Spring 2020 Schedule
Abstract: You are the owner of Hotel Infinity. It has infinitely many rooms, and it's full. A new guest arrives and insists you give her a room. How do you accommodate her? The next day, a family with infinitely many members arrives, each of whom wants a private room. The Hotel is still full. The next day infinitely many families, each with infinitely many members, arrive. Each member of each family insists on a private room. What do you do? We'll use this puzzle as an introduction to some subtleties of the concept of infinity.
Cryptography, Freedom, Democracy
How Basic Science Affects Everyone
Abstract: To most people, research in basic science seems irrelevant, and consequently, citizens,
legislators, government funding agencies, and corporations are disinclined to support
Nevertheless, basic science can have deep impacts on our lives. This talk examines two developments in basic science in the Twentieth Century. The first of them, Albert Einstein’s work in 1905, changed the field of physics, and the course of history. The second, the invention of public-key cryptography in 1975, has important consequences for secure communications.
Many of mankind’s discoveries have potential for both good and bad.The talk concludes with a discussion of some recent uses of technology that pose the very serious risk of our complete loss of privacy, freedom, and democracy.
Automorphisms of varieties of general type
Abstract: If X is a Riemann surface of genus g at least 2, then it is well known that X has at most 84(h-1) automorphisms (symmetries). In this talk we will explain this result and its generalization to higher dimensional varieties.
Tex, LaTex and writing a math paper. Students enrolled in MATH 3000 are strongly encouraged to attend this session.
The Marriage Problem
Abstract: In one of the earliest mathematical textbooks, Euclid set out the rules of geometry: any two points are connected by a straight line; any straight line segment can be extended to a line; and so on. This Euclidean geometry is very familiar to us: the interior angles of every triangle add to 180 degrees; two lines that start parallel to each other remain parallel forever; and, polygons with four right angles exist. However, not every geometry behaves in this way. For example, the geometry of sphere is quite different. There is a third planar geometry to explore - hyperbolic geometry - that was borne out of the realization that one of Euclid's original axioms could not be derived from the others. This talk will be an introduction to hyperbolic geometry, a beautiful field that revolutionized mathematics and remains at the forefront of modern research in topology, dynamics, and algebra.
Utah Undergraduate Colloquium, March 2020
Abstract: Categories are ubiquitous in mathematics, and "thinking categorically" is a framework
for reviewing some high points of the undergraduate curriculum. For example, there
are the categories of (finite) sets, vector spaces, topological spaces and various
flavors of groups. We get quickly to interesting mathematics when we consider automorphism
groups Aut(X) of symmetries of an object in a category. One of the central problems in geometry (and physics
and chemistry) is to understand symmetries of manifolds via their representations as symmetries of vector spaces. This gives us the opportunity
to review more high points of the undergraduate curriculum and to segue into graduate
mathematics by introducing students to Lie Groups, Lie Algebras and Algebraic Geometry.
This talk is an advertisement for my Math 4800 course in the Fall semester.
Math 3000 (Receive Credit for Attending)
The Undergraduate Colloquium is open to anyone to attend; however, if students would
like to receive credit, you may register for Math 3000.
This is a 1 credit hour CR/NC course. To receive credit:
- You may not miss more than 2 of the colloquia
- You will need to write a short paper on one of the topics presented during the semester.
|Kevin Wortman||Lisa Penfold|
|Course Instructor||Administrative Coordinator|