Frattini Extensions of Groups, presented by Martin J. Evans (University of Alabama, Tuscaloosa)
Let G and H be groups. We say that G is a Frattini extension of H if there exists a normal subgroup N of G such that G/N ≅ H and N ≤ Φ(G). We'll discuss ways of constructing Frattini extensions of a given group H, paying particular attention to the case H ≅ PSL(2, F) where F is a locally finite infinite field.
Frattini Subgroups of Finitely Generated Groups, presented by Martin J. Evans (University of Alabama, Tuscaloosa)
The Frattini subgroup Φ(G) of a group G is defined to be the intersection of all the maximal subgroups of G, with the understanding that Φ(G) = G if G has no maximal subgroups. We'll discuss some interesting questions about the Frattini subgroups of finitely generated groups: What groups H can occur as the Frattini subgroup of a finitely generated group? What can be said about a group K if K is isomorphic to a subgroup of Φ(G) for some finitely generated group G?
